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  • Numerical simulations of thermal convection in rotating spherical shells under laboratory conditions

     Garcia Gonzalez, Fernando; Sanchez Umbria, Juan Jose; Net Marce, Marta
    Physics of the Earth and planetary interiors
    Vol. 230, p. 28-44
    DOI: 10.1016/j.pepi.2014.02.004
    Date of publication: 2014-03-05
    Journal article

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    An exhaustive study, based on numerical three-dimensional simulations, of the Boussinesq thermal convection of a fluid confined in a rotating spherical shell is presented. A moderately low Prandtl number fluid (ro = 0.1) bounded by differentially-heated solid spherical shells is mainly considered. Asymptotic power laws for the mean physical properties of the flows are obtained in the limit of low Rossby number and compared with laboratory experiments and with previous numerical results computed by taking either stress-free boundary conditions or quasi-geostrophic restrictions, and with geodynamo models. Finally, using parameters as close as possible to those of the Earth's outer core, some estimations of the characteristic time and length scales of convection are given. © 2014 Elsevier B.V.

  • A comparison of high-order time integrators for highly supercritical thermal convection in rotating spherical shells

     Garcia Gonzalez, Fernando; Net Marce, Marta; Sanchez Umbria, Juan Jose
    Lecture notes in computational science and engineering
    Vol. 95, p. 273-284
    DOI: 10.1007/978-3-319-01601-6_22
    Date of publication: 2014-01-10
    Journal article

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    The efficiency of implicit and semi-implicit time integration codes based on backward differentiation and extrapolation formulas for the solution of the three-dimensional Boussinesq thermal convection equations in rotating spherical shells was studied in Garcia et al. (J Comput Phys 229:7997¿8010, 2010) at weakly supercritical Rayleigh numbers R, moderate (10-3) and low (10-4) Ekman numbers, E, and Prandtl number s = 1. The results presented here extend the previous study and focus on the effect of s and R by analyzing the efficiency of the methods for obtaining solutions at TeX, s = 0. 1 and low and high supercritical R. In the first case (quasiperiodic solutions) the decrease of one order of magnitude does not change the results significantly. In the second case (spatio-temporal chaotic solutions) the differences in the behavior of the semi-implicit codes due to the different treatment of the Coriolis term disappear because the integration is dominated by the nonlinear terms. As in Garcia et al. (J Comput Phys 229:7997¿8010, 2010), high order methods, either with or without time step and order control, increase the efficiency of the time integrators and allow to obtain more accurate solutions.

    The efficiency of implicit and semi-implicit time integration codes based on backward differentiation and extrapolation formulas for the solution of the three-dimensional Boussinesq thermal convection equations in rotating spherical shells was studied in [5] at weakly supercritical Rayleigh numbers R, moderate (10−3) and low (10−4) Ekman numbers, E, and Prandtl number = 1. The results presented here extend the previous study and focus on the effect of and R by analyzing the efficiency of the methods for obtaining solutions at E = 10−4, = 0.1 and low and high supercritical R. In the first case (quasiperiodic solutions) the decrease of one order of magnitude does not change the results significantly. In the second case (spatio-temporal chaotic solutions) the differences in the behavior of the semi-implicit codes due to the different treatment of the Coriolis term disappear because the integration is dominated by the nonlinear terms. As in [5], high order methods, either with or without time step and order control, increase the efficiency of the time integrators and allow to obtain more accurate solutions.

