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  • Symmetry-preserving discretization of Navier-Stokes equations on collocated unstructured meshes

     Trias Miquel, Francesc Xavier; Lehmkuhl Barba, Oriol; Oliva Llena, Asensio; Perez Segarra, Carlos David; Verstappen, R.W.C.P.
    Journal of computational physics
    Date of publication: 2014-02-01
    Journal article

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    A fully-conservative discretization is presented in this paper. The same principles followed by Verstappen and Veldman (2003) are generalized for unstructured meshes. Here, a collocated-mesh scheme is preferred over a staggered one due to its simpler form for such meshes. The basic idea behind this approach remains the same: mimicking the crucial symmetry properties of the underlying differential operators, i.e., the convective operator is approximated by a skew-symmetric matrix and the diffusive operator by a symmetric, positive-definite matrix. A novel approach to eliminate the checkerboard spurious modes without introducing any non-physical dissipation is proposed. To do so, a fully-conservative regularization of the convective term is used. The supraconvergence of the method is numerically showed and the treatment of boundary conditions is discussed. Finally, the new discretization method is successfully tested for a buoyancy-driven turbulent flow in a differentially heated cavity.

  • DNS and regularization modeling of a turbulent differentially heated cavity of aspect ratio 5

     Trias Miquel, Francesc Xavier; Gorobets, Andrey; Perez Segarra, Carlos David; Oliva Llena, Asensio
    International journal of heat and mass transfer
    Date of publication: 2013-01-15
    Journal article

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  • Conservation properties of unstructured finite-volume mesh schemes for the Navier-Stokes equations

     Jofre Cruanyes, Lluís; Lehmkuhl Barba, Oriol; Ventosa Molina, Jordi; Trias Miquel, Francesc Xavier; Oliva Llena, Asensio
    Numerical heat transfer. Part B, fundamentals
    Date of publication: 2013-11-09
    Journal article

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    The Navier-Stokes equations describe fluid flow by conserving mass and momentum. There are two main mesh discretizations for the computation of these equations, the collocated and staggered schemes. Collocated schemes locate the velocity field at the same grid points as the pressure one, while staggered discretizations locate variables at different points within the mesh. One of the most important characteristic of the discretization schemes, aside from accuracy, is their capacity to discretely conserve kinetic energy, specially when solving turbulent flow. Hence, this work analyzes the accuracy and conservation properties of two particular collocated and staggered schemes by solving various problems.

  • Direct and large-eddy simulation of non-oberbeck-boussinesq effects in a turbulent differentially heated cavity

     Kizildag, Deniz; Trias Miquel, Francesc Xavier; Rodriguez Pérez, Ivette Maria; Oliva Llena, Asensio
    ERCOFTAC Workshop on Direct and Large-Eddy Simulation
    Presentation's date: 2013-04-04
    Presentation of work at congresses

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  • An OpenCL-based parallel CFD code for simulations on hybrid systems with massively-parallel accelerators

     Gorobets, Andrei; Trias Miquel, Francesc Xavier; Oliva Llena, Asensio
    International Conference on Parallel Computational Fluid Dynamics
    Presentation's date: 2013-05-23
    Presentation of work at congresses

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  • Blending regularization and large-eddy simulation. From homogeneous isotropic turbulence to wind farm boundary layers

     Folch Flórez, David; Trias Miquel, Francesc Xavier; Gorobets, Andrei; Oliva Llena, Asensio
    European Turbulence Conference
    Presentation's date: 2013-08
    Presentation of work at congresses

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    The incompressible Navier-Stokes equations form an excellent mathematical model for turbulent flows. However, direct simulations at high Reynolds numbers are not feasible because the convective term produces far too many relevant scales of motion. Therefore, in the foreseeable future numerical simulations of turbulent flows will have to resort to models of the small scales. Large-eddy simulation (LES) and regularization models are examples thereof. In the present work, we propose to combine both approaches. Restoring the Galilean invariance of the regularization method results into an additional hyperviscosity term. This approach provides a natural blending between regularization and LES. The performance of these recent improvements will be assessed through application to homogeneous isotropic turbulence, a turbulent channel flow and a wind-farm turbulent boundary layer.

  • Progress on eddy-viscosity models for LES: new differential operators and discretization methods

     Trias Miquel, Francesc Xavier; Verstappen, Roel; Gorobets, Andrei; Oliva Llena, Asensio
    European Turbulence Conference
    Presentation's date: 2013-09-04
    Presentation of work at congresses

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    The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Reynolds numbers. Therefore, dynamically less complex mathematical formulations are necessary for coarse-grain simulations. Eddy-viscosity models for Large-Eddy Simulation (LES) is an example thereof: they rely on differential operators that should be able to capture well different flow configurations (laminar and 2D flows, near-wall behavior, transitional regime...). In the present work, several differential operators are derived from the criterion that vortex-stretching mechanism must stop at the smallest grid scale. Moreover, since the discretization errors may play a n important role a novel approach to discretize the viscous term with spatially varying eddy-viscosity is used. It is based on basic operators; therefore, the implementation is straightforward even for staggered formulations.

