An unconditionally stable pressure correction scheme for the compressible barotropic Navier-Stokes equations

Thierry Gallouët; Laura Gastaldo; Raphaele Herbin; Jean-Claude Latché

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 42, Issue: 2, page 303-331
  • ISSN: 0764-583X

Abstract

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We present in this paper a pressure correction scheme for the barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the continuous problem also hold for the discrete solution. The stability proof is based on two independent results for general finite volume discretizations, both interesting for their own sake: the L2-stability of the discrete advection operator provided it is consistent, in some sense, with the mass balance and the estimate of the pressure work by means of the time derivative of the elastic potential. The proposed scheme is built in order to match these theoretical results, and combines a fractional-step time discretization of pressure-correction type with a space discretization associating low order non-conforming mixed finite elements and finite volumes. Numerical tests with an exact smooth solution show the convergence of the scheme.

How to cite

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Gallouët, Thierry, et al. "An unconditionally stable pressure correction scheme for the compressible barotropic Navier-Stokes equations." ESAIM: Mathematical Modelling and Numerical Analysis 42.2 (2008): 303-331. <http://eudml.org/doc/250414>.

@article{Gallouët2008,
abstract = { We present in this paper a pressure correction scheme for the barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the continuous problem also hold for the discrete solution. The stability proof is based on two independent results for general finite volume discretizations, both interesting for their own sake: the L2-stability of the discrete advection operator provided it is consistent, in some sense, with the mass balance and the estimate of the pressure work by means of the time derivative of the elastic potential. The proposed scheme is built in order to match these theoretical results, and combines a fractional-step time discretization of pressure-correction type with a space discretization associating low order non-conforming mixed finite elements and finite volumes. Numerical tests with an exact smooth solution show the convergence of the scheme. },
author = {Gallouët, Thierry, Gastaldo, Laura, Herbin, Raphaele, Latché, Jean-Claude},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Compressible Navier-Stokes equations; pressure correction schemes.; compressible Navier-Stokes equations; pressure correction schemes},
language = {eng},
month = {3},
number = {2},
pages = {303-331},
publisher = {EDP Sciences},
title = {An unconditionally stable pressure correction scheme for the compressible barotropic Navier-Stokes equations},
url = {http://eudml.org/doc/250414},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Gallouët, Thierry
AU - Gastaldo, Laura
AU - Herbin, Raphaele
AU - Latché, Jean-Claude
TI - An unconditionally stable pressure correction scheme for the compressible barotropic Navier-Stokes equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/3//
PB - EDP Sciences
VL - 42
IS - 2
SP - 303
EP - 331
AB - We present in this paper a pressure correction scheme for the barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the continuous problem also hold for the discrete solution. The stability proof is based on two independent results for general finite volume discretizations, both interesting for their own sake: the L2-stability of the discrete advection operator provided it is consistent, in some sense, with the mass balance and the estimate of the pressure work by means of the time derivative of the elastic potential. The proposed scheme is built in order to match these theoretical results, and combines a fractional-step time discretization of pressure-correction type with a space discretization associating low order non-conforming mixed finite elements and finite volumes. Numerical tests with an exact smooth solution show the convergence of the scheme.
LA - eng
KW - Compressible Navier-Stokes equations; pressure correction schemes.; compressible Navier-Stokes equations; pressure correction schemes
UR - http://eudml.org/doc/250414
ER -

References

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