    Postprint (author’s final draft)

  • Exponential versus IMEX high-order time integrators for thermal convection in rotating spherical shells

     Garcia Gonzalez, Fernando; Bonaventura, Luca; Net Marce, Marta; Sanchez Umbria, Juan Jose
    Journal of computational physics
    Vol. 264, p. 41-54
    DOI: 10.1016/j.jcp.2014.01.033
    Date of publication: 2014-05-01
    Journal article

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    We assess the accuracy and efficiency of several exponential time integration methods coupled to a spectral discretization of the three-dimensional Boussinesq thermal convection equations in rotating spherical shells. Exponential methods are compared to implicit-explicit (IMEX) multi-step methods already studied previously in [1]. The results of a wide range of numerical simulations highlight the superior accuracy of exponential methods for a given time step, especially when employed with large time steps and at low Ekman number. However, presently available implementations of exponential methods appear to be in general computationally more expensive than those of IMEX methods and further research is needed to reduce their computational cost per time step. A physically justified extrapolation argument suggests that some exponential methods could be the most efficient option for integrating flows near Earth's outer core conditions. (C) 2014 Elsevier Inc. All rights reserved.

    We assess the accuracy and efficiency of several exponential time integration methods coupled to a spectral discretization of the three-dimensional Boussinesq thermal convection equations in rotating spherical shells. Exponential methods are compared to implicit–explicit (IMEX) multi-step methods already studied previously in [1]. The results of a wide range of numerical simulations highlight the superior accuracy of exponential methods for a given time step, especially when employed with large time steps and at low Ekman number. However, presently available implementations of exponential methods appear to be in general computationally more expensive than those of IMEX methods and further research is needed to reduce their computational cost per time step. A physically justified extrapolation argument suggests that some exponential methods could be the most efficient option for integrating flows near Earthʼs outer core conditions.

  • Stability analysis of the onset of convection in rotating fluid binary mixtures in spherical shells

     Net Marce, Marta; Garcia, Ferran; Sanchez Umbria, Juan Jose
    Nuevas Técnicas Numéricas para Problemas de Fluidos
    p. 1
    Presentation's date: 2014-02-07
    Presentation of work at congresses

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  • A parallel algorithm for the computation of invariant tori in large-scale dissipative systems

     Sanchez Umbria, Juan Jose; Net Marce, Marta
    Physica. D, Nonlinear phenomena
    Vol. 252, p. 22-33
    DOI: 10.1016/j.physd.2013.02.008
    Date of publication: 2013-06
    Journal article

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    A parallelizable algorithm to compute invariant tori of high-dimensional dissipative systems, obtained upon discretization of PDEs is presented. The size of the set of equations to be solved is only a small multiple of the dimension of the original system. The sequential and parallel implementations are compared with a previous method (Sánchez et al. (2010)) [11], showing that important savings in wall-clock time can be achieved. In order to test it, a thermal convection problem of a binary mixture of fluids has been used. The new method can also be applied to problems with very low rotation numbers, for which the previous is not suitable. This is tested in two examples of two-dimensional maps.

    A parallelizable algorithm to compute invariant tori of high-dimensional dissipative systems, obtained upon discretization of PDEs is presented. The size of the set of equations to be solved is only a small multiple of the dimension of the original system. The sequential and parallel implementations are compared with a previous method (Sánchez et al. (2010)) [11], showing that important savings in wall-clock time can be achieved. In order to test it, a thermal convection problem of a binary mixture of fluids has been used. The new method can also be applied to problems with very low rotation numbers, for which the previous is not suitable. This is tested in two examples of two-dimensional maps.

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    Computation of azimuthal waves and their stability in thermal convection in rotating spherical shells with application to the study of a double-Hopf bifurcation  Open access

     Sanchez Umbria, Juan Jose; Garcia Gonzalez, Fernando; Net Marce, Marta
    Physical review E: statistical, nonlinear, and soft matter physics
    Vol. 87, num. 3, p. 1-11
    DOI: 10.1103/PhysRevE.87.033014
    Date of publication: 2013-03-22
    Journal article

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    A methodology to compute azimuthal waves, appearing in thermal convection of a pure fluid contained in a rotating spherical shell, and to study their stability is presented. It is based on continuation, Newton-Krylov, and Arnoldi methods. An application to the study of a double-Hopf bifurcation of the basic state is shown for Ekman and Prandtl numbers E=10-4 and =0.1, respectively, radius ratios n[0.32,0.35], Rayleigh numbers R[1.8105,6105], and nonslip and perfectly conducting boundary conditions. The knowledge of the bifurcation diagrams, including the unstable solutions, allows one to understand the coexistence of stable thermal Rossby waves of different azimuthal wave numbers at some parameter regions, and the origin of some new intermittent solutions found, as trajectories close to heteroclinic chains. Moreover, the structure of the eigenfunctions at the secondary bifurcations explains the existence of the amplitude and shape modulated waves.