  • New differential operators and discretization methods for eddy-viscosity models for LES

     Trias Miquel, Francesc Xavier; Gorobets, Andrei; Zhang, Hao; Oliva Llena, Asensio
    International Conference on Parallel Computational Fluid Dynamics
    Presentation's date: 2013-05-22
    Presentation of work at congresses

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    The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, at- tempts at performing direct numerical simulations (DNS) are limited to relatively low-Reynolds numbers. Therefore, dynamically less complex mathematical formulations are necessary for coarse-grain simulations. Eddy-viscosity models for Large-Eddy Sim- ulation (LES) is an example thereof: they rely on differential operators that should be able to capture well different flow config- urations (laminar and 2D flows, near-wall behavior, transitional regime...). In the present work, several differential operators are derived from the criterion that vortex-stretching mechanism must stop at the smallest grid scale. Moreover, since the discretization errors may play an important role a novel approach to discretize the viscous term with spatially varying eddy-viscosity is used. It is based on basic operators; therefore, the implementation is straightforward even for staggered formulations. The performance of the proposed models will be assessed by means of direct comparison to DNS reference results.

  • Parallel algorithms for Sn transport sweeps on unstructured meshes

     Borrell Pol, Ricard; Colomer Rey, Guillem; Trias Miquel, Francesc Xavier; Rodriguez Pérez, Ivette Maria
    Journal of computational physics
    Date of publication: 2013-01-01
    Journal article

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    The Boltzmann Transport Equation is solved on unstructured meshes using the Discrete Ordinates Method. The flux for each ordinate is swept across the computational grid, within a source iteration loop that accounts for the coupling between the different ordinates. In this paper, a spatial domain decomposition strategy is used to divide the work among the available CPUs. The sequential nature of the sweep process makes the parallelization of the overall algorithm the most challenging aspect. Several parallel sweep algorithms, which represent different options of interleaving communications and calculations in the solution process, are analysed. The option of grouping messages by means of buffering is also considered. One of the heuristics proposed consistently stands out as the best option in all the situations analyzed, which include different geometries and different sizes of the ordinate set. With this algorithm, good scalability results have been achieved regarding both weak and strong speedup tests with up to 2560 CPUs.

  • A parallel MPI+OpenMP+OpenCL algorithm for hybrid supercomputations of incompressible flows

     Gorobets, Andrey; Trias Miquel, Francesc Xavier; Oliva Llena, Asensio
    Computers and fluids
    Date of publication: 2013-12
    Journal article

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    The work is devoted to the development of efficient parallel algorithms for large-scale simulations of incompressible flows on hybrid supercomputers based on massively-parallel accelerators. The governing equations are discretized using a high-order finite-volume scheme for Cartesian staggered meshes with the only restriction that, at least, one direction is periodic. Its ¿classical¿ MPI + OpenMP parallel implementation for CPUs was designed to scale till 100,000 CPU cores. The new hybrid algorithm is developed on a base of a multi-level parallel model that exploits several layers of parallelism of a modern hybrid supercomputer. In this model, MPI and OpenMP are used on the first two levels to couple nodes of a supercomputer and to engage its CPU cores. Then, computing accelerators are further used by means of the hardware independent OpenCL computing standard. In this way, the implementation is adapted to a general computing model with central processors and math co-processors. In this paper the work is focused on adapting the basic operations of the algorithm to architectures of Graphics Processing Units (GPU) without considering the multi-GPU communication scheme. Technology of porting the code to OpenCL is described, certain optimization approaches are presented and relevant performance results obtaining up to 80¿90 GFLOPS on a GPU accelerator are demonstrated. Moreover, the experience with different GPU architectures is summarized and a comparison based on the particular application is given for AMD and NVIDIA GPUs as well as for CUDA and OpenCL frameworks.

  • New differential operators and discretization methods for eddy-viscosity models for LES

     Trias Miquel, Francesc Xavier; Gorobets, Andrey; Zhang, Hao; Oliva Llena, Asensio
    Procedia engineering
    Date of publication: 2013
    Journal article

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    The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, at- tempts at performing direct numerical simulations (DNS) are limited to relatively low-Reynolds numbers. Therefore, dynamically less complex mathematical formulations are necessary for coarse-grain simulations. Eddy-viscosity models for Large-Eddy Sim- ulation (LES) is an example thereof: they rely on differential operators that should be able to capture well different flow config- urations (laminar and 2D flows, near-wall behavior, transitional regime...). In the present work, several differential operators are derived from the criterion that vortex-stretching mechanism must stop at the smallest grid scale. Moreover, since the discretization errors may play an important role a novel approach to discretize the viscous term with spatially varying eddy-viscosity is used. It is based on basic operators; therefore, the implementation is straightforward even for staggered formulations. The performance of the proposed models will be assessed by means of direct comparison to DNS reference results.

  • An openCL-based parallel CFD code for simulations on hybrid systems with massively-parallel accelerators

     Gorobets, Andrey; Trias Miquel, Francesc Xavier; Oliva Llena, Asensio
    Procedia engineering
    Date of publication: 2013
    Journal article

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    A parallel finite-volume CFD algorithm for modeling of incompressible flows on hybrid supercomputers is presented. It is based on a symmetry-preserving high-order numerical scheme for structured meshes. A multilevel approach that combines different parallel models is used for large-scale simulations on computing systems with massively-parallel accelerators. MPI is used on the first level within the distributed memory model to couple computing nodes of a supercomputer. On the second level OpenMP is used to engage multiple CPU cores of a computing node. The third level exploits the computing potential of massively-parallel accelerators such as GPU (Graphics Processing Units) of AMD and NVIDIA, or Intel Xeon Phi accelerators of the MIC (Many Integrated Core) architecture. The hardware independent OpenCL standard is used to compute on accelerators of different archi- tectures within a general model for a combination of a central processor and a math co-processor.

