TY - CONF
AU - Ventosa-Molina, J.
AU - Chiva, J.
AU - Lehmkuhl, O.
AU - Perez, C.
AU - Oliva, A.
T3 - Conference on Modelling Fluid Flow 2012
PY - 2012
Y1 - 2012
SP - 979
EP - 986
UR - http://cataleg.upc.edu/record=b1419227~S1*cat
AB - Numerical methods for fluxes with strong
density variations but with speeds much lower
than the sound speed, known as low Mach
flows, present some particularities with respect to
incompressible formulations. Despite having similar
application ranges, incompressible formulations
using the Boussinesq approximation with constant
fluid properties cannot correctly describe fluxes with
high density variations. According to Gray and
Giorgini [1], use of the Boussinesq approximation
can be considered valid for variations of the density
up to 10% with respect to the mean value, so when
strong density variations are present, variable density
formulations are required. In the low Mach number
Navier-Stokes equations the velocity divergence is
not zero and acoustic waves are not considered. Also,
the pressure is split into a dynamic pressure and a
thermodynamic part. The latter is used to evaluate
the density, by means of the ideal gas state law.
Here will be presented an extension of an
incompressible pressure projection-type algorithm
(fractional-step) to simulate low Mach fluxes, using
a Runge-Kutta/Crank-Nicolson time integration
scheme, similar to the one presented by Najm
et al. [2] and Nicoud in [3]. The use of
a predictor-corrector substeps is related to the
instabilities introduced by the density time derivative
into the constant coefficient Poisson equation, as
reported in [2, 3]. The spatial discretisation is
performed by means of an unstructured finite volume
technique, using both the collocated formulation by
Felten [4] and the staggered formulation by Perot [5].
Finally, the algorithm is tested against benchmark
test cases, such as the differentially heated cavity
with large temperature differences and cases with
reactive fluxes.
T2 - Conference on Modelling Fluid Flow
TI - Low Mach Navier-Stokes equations on unstructured meshes
ER -