    A methodology to compute azimuthal waves, appearing in thermal convection of a pure fluid contained in a rotating spherical shell, and to study their stability is presented. It is based on continuation, Newton-Krylov, and Arnoldi methods. An application to the study of a double-Hopf bifurcation of the basic state is shown for Ekman and Prandtl numbers E=10−4 and σ=0.1, respectively, radius ratios η∈[0.32,0.35], Rayleigh numbers R∈[1.8×105,6×105], and nonslip and perfectly conducting boundary conditions. The knowledge of the bifurcation diagrams, including the unstable solutions, allows one to understand the coexistence of stable thermal Rossby waves of different azimuthal wave numbers at some parameter regions, and the origin of some new intermittent solutions found, as trajectories close to heteroclinic chains. Moreover, the structure of the eigenfunctions at the secondary bifurcations explains the existence of the amplitude and shape modulated waves.

  • Optimization of dialyzers. Solute clearance kinetics based on time and infusion flow

     Net Marce, Marta; Sanchez Umbria, Juan Jose; Gómez Umbert, Miquel; Maduell, Francesc; Campistol Plana, Josep Maria
    Symposium Update in Dialysis
    p. 1
    Presentation's date: 2013-04-11
    Presentation of work at congresses

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  • Simulations of thermal convection in rotating spherical shells

     Garcia Gonzalez, Fernando; Bonaventura, Luca; Net Marce, Marta; Sanchez Umbria, Juan Jose
    SIAM Conference on Mathematical Computational Issues in the Geosciences
    p. 1
    Presentation's date: 2013-06-17
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  • Newton-Krylov methods beyond the computation of steady solutions: two applications to Fluid Dynamics problems

     Sanchez Umbria, Juan Jose; Net Marce, Marta; Garcia, Ferran
    Efficient solution of large systems of nonlinear PDEs in science
    p. 1
    Presentation's date: 2013-10-07
    Presentation of work at congresses

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    The computation by continuation methods of steady solutions of large-scale dynamical systems (ODE/DAE), obtained by discretizing systems of elliptic and/or parabolic PDEs, is a common tool used by researchers in Nonlinear Elasticity and Fluid Mechanics since the late seventies. The efficient computation of other invariant objects by other means than just time evolution is very recent. In the first part of the talk, algorithms based on Newton-Krylov techniques for computing fixed points, periodic orbits, and invariant tori will be presented. Some results of the application of these methods to the thermal convection of a binary fluid mixture in a rectangular two-dimensional box will be shown In the second part the results of the application of Newton-Krylov methods for the computation of travelling waves appearing in the thermal convection of a pure fluid contained in a spherical shell with differential heating are studied. They are computed as steady solutions of a system for the waves, in the frame of reference of the spheres. In this case the special blocktridiagonal structure of the linear part of the equations provides a preconditioner, which allows an efficient calculation. Their stability is also studied, and the secondary bifurcations to modulated waves are detected.