  • A simple approach to discretize the viscous term with spatially varying (eddy-)viscosity

     Trias Miquel, Francesc Xavier; Gorobets, Andrey; Oliva Llena, Asensio
    Journal of computational physics
    Date of publication: 2013-11-15
    Journal article

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    A simple approach to discretize the viscous dissipation term in the incompressible Navier¿Stokes equations with spatially varying viscosity is presented. Unlike the case where the viscosity remains constant, its discretization may be quite cumbersome especially for high-order staggered formulations. To circumvent this problem, we propose an alternative form of the viscous term whose discretization is straightforward. Notice that this approach is also suitable for eddy-viscosity models for Large-Eddy Simulation. Moreover, since it is based on already available operators, it can be easily implemented on any structured or unstructured code. The (supra)convergence of the method is numerically shown on both a fourth-order Cartesian staggered and an unstructured collocated formulation.

  • Spectrally-consistent regularization modeling at very high Rayleigh numbers

     Trias Miquel, Francesc Xavier; Verstappen, R.W.C.P.; Gorobets, Andrey; Oliva Llena, Asensio
    International Symposium on Turbulence, Heat and Mass Transfer
    Presentation's date: 2012-09-19
    Presentation of work at congresses

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    The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Rayleigh numbers because of the almost numberless small scales produced by the non-linear convective term. Alternatively, a dynamically less complex formulation is proposed here. Namely, regularizations of the Navier-Stokes equations that preserve the symmetry and conservation properties exactly. To do so, both convective and diffusive term are altered in the same vein. In this way, the convective production of small scales is effectively restrained whereas the modified diffusive term introduces a hyperviscosity effect and consequently enhances the destruction of small scales. In practice, the only additional ingredient is a selfadjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must stop at the smallest grid scale. The performance of the novel regularization modeling approach is assessed through application to turbulent natural convection flows at very high Rayleigh numbers

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    Spectrally-consistent regularization modeling of wind farm boundary layers  Open access

     Trias Miquel, Francesc Xavier; Gorobets, Andrey; Folch, David; Oliva Llena, Asensio
    Conference on Modelling Fluid Flow
    Presentation's date: 2012-09-06
    Presentation of work at congresses

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    The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Reynolds numbers because of the almost numberless small scales produced by the non-linear convective term. Alternatively, a dynamically less complex formulation is proposed here. Namely, regularizations of the Navier-Stokes equations that preserve the symmetry and conservation properties exactly. To do so, both convective and diffusive term are altered in the same vein. In this way, the convective production of small scales is effectively restrained whereas the modified diffusive term introduces a hyperviscosity effect and consequently enhances the destruction of small scales. In practise, the only additional ingredient is a self-adjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must stop at the smallest grid scale. In the present work, the performance of the above-mentioned recent improvements is assessed through application to homogeneous isotropic turbulence, a turbulent channel flow and a turbulent boundary layer. As a final application, regularization modelling will be applied for large-scale numerical simulation of the atmospheric boundary layer through wind farms.

  • Eulerian-Lagrangian modeling of fluidized bed

     Tan, Y; Zhang, Hao; Yang, D; Trias Miquel, Francesc Xavier; Sheng, Y.; Oliva Llena, Asensio
    National Conference on Computational Mechanics of Granular Materials
    Presentation's date: 2012-06-14
    Presentation of work at congresses

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  • An eulerian-lagrangian modeling of fluidized bed

     Zhang, Hao; Yuan-Qiang, Tan; Dong-Min, Yang; Trias Miquel, Francesc Xavier; Sheng, Yong; Oliva Llena, Asensio
    National Conference on Computational Mechanics of Granular Materials
    Presentation's date: 2012-09-17
    Presentation of work at congresses

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    Spectrally-consistent regularization modeling of turbulent natural convection flows  Open access

     Trias Miquel, Francesc Xavier; Verstappen, R.W.C.P.; Oliva Llena, Asensio; Gorobets, Andrey
    European Thermal Sciences Conference
    Presentation's date: 2012-09-05
    Presentation of work at congresses

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    The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Reynolds numbers because of the almost numberless small scales produced by the non-linear convective term. Alternatively, a dynamically less complex formulation is proposed here. Namely, regularizations of the Navier-Stokes equations that preserve the symmetry and conservation properties exactly. To do so, both convective and diffusive terms are altered in the same vein. In this way, the convective production of small scales is effectively restrained whereas the modified diffusive term introduces a hyperviscosity effect and consequently enhances the destruction of small scales. In practice, the only additional ingredient is a self-adjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must stop at the smallest grid scale. In the present work, the performance of the above-mentioned recent improvements is assessed through application to turbulent natural convection flows by means of comparison with DNS reference data.

    The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Reynolds numbers because of the almost numberless small scales produced by the non-linear convective term. Alternatively, a dynamically less complex formulation is proposed here. Namely, regularizations of the Navier-Stokes equations that preserve the symmetry and conservation properties exactly. To do so, both convective and diffusive terms are altered in the same vein. In this way, the convective production of small scales is effectively restrained whereas the modified diffusive term introduces a hyperviscosity effect and consequently enhances the destruction of small scales. In practice, the only additional ingredient is a self-adjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must stop at the smallest grid scale. In the present work, the performance of the above-mentioned recent improvements is assessed through application to turbulent natural convection flows by means of comparison with DNS reference data.

  • Numerical simulation of turbulence at lower cost: regularization modeling

     Trias Miquel, Francesc Xavier; Gorobets, Andrey; Perez Segarra, Carlos David; Oliva Llena, Asensio
    Computers and fluids
    Date of publication: 2012-03-13
    Journal article

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  • Effect of mesh partition on the scalability of the parallel solution of the radiative transfer equation

     Colomer Rey, Guillem; Borrell Pol, Ricard; Trias Miquel, Francesc Xavier; Oliva Llena, Asensio
    International Conference on Computational Heat and Mass Transfer
    Presentation's date: 2011-07-18
    Presentation of work at congresses

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    The radiative transfer equation is solved in parallel using spatial domain decomposition. The effect of several kinds of mesh partitioning strategies is analyzed in this work. Geometries discretized with both structured and unstructured meshes have been considered, and significant differences in performance have been observed in both cases.