  • Time integration of thermal convection in rotating spherical shells

     Garcia Gonzalez, Fernando; Bonaventura, Luca; Net Marce, Marta; Sanchez Umbria, Juan Jose
    Semi-Lagrangian Day Workshop
    p. 1
    Presentation's date: 2013-02-06
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  • Bifurcations from travelling waves in radially heated rotating spherical shells

     Sanchez Umbria, Juan Jose; Garcia Gonzalez, Fernando; Net Marce, Marta
    Reunión Científica sobre Nuevas Técnicas Numéricas para Problemas No Estacionarios de Fluidos
    p. 1
    Presentation's date: 2013-02-17
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    Travelling waves appearing in the thermal convection of a pure fluid contained in a spherical shell with the boundaries at different temperatures are studied. They are computed, by using continuation methods, as steady solutions of a system for the waves, in the frame of reference of the spheres. Navier-Stokes equations are written in terms of two scalar potentials for the velocity, which are expanded, as the temperature, in spherical harmonics, and collocation is employed in the radius. The special block-tridiagonal structure of the linear part of the equations provides a preconditioner, which allows an efficient calculation of the waves. Their stability is also studied, and the secondary bifurcations to subharmonic or modulated waves are detected.

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    Numerical study of the onset of thermosolutal convection in rotating spherical shells  Open access

     Net Marce, Marta; Garcia Gonzalez, Fernando; Sanchez Umbria, Juan Jose
    Physics of fluids
    Vol. 24, num. 6, p. 1-21
    DOI: 10.1063/1.4723865
    Date of publication: 2012-06-01
    Journal article

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    The influence of an externally enforced compositional gradient on the onset of convection of a mixture of two components in a rotating fluid spherical shell is studied for Ekman numbers E = 10−3 and E = 10−6, Prandtl numbers σ = 0.1, 0.001, Lewis numbers τ = 0.01, 0.1, 0.8, and radius ratio η = 0.35. The Boussinesq approximation of the governing equations is derived by taking the denser component of the mixture for the equation of the concentration. Differential and internal heating, an external compositional gradient, and the Soret and Dufour effects are included in the model. By neglecting these two last effects, and by considering only differential heating, it is found that the critical thermal Rayleigh number Rec depends strongly on the direction of the compositional gradient. The results are compared with those obtained previously for pure fluids of the same σ. The influence of the mixture becomes significant when the compositional Rayleigh number Rc is at least of the same order of magnitude as the known Rec computed without mixture. For positive and sufficiently large compositional gradients, Rec decreases and changes sign, indicating that the compositional convection becomes the main source of instability. Then the critical wave number mc decreases, and the drifting waves slow down drastically giving rise to an almost stationary pattern of convection. Negative gradients delay the onset of convection and determine a substantial increase of mc and ωc for Rc sufficiently high. Potential laws are obtained numerically from the dependence of Rec and of the critical frequency ωc on Rc, for the moderate and small Ekman numbers explored.

  • Thermal convection in rotating spherical shells

     Garcia Gonzalez, Fernando
    Department of Applied Physics, Universitat Politècnica de Catalunya
    Theses

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  • Calculo paralelo de toros invariantes en EDP's disipativas

     Sanchez Umbria, Juan Jose; Net Marce, Marta
    Congreso No Lineal
    p. 1
    Presentation's date: 2012-06-05
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  • A comparison of high-order time integrators for highly supercritical thermal convection in rotating spherical shells

     Garcia Gonzalez, Fernando; Net Marce, Marta; Sanchez Umbria, Juan Jose
    International Conference on Spectral and High-Order Methods
    p. 139-140
    Presentation's date: 2012-06-28
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  • Cálculo paralelo de toros invariantes en EDP¿s disipativas

     Sanchez Umbria, Juan Jose; Net Marce, Marta
    Congreso No Lineal
    p. 1
    Presentation's date: 2012-06-06
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  • Cálculo numérico de variedades invariantes en EDPS disipativas. Aplicaciones a la convección térmica

     Net Marce, Marta; Garcia Gonzalez, Fernando; Sanchez Umbria, Juan Jose
    Competitive project

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  • Stability analysis for the onset of convection in rotating fluid binary mixtures in spherical shells

     Net Marce, Marta; Garcia Gonzalez, Fernando; Sanchez Umbria, Juan Jose
    European Nonlinear Oscillations Conferences
    Presentation's date: 2011-07
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  • Azimuthal waves, their stability and connecting orbits in thermal convection in rotating spherical shells

     Sanchez Umbria, Juan Jose; Garcia Gonzalez, Fernando; Net Marce, Marta
    Computational Methods in Dynamics
    Presentation's date: 2011-07-08
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  • Bifurcations from travelling waves in radially heated rotating spherical shells

     Sanchez Umbria, Juan Jose; Garcia Gonzalez, Fernando; Net Marce, Marta
    Coherent Structures in Dynamical Systems
    Presentation's date: 2011-05
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  • Azimuthal waves and their stability in externally heated rotating spherical shells

     Sanchez Umbria, Juan Jose; Garcia Gonzalez, Fernando; Net Marce, Marta
    European Nonlinear Oscillations Conferences
    Presentation's date: 2011-07
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  • Secondary bifurcations in radially heated rotating spherical shells

     Sanchez Umbria, Juan Jose; Garcia Gonzalez, Fernando; Net Marce, Marta
    International Congress on Industrial and Applied Mathematics
    Presentation's date: 2011-07-19
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  • Computation of periodic orbits and invariant tori in large-scale dissipative systems

     Sanchez Umbria, Juan Jose; Net Marce, Marta; Simo, Carles
    Tipping Points in Complex Flows - Numerical Methods for Bifurcation Analysis of Large-Scale Systems
    Presentation's date: 2011-11-01
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  • Dinámica supercrítica en la convección térmica de un fluido en geometría esférica en rotación

     Garcia Gonzalez, Fernando; Net Marce, Marta; Sanchez Umbria, Juan Jose
    Congreso de Ecuaciones Diferenciales y Aplicaciones y Congreso de Matemàtica Aplicada
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    A comparison of high-order time integrators for thermal convection in rotating spherical shells  Open access

     Garcia Gonzalez, Fernando; Net Marce, Marta; Garcia-Archilla, Bosco; Sanchez Umbria, Juan Jose
    Journal of computational physics
    Vol. 229, num. 20, p. 7997-8010
    DOI: 10.1016/j.jcp.2010.07.004
    Date of publication: 2010-10-01
    Journal article

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    A numerical study of several time integration methods for solving the threedimensional Boussinesq thermal convection equations in rotating spherical shells is presented. Implicit and semi-implicit time integration techniques based on backward differentiation and extrapolation formulae are considered. The use of Krylov techniques allows the implicit treatment of the Coriolis term with low storage requirements. The codes are validated with a known benchmark, and their efficiency is studied. The results show that the use of high order methods, especially those with time step and order control, increase the efficiency of the time integration, and allows to obtain more accurate solutions.

    Postprint (author’s final draft)

  • On the multiple shooting continuation of periodic orbits by Newton-Krylov methods

     Sanchez Umbria, Juan Jose; Net Marce, Marta
    International journal of bifurcation and chaos
    Vol. 20, num. 1, p. 43-61
    DOI: 10.1142/S0218127410025399
    Date of publication: 2010
    Journal article

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  • Computation of invariant tori by Newton-Krylov methods in large-scale dissipative systems

     Sanchez Umbria, Juan Jose; Net Marce, Marta; Simó, Carles
    Physica. D, Nonlinear phenomena
    Vol. 239, num. 3-4, p. 123-133
    DOI: 10.1016/j.physd.2009.10.012
    Date of publication: 2010-02
    Journal article

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  • On the multiple shooting continuation of periodic orbits by Newton-Krylov methods

     Sanchez Umbria, Juan Jose; Net Marce, Marta
    International journal of bifurcation and chaos
    Vol. 20, num. 1, p. 43-61
    DOI: 10.1142/S0218127410025399
    Date of publication: 2010-01
    Journal article

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  • Computation of periodic orbits and invariant tori in large-scale systems by Newton-Krylov methods

     Sanchez Umbria, Juan Jose; Net Marce, Marta; Simó, Carles
    Conference on Dynamical Systems, Differential Equations and Applications
    Presentation's date: 2010-05-25
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  • Amplitude equations close to a triple +1 bifurcation point of D4-symmetric periodic orbits in O(2)-equivariant systems