  • Numerical simulation of turbulence at lower costs: regularization modeling

     Trias Miquel, Francesc Xavier; Gorobets, Andrey; Soria Guerrero, Manel; Oliva Llena, Asensio
    International Conference on Parallel Computational Fluid Dynamics
    Presentation's date: 2011-05-07
    Presentation of work at congresses

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  • Hybrid MPI+OpenMP parallelization of a Navier-Stokes solver for large-scale DNS

     Gorobets, Andrey; Trias Miquel, Francesc Xavier; Borrell Pol, Ricard; Soria Guerrero, Manel; Oliva Llena, Asensio
    International Conference on Computational Heat and Mass Transfer
    Presentation's date: 2011-07-07
    Presentation of work at congresses

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    This work presents a parallel Navier-Stokes solver for the large-scale direct numerical simulation (DNS) of incompressible flows with one periodic direction. It is based on a scalable Poisson solver that combines an FFT diagonalization with a preconditioned conjugate gradient (PCG) method and a direct Schurcomplement based method. Modern architectures of supercomputers with multi-core nodes motivate the use of a two-level hybrid MPI+OpenMP parallelization. The use of the more complex two-level approach has allowed to significantly extend the number of CPUs the solver can efficiently use. Here, the solver has been successfully tested on up to 12800 CPU cores for meshes with up to 109 grid points. However, estimations based on presented results show that more than 50000 CPU cores can potentially be exploited.

  • Numerical simulations of turbulent natural convection coupled and uncoupled with radiation

     Capdevila Paramio, Roser; Lehmkuhl Barba, Oriol; Colomer Rey, Guillem; Trias Miquel, Francesc Xavier; Perez Segarra, Carlos David
    International Conference on Computational Heat and Mass Transfer
    Presentation's date: 2011-07-18
    Presentation of work at congresses

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    In the present work, turbulent natural convection in a tall differentially heated cavity of aspect ratio 5:1, filled with air (Pr = 0.7) under a Rayleigh number based on the height of 4.5 · 1010, is studied numerically. Two different situations have been analysed. In the first one, the cavity is filled with a transparent medium. In the second one, the cavity contains a grey participating gas. The turbulent flow is described by means of Large Eddy Simulation (LES) using symmetry-preserving discretizations. Simulations are compared with experimental data available in the literature and with Direct Numerical Simulations (DNS). Surface and gas radiation have been simulated using the Discrete Ordinates Method (DOM). The influence of radiation on fluid flow behaviour has also been analysed.

  • Symmetry-preserving regularization of wall-bounded turbulent flows

     Trias Miquel, Francesc Xavier; Gorobets, Andrey; Verstappen, R.W.C.P.; Oliva Llena, Asensio
    European Turbulence Conference
    Presentation's date: 2011-09-12
    Presentation of work at congresses

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    The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Reynolds numbers because of the almost numberless small scales produced by the non-linear convective term. Alternatively, a dynamically less complex formulation is proposed here. Namely, regularizations of the Navier-Stokes equations that preserve the symmetry and conservation properties exactly. To do so, both convective and diffusive term are altered in the same vein. In this way, the convective production of small scales is effectively restrained whereas the modified diffusive term introduces an hyper-viscosity effect and consequently enhances the destruction of small scales. In practice, the only additional ingredient is a self-adjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must stop at the smallest grid scale. To do so, a new criterion based on the invariants of the local strain tensor is proposed here. Altogether, the proposed method constitutes a parameter-free turbulence model.

  • Turbulent differentially heated cavity of aspect ratio 5 : direct numerical simulation and regularization modeling

     Trias Miquel, Francesc Xavier; Gorobets, Andrey; Oliva Llena, Asensio
    International Conference on Computational Heat and Mass Transfer
    Presentation's date: 2011-07-07
    Presentation of work at congresses

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    This work is devoted to the study of turbulent natural convection flows in differentially heated cavities. The adopted configuration corresponds to an air-filled (Pr = 0.7) cavity of aspect ratio 5 and Rayleigh number Ra = 4.5 × 1010 (based on the cavity height). Firstly, a complete direct numerical simulation (DNS) has been performed. Then, the DNS results have been used as reference solution to assess the performance of symmetry-preserving regularization as a simulation shortcut: a novel class of regularization that restrain the convective production of small scales of motion in an unconditionally stable manner. In this way, the new set of equations are dynamically less complex than the original Navier-Stokes equations, and therefore more amenable to be numerically solved. Time-averaged DNS results have revealed that the transition of the vertical boundary layer occurs at more downstream positions than those observed in the experiments.

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    Hybrid MPI+OpenMP parallelization of an FFT-based 3D Poisson solver that can reach 100000 CPU cores  Open access

     Gorobets, Andrey; Trias Miquel, Francesc Xavier; Borrell Pol, Ricard; Soria Guerrero, Manel; Oliva Llena, Asensio
    International Conference on Parallel Computational Fluid Dynamics
    Presentation's date: 2011-05-07
    Presentation of work at congresses

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    This work is devoted to the development of efficient parallel algorithms for the direct numerical simulation (DNS) of incompressible flows on modern supercomputers. A Poisson solver for problems with one uniform periodic direction is presented here. It is extended with a two-level hybrid MPI+OpenMP parallelization. Advantages and implementation details for the additional OpenMP parallelization are presented and discussed. This upgrade has allowed to significantly extend the range of efficient scalability. Here, the solver has been tested up to 12800 CPU cores for meshes with up to 10 9 nodes. However, estimations based on the presented results show that this range can be potentially stretched beyond 10 5 cores.