     Sanchez Umbria, Juan Jose; Net Marce, Marta; José Manuel, Vega de Prada
    Emerging Topics in Dynamical Systems and Partial Differential Equations
    Presentation of work at congresses

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  • Computation of invariant tori by Newton-Krylov methods in large-scale dissipative systems

     Sanchez Umbria, Juan Jose; Net Marce, Marta; Simó, Carles
    Emerging Topics in Dynamical Systems and Partial Differential Equations
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  • Computation of invariant tori by Newton-Krylov methods in large-scale dissipative systems

     Sanchez Umbria, Juan Jose; Net Marce, Marta; Simó, Carles
    Bifurcation Analysis and its Applications
    Presentation's date: 2010-06-08
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    Estudio comparativo de la eficiencia de diversos integradores para la simulación numérica de la convección térmica en geometría esférica y rotación  Open access

     Garcia Gonzalez, Fernando; Net Marce, Marta; Garcia-Archilla, Bosco; Sanchez Umbria, Juan Jose
    Congreso de Ecuaciones Diferenciales y Aplicaciones / Congreso de Matemática Aplicada
    Presentation's date: 2009-09-24
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    The efficiency of implicit and semi-implicit time integration codes based on bac- kward differentiation and extrapolation formulae for the solution of the three-dimensio- nal Boussinesq thermal convection equations in rotating spherical shells is studied. The use of Krylov techniques allows the implicit treatment of the Coriolis term with low storage requirements. The results show that high order methods, either with or without time step and order control, increase the efficiency of the time integrators, and allow to obtain more accurate solutions.

  • Computation of periodic orbits in large-scale dissipative systems by multiple shooting

     Sanchez Umbria, Juan Jose; Net Marce, Marta
    Trends in Bifurcation Analysis: Methods and Applications
    Presentation of work at congresses

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  • Multiple shooting continuation of periodic orbits in large-scale dissipative systems

     Sanchez Umbria, Juan Jose; Net Marce, Marta
    SIAM Conference on Applications of Dynamical Systems
    Presentation's date: 2009-05-18
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  • Computation of invariant tori large-scale dissipative systems

     Net Marce, Marta; Sanchez Umbria, Juan Jose; Simó, Carles
    SIAM Conference on Applications of Dynamical Systems
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    Antisymmetric polar modes of thermal convection in rotating spherical fluid shells at high Taylor numbers  Open access

     Garcia Gonzalez, Fernando; Net Marce, Marta; Sanchez Umbria, Juan Jose
    Physical review letters
    Vol. 101, num. 19, p. 194501-1-194501-4
    DOI: 10.1103/PhysRevLett.101.194501
    Date of publication: 2008-11-03
    Journal article

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    The onset of thermal convection in a rotating spherical shell of intermediate radius ratio ¼ 0:4 is studied numerically for Taylor numbers Ta 1011 and the Prandtl number of the liquid sodium ( ¼ 0:01). For the first time, it is shown that at very high Taylor numbers the first unstable mode can be antisymmetric with respect to the equator and confined inside a cylinder tangent to the inner sphere at the equator (polar mode). The exponent of the power law determined from the asymptotic dependence of the critical Rayleigh number for very high Ta is 0.57, lower than 2=3, given theoretically for the spiraling columnar modes, and than 0.63, found numerically for the outer equatorially attached modes

  • Computation of invariant manifolds in large-scale dissipative systems

     Net Marce, Marta
    World Congress on Computational Mechanis and European Congres on Computational Methods in Applied Sciences and Engineering
    Presentation's date: 2008-06-30
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  • Estudio comparativo de la eficiencia de diversos integradores para la simulación numérica de la convección térmica en geometría esférica en rotación

     Garcia Gonzalez, Fernando; Net Marce, Marta; Garcia-Archilla, Bosco; Sanchez Umbria, Juan Jose
    Congreso No Lineal
    p. 52
    Presentation's date: 2008-06-16
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  • Computation of invariant manifolds in large-scale dissipative systems

     Net Marce, Marta
    Workshop Computational Dynamics
    Presentation's date: 2008-06-16
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    On the onset of low-Prandtl-number convection in rotating spherical shells: non-slip boundary conditions  Open access

     Net Marce, Marta; Garcia, Ferran; Sanchez Umbria, Juan Jose
    Journal of fluid mechanics
    Vol. 601, p. 317-337
    DOI: 10.1017/S002211200800061X
    Date of publication: 2008-04
    Journal article

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    Accurate numerical computations of the onset of thermal convection in wide rotating spherical shells are presented. Low-Prandtl-number (σ) fluids, and non-slip boundary conditions are considered. It is shown that at small Ekman numbers (E), and very low σ values, the well-known equatorially trapped patterns of convection are superseded by multicellular outer-equatorially-attached modes. As a result, the convection spreads to higher latitudes affecting the body of the fluid, and increasing the internal viscous dissipation. Then, from E<10−5, the critical Rayleigh number (Rc) fulfils a power-law dependence Rc ∼E −4/3, as happens for moderate and high Prandtl numbers. However, the critical precession frequency (|ωc|) and the critical azimuthal wavenumber (mc) increase discontinuously, jumping when there is a change of the radial and latitudinal structure of the preferred eigenfunction. In addition, the transition between spiralling columnar (SC), and outer-equatorially-attached (OEA) modes in the (σ, E)-space is studied. The evolution of the instability mechanisms with the parameters prevents multicellular modes being selected from σ 0.023. As a result, and in agreement with other authors, the spiralling columnar patterns of convection are already preferred at the Prandtl number of the liquid metals. It is also found that, out of the rapidly rotating limit, the prograde antisymmetric (with respect to the equator) modes of small mc can be preferred at the onset of the primary instability.

  • Numerical techniques for the onset of thermal convection in spherical geometry

     Net Marce, Marta
    SIAM Conference on Applications of Dynamical Systems
    Presentation's date: 2007-05-28
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  • Newton-Krylov continuation of periodic orbits in large-scale dissipative systems

     Net Marce, Marta
    SIAM Conference on Applications of Dynamical Systems
    Presentation's date: 2007-05-28
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  • Numerical techniques for the onset of thermal convection in spherical geometry

     Net Marce, Marta; Sanchez Umbria, Juan Jose; Garcia Gonzalez, Fernando
    SIAM Conference on Applications of Dynamical Systems
    p. 190
    Presentation's date: 2007
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  • Thermal convection in rotating spherical shells

     Net Marce, Marta
    Jornades de doctorat del programa Física Aplicada i Simulació en Ciències
    Presentation's date: 2006-06-23
    Presentation of work at congresses

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  • Computation of the normal form near a triple +1 bifurcation of a periodic orbit in a large scale O(2)-equivariant system.

     Net Marce, Marta
    Carles Simó Fest (60th birthday). Conference on Dynamical Systems
    Presentation's date: 2006-05-29
    Presentation of work at congresses

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  • Computation of a normal form near a multicritical periodic orbit in a thermal convection problem.

     Net Marce, Marta
    Applied Dynamical Systems Workshop. Advanced numerical methods for mathematical modelling.
    Presentation's date: 2006-06-22
    Presentation of work at congresses

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  • Low Prandtl number convection in rotating spherical shells

     Garcia Gonzalez, Fernando; Net Marce, Marta; Sanchez Umbria, Juan Jose
    Novena Trobada Matemàtica de la Societat Catalana de Matemàtiques
    p. 1
    Presentation's date: 2006-04-22
    Presentation of work at congresses

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  • Metodos de Krylov, determinantes y bifurcaciones en EDPs.

     Net Marce, Marta
    Ddays2006 (Reunion de la red DANCE)
    Presentation's date: 2006-10-18
    Presentation of work at congresses

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