    Postprint (author’s final draft)

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    Parallelization of a DEM/CFD code for the numerical simulation of particle-laden turbulent flows  Open access

     Zhang, Hao; Trias Miquel, Francesc Xavier; Tan, Y.Q.; Sheng, Y.; Oliva Llena, Asensio
    International Conference on Parallel Computational Fluid Dynamics
    Presentation's date: 2011-05-07
    Presentation of work at congresses

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    The interaction between a turbulent fluid flow and particle motion is investigated numerically. A complete direct numerical simulation (DNS) is carried out to solve the governing equations of the fluid phase, to investigate the behavior of inter-particle collision and its effects on particle dispersion, the discrete element method (DEM) is employed to calculate the particle motion.The parallelization strategy of the DNS part is based on a domain decomposition method and uses a hybrid MPI+OpenMP approach. On the other hand, the OpenMP is used for the parallelization of DEM: the total number of particles to be tracked are equally distributed among processors. Finally, the method is tested for a turbulent flow through a square duct.

    Postprint (author’s final draft)

  • Turbulent natural convection in a differentially heated cavity of aspect ratio 5 filled with non-participating and participating grey media

     Capdevila Paramio, Roser; Lehmkuhl Barba, Oriol; Trias Miquel, Francesc Xavier; Perez Segarra, Carlos David; Colomer, G.
    European Turbulence Conference
    Presentation's date: 2011-12-22
    Presentation of work at congresses

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    In the present work, turbulent natural convection in a tall differentially heated cavity of aspect ratio 5:1, filled with air (Pr = 0.7) under a Rayleigh number based on the height of 4.5 centerdot 1010, is studied numerically. Two different situations have been analysed. In the first one, the cavity is filled with a transparent medium. In the second one, the cavity contains a grey participating gas. The turbulent flow is described by means of Large Eddy Simulation (LES) using symmetry-preserving discretizations. Simulations are compared with experimental data available in the literature and with Direct Numerical Simulations (DNS). Surface and gas radiation have been simulated using the Discrete Ordinates Method (DOM). The influence of radiation on fluid flow behaviour has also been analysed.

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    FFT-based Poisson Solver for large scale numerical simulations of incompressible flows  Open access

     Borrell Pol, Ricard; Lehmkuhl Barba, Oriol; Trias Miquel, Francesc Xavier; Oyarzun Altamirano, Guillermo; Oliva Llena, Asensio
    International Conference on Parallel Computational Fluid Dynamics
    Presentation's date: 2011-05-16
    Presentation of work at congresses

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    In the context of time-accurate numerical simulation of incompressible flows, a Poisson equation needs to be solved at least once per time-step to project the velocity field onto a divergence-free space. Due to the non-local nature of its solution, this elliptic system is one of the most time consuming and difficult to parallelise parts of the code. In this paper, a parallel direct Poisson solver restricted to problems with one uniform periodic direction is presented. It is a combination of a Direct Schur-complement based Decomposition (DSD) and a Fourier diagonalisation. The latter decomposes the original system into a set of mutually independent 2D systems which are solved by means of the DSD algorithm. Since no restrictions are imposed in the non-periodic directions, the overall algorithm is well-suited for solving problems discretised on extruded 2D unstructured meshes. A new overall parallelisation strategy with respect to our earlier works is presented. This has allowed us to solve discrete Poisson equations with up to 109 grid points in less than half a second, using up to 8192 CPU cores of the MareNostrum Supercomputer.

    Postprint (author’s final draft)

  • A self-adaptive strategy for the time integration of Navier-Stokes equations

     Trias Miquel, Francesc Xavier; Lehmkuhl Barba, Oriol
    Numerical heat transfer. Part B, fundamentals
    Date of publication: 2011-08
    Journal article

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    An efficient self-adaptive strategy for the explicit time integration of Navier-Stokes equations is presented. Unlike the conventional explicit integration schemes, it is not based on a standard CFL condition. Instead, the eigenvalues of the dynamical system are analytically bounded and the linear stability domain of the time-integration scheme is adapted in order to maximize the time step. The method works independently of the underlying spatial mesh; therefore, it can be easily integrated into structured or unstructured codes. The additional computational cost is minimal, and a significant increase of the time step is achieved without losing accuracy. The effectiveness and robustness of the method are demonstrated on both a Cartesian staggered and an unstructured collocated formulation. In practice, CPU cost reductions up to more than 4 with respect to the conventional approach have been measured.

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    Numerical investigation of the location of maximum erosive wear damage in elbow: Effect of slurry velocity, bend orientation and angle of elbow  Open access

     Zhang, Hao; Tan, Yuanqiang; Yang, Dongmin; Trias Miquel, Francesc Xavier; Jiang, Shengqiang; Sheng, Yong; Oliva Llena, Asensio
    Powder technology
    Date of publication: 2011-02-01
    Journal article

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  • Symmetry-preserving regularization of wall-bounded turbulent flows

     Trias Miquel, Francesc Xavier; Gorobets, Andrey; Verstappen, Roel; Oliva Llena, Asensio
    Journal of physics: conference series
    Date of publication: 2011
    Journal article

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    The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Reynolds numbers because of the almost numberless small scales produced by the non-linear convective term. Alternatively, a dynamically less complex formulation is proposed here. Namely, regularizations of the Navier-Stokes equations that preserve the symmetry and conservation properties exactly. To do so, both convective and diffusive term are altered in the same vein. In this way, the convective production of small scales is effectively restrained whereas the modified diffusive term introduces an hyper-viscosity effect and consequently enhances the destruction of small scales. In practice, the only additional ingredient is a self-adjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must stop at the smallest grid scale. To do so, a new criterion based on the invariants of the local strain tensor is proposed here. Altogether, the proposed method constitutes a parameter-free turbulence model.

  • DESARROLLO CODIGOS Y ALGORITMOS PARALELOS ALTA PRESTACIONES FINES DISEÑO OPTIMIZADO SISTEMAS Y EQUIPOS TERMICOS

     Perez Segarra, Carlos David; Trias Miquel, Francesc Xavier; Capdevila Paramio, Roser; Chiva Segura, Jorge; Gorobets, Andrey; Giraldez Garcia, Hector; Ventosa Molina, Jordi; Oliva Llena, Asensio
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  • DNS and RANS modelling of a turbulent plane impinging jet

     Jaramillo Ibarra, Julian Ernesto; Trias Miquel, Francesc Xavier; Gorobets, Andrey; Perez Segarra, Carlos David; Oliva Llena, Asensio
    International journal of heat and mass transfer
    Date of publication: 2011-01-31
    Journal article

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  • Parallel direct Poisson solver for discretisations with one Fourier diagonalisable direction

     Borrell Pol, Ricard; Lehmkuhl Barba, Oriol; Trias Miquel, Francesc Xavier; Oliva Llena, Asensio
    Journal of computational physics
    Date of publication: 2011-06-01
    Journal article

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  • Hybrid MPI+OpenMP parallelization of an FFT-based 3D Poisson solver with one periodic direction

     Gorobets, Andrey; Trias Miquel, Francesc Xavier; Borrell Pol, Ricard; Lehmkuhl Barba, Oriol; Oliva Llena, Asensio
    Computers and fluids
    Date of publication: 2011-10
    Journal article

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    This work is devoted to the development of efficient parallel algorithms for the direct numerical simulation (DNS) of incompressible flows on modern supercomputers. In doing so, a Poisson equation needs to be solved at each time-step to project the velocity field onto a divergence-free space. Due to the non-local nature of its solution, this elliptic system is the part of the algorithm that is most difficult to parallelize. The Poisson solver presented here is restricted to problems with one uniform periodic direction. It is a combination of a block preconditioned Conjugate Gradient (PCG) and an FFT diagonalization. The latter decomposes the original system into a set of mutually independent 2D systems that are solved by means of the PCG algorithm. For the most ill-conditioned systems, that correspond to the lowest Fourier frequencies, the PCG is replaced by a direct Schur-complement based solver. The previous version of the Poisson solver was conceived for single-core (also dual-core) processors and therefore, the distributed memory model with message-passing interface (MPI) was used. The irruption of multi-core architectures motivated the use of a two-level hybrid MPI + OpenMP parallelization with the shared memory model on the second level. Advantages and implementation details for the additional OpenMP parallelization are presented and discussed in this paper. Numerical experiments show that, within its range of efficient scalability, the previous MPI-only parallelization is slightly outperformed by the MPI + OpenMP approach. But more importantly, the hybrid parallelization has allowed to significantly extend the range of efficient scalability. Here, the solver has been successfully tested up to 12800 CPU cores for meshes with up to 109 grid points. However, estimations based on the presented results show that this range can be potentially stretched up until 200,000 cores approximately. Finally, several examples of DNS simulations are briefly presented to illustrate some potential applications of the solver.

  • On the construction of discrete filters for symmetry-preserving regularization models

     Trias Miquel, Francesc Xavier; Verstappen, R.W.C.P.
    Computers and fluids
    Date of publication: 2011-01
    Journal article

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  • Regularization modeling of wall-bounded turbulent flows

     Trias Miquel, Francesc Xavier; Gorobets, Andrey; Verstappen, R.W.C.P.; Oliva Llena, Asensio
    European Conference on Computational Fluid Dynamics
    Presentation's date: 2010-06-15
    Presentation of work at congresses

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    Since direct numerical simulations cannot be computed at high Reynolds numbers, a dynamically less complex formulation is sought. In the quest for such a formulation, we consider regularizations of the convective term that preserve the symmetry and conservation properties exactly. This requirement yielded a novel class of regularizations (Computers & Fluids 37 (2008) 887) that restrain the convective production of smaller and smaller scales of motion in an unconditionally stable manner, meaning that the velocity cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations must preserve the symmetry and conservation properties too. To do so, one of the most critical issues is the discrete filtering. The method requires a list of properties that, in general, are not preserved by classical filters for LES unless they are imposed a posteriori. In the present paper, we propose a novel class of discrete filters that preserves such properties per se. They are based on polynomial functions of the discrete diffusive operator, ˜D, with the general form F = I + PM m=1 dm ˜D m. Then, the coefficients, dm, follow from the requirement that, at the smallest grid scale kc, the amount by which the interactions between the wavevector-triples (kc, kc − q, q) are damped must become virtually independent of the q-th Fourier-mode. This allows an optimal control of the subtle balance between convection and diffusion at the smallest grid scale to stop the vortex-stretching. Finally, the proposed method is tested for an air-filled differentially heated cavity of height aspect ratio 4.

  • Efficiency of large-scale CFD simulations on modern supercomputers using thousands of CPUS and hybrid MPI+OPENMP parallelization

     Gorobets, Andrey; Borrell Pol, Ricard; Trias Miquel, Francesc Xavier; Kozubskaya, T.K.; Oliva Llena, Asensio
    European Conference on Computational Fluid Dynamics
    Presentation's date: 2010-06-17
    Presentation of work at congresses

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    This work represents an experience in using the hybrid parallel model to perform large-scale DNS. Advantages of the hybrid approach compared to the MPI-only approach are presented and discussed. The use of OpenMP in addition to MPI is demonstrated for modelling of compressible and incompressible flows using both structured and unstructured meshes. A parallel Poisson solver for incompressible flows with one periodic direction extended with the hybrid parallelization is presented. A two-level domain decomposition approach is considered for improving parallel algorithms for compressible flows. An alternative strategy with partial data replication is represented as well. Several DNS examples with mesh sizes varying from 106 to 108 control volumes are given to demonstrate e±cient usage of the upgraded algorithms. Performance tests and simulations have been carried out on several parallel systems including Marenostrum, MVS-100000 and Lomonosov supercomputers.

  • Turbulent flow in a differentially heated cavity: direct numérical simulation and regularization modeling

     Trias Miquel, Francesc Xavier; Gorobets, Andrey; Oliva Llena, Asensio; Verstappen, R.W.C.P.
    International Heat Transfer Conference
    Presentation's date: 2010-08-09
    Presentation of work at congresses

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    We consider regularizations of the convective term that preserve symmetry and conservation properties exactly. This yields a novel class of regularizations that restrain the convective production of small scales in an unconditionally stable manner Numerically, one of the most critical issues is the discrete filtering; properties required are, in general, not preserved by classical LES filters. Alternatively, here we propose to construct filters with the general form F = I + ΣMm =1 dm ˜Dm where ˜D is the discrete diffusive operator. Then, the coefficients, dm, follow from the requirement that, at the smallest grid scale kc, the damping effect to the wavevector-triple (kc, p,kc− p) interactions must be virtually independent of the p-th Fourier-mode. This allows an optimal control of the subtle balance between convection and diffusion to stop the vortex-stretching. Finally, the proposed method is tested for an air-filled differentially heated cavity of aspect ratio 4 by direct comparison with DNS reference results.

  • Regularization modeling of buoyancy-driven flows

     Trias Miquel, Francesc Xavier; Gorobets, Andrey; Oliva Llena, Asensio; Verstappen, R.W.C.P.
    ERCOFTAC Workshop on Direct and Large-Eddy Simulation
    Presentation's date: 2010-07-07
    Presentation of work at congresses

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  • Direct numerical simulation of a differentially heated cavity of aspect ratio 4 with Rayleigh numbers up to 10(11) - Part I: Numerical methods and time-averaged flow

     Trias Miquel, Francesc Xavier; Gorobets, Andrey; Soria Guerrero, Manel; Oliva Llena, Asensio
    International journal of heat and mass transfer
    Date of publication: 2010-01-31
    Journal article

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    A set of direct numerical simulations of a differentially heated cavity of aspect ratio 4 with adiabatic horizontal walls is presented. The five configurations selected here (Rayleigh numbers based on the cavity height View the MathML source and View the MathML source) cover a relatively wide range of Ra from weak to fully developed turbulence. A short overview of the numerical methods and the methodology used to verify the code and the simulations is presented. The time-averaged flow results are presented and discussed in this first part. Significant changes are observed for the two highest Ra for which the transition point at the boundary layers clearly moves upstream. Such displacement increases the top and bottom regions of disorganisation shrinking the area in the cavity core where the flow is stratified. Consequently, thermal stratification values are significantly greater than unity (1.25 and 1.41, respectively).

  • A scalable parallel Poisson solver for three-dimensional problems with one periodic direction

     Gorobets, Andrey; Trias Miquel, Francesc Xavier; Soria Guerrero, Manel; Oliva Llena, Asensio
    Computers and fluids
    Date of publication: 2010-03
    Journal article

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  • Direct numerical simulation of a differentially heated cavity of aspect ratio 4 with Rayleigh numbers up to 10(11) - Part II: Heat transfer and flow dynamics

     Trias Miquel, Francesc Xavier; Gorobets, Andrey; Soria Guerrero, Manel; Oliva Llena, Asensio
    International journal of heat and mass transfer
    Date of publication: 2010-01-31
    Journal article

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    This is the second of a two-part paper on five direct numerical simulations of a differentially heated cavity of aspect ratio 4 with adiabatic horizontal walls (Rayleigh numbers based on the cavity height. The numerical methods and the time-averaged flow results were presented in the Part I. The heat transfer and the flow dynamics, including the turbulent statistics, the global kinetic energy balances and the internal waves motion phenomenon, are herewith described and discussed. The power-law scalings of the total kinetic dissipation rate and the Nusselt number suggest that a state of transition to a new scaling regime has been reached for the highest Ra.

  • Problems of using modern computing systems for direct numerical simulations in fluid dynamics and aeroacoustics

     Gorobets, Andrey; Soukov, Sergey; Trias Miquel, Francesc Xavier
    TsAGI Science journal
    Date of publication: 2010
    Journal article

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    Considered in this article are various aspects associated with the implementation of large-scale supercomputer calculations of hydrodynamic and aeroacoustic problems; the problems of computational optimization are considered. Given are the means of achievement of high parallel efficiency for a large number of processors (up to several thousand). The implementation features of architecturally adapted hybrid paralleling, the optimization of memory access, and parallel processing of computational data and large grids are described. Given here are examples of direct numerical simulation applications for the simulation of both compressible and incompressible turbulent flows with the use of high-accuracy numerical algorithms on structured and unstructured grids.

  • From extruded-2D to fully-3D geometries for DNS: a multigrid-based extension of the Poisson solver

     Gorobets, Andrey; Trias Miquel, Francesc Xavier; Soria Guerrero, Manel; Perez Segarra, Carlos David; Oliva Llena, Asensio
    Lecture notes in computational science and engineering
    Date of publication: 2010
    Journal article

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    Direct numerical simulation (DNS) of incompressible flows is an essential tool for improving the understanding of the physics of turbulence and for the development of better turbulence models. The Poisson equation, the main bottleneck from a parallel point of view, usually also limits its applicability for complex geometries. In this context, efficient and scalable Poisson solvers on fully-3D geometries are of high interest.In our previous work, a scalable algorithm for Poisson equation was proposed. It performed well on both small clusters with poor network performance and supercomputers using efficiently up to a thousand of CPUs. This algorithm named Krylov-Schur-Fourier Decomposition (KSFD) can be used for problems in parallelepipedic 3D domains with structured meshes and obstacles can be placed inside the flow. However, since a FFT decomposition is applied in one direction, mesh is restricted to be uniform and obstacles to be 2D shapes extruded along this direction.The present work is devoted to extend the previous KSFD algorithm to eliminate these limitations. The extension is based on a two-level Multigrid (MG) method that uses KSFD as a solver for second level. The algorithm is applied for a DNS of a turbulent flow in a channel with wall-mounted cube. Illustrative results at Re t = 590 (based on the cube height and the bulk velocity Re h = 7235) are shown.

  • Parameter-free symmetry-preserving regularization modeling of a turbulent differentially heated cavity

     Trias Miquel, Francesc Xavier; Verstappen, R.W.C.P.; Gorobets, Andrey; Soria Guerrero, Manel; Oliva Llena, Asensio
    Computers and fluids
    Date of publication: 2010-06-23
    Journal article

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    Since direct numerical simulations of buoyancy driven flows cannot be computed at high Rayleigh numbers, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider regularizations (smooth approximations) of the non-linearity: the convective term is altered to reduce the production of small scales of motion by means of vortex stretching. In doing so, we propose to preserve the symmetry and conservation properties of the convective terms exactly. This requirement yielded a novel class of regularizations [Comput Fluids 2008;37:887] that restrain the convective production of smaller and smaller scales of motion in an unconditionally stable manner, meaning that the velocity cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. In the present work, a criterion to determine dynamically the regularization parameter (local filter length) is proposed: it is based on the requirement that the vortex stretching must stop at the scale set by the grid. Therefore, the proposed method constitutes a parameter-free turbulence model. The resulting regularization method is tested for a 3D natural convection flow in an air-filled (Pr = 0.71) differentially heated cavity of height aspect ratio 4. Direct comparison with DNS results at Rayleigh number 6.4 X 10 8 ≤ Ra ≤ 10 11 shows fairly good agreement even for very coarse grids. Finally, the robustness of the method is tested by performing simulations with Ra up to 10 17. A 2/7 scaling law of Nusselt number has been obtained for the investigated range of Ra.

  • The problems of modern supercomputer applications in hydrodinamic and aeroacoustic numerical simulations

     Gorobets, Andrey; Sukov, S.A.; Trias Miquel, Francesc Xavier
    TsAGI Science journal
    Date of publication: 2010
    Journal article

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    Parameter-free symmetry-preserving regularization modelling of turbulent natural convection flows  Open access

     Trias Miquel, Francesc Xavier; Verstappen, R.W.C.P.; Soria Guerrero, Manel; Oliva Llena, Asensio
    Conference on Turbulence and Interactions
    Presentation's date: 2009-06
    Presentation of work at congresses

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    Since direct numerical simulations of natural convection flows cannot be performed at high Ra-numbers, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider regularizations (smooth approximations) of the nonlinearity. The regularization method basically alters the convective terms to reduce the production of small scales of motion by means of vortex stretching. In doing so, we propose to preserve the symmetry and conservation properties of the convective terms exactly. This requirement yields a novel class of regularizations that restrain the convective production of smaller and smaller scales of motion by means of vortex stretching in an unconditional stable manner, meaning that the velocity cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. The regularization model is successfully tested for a 3D natural convection flow in air-filled (Pr = 0.71) differentially heated cavity of height aspect ratio 4 at Ra = 10 10 and 10 11. Moreover, a method to dynamically determine the regularization parameter (local filter length) is also proposed and tested.

    Postprint (author’s final draft)

  • DNS of turbulent natural convection flows on the MareNostrum supercomputer

     Trias Miquel, Francesc Xavier; Gorobets, Andrey; Soria Guerrero, Manel; Oliva Llena, Asensio
    Lecture notes in computational science and engineering
    Date of publication: 2009
    Journal article

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    A code for the direct numerical simulation (DNS) of incompressible turbulent flows that provides a fairly good scalability for a wide range of computer architectures has been developed. The spatial discretization of the incompressible Navier-Stokes equations is carried out using a fourth-order symmetry-preserving discretization. Since the code is fully explicit, from a parallel point of view, the main bottleneck is the Poisson equation. In the previous version of the code, that was conceived for low cost PC clusters with poor network performance, a Direct Schur-Fourier Decomposition (DSFD) algorithm was used to solve the Poisson equation. Such method, that was very efficient for PC clusters, can not be efficiently used with an arbitrarily large number of processors, mainly due to the RAM requirements (that grows with the number of processors). To do so, a new version of the solver, named Krylov-Schur-Fourier Decomposition (KSFD), is presented here. Basically, it is based on the Direct Schur Decomposition (DSD) algorithm that is used as a preconditioner for a Krylov method (CG) after Fourier decomposition. Benchmark results illustrating the robustness and scalability of the method on the MareNostrum supercomputer are presented and discussed. Finally, illustrative DNS simulations of wall-bounded turbulent flows are also presented.