On the solution of linear algebraic systems arising from the semi–implicit DGFE discretization of the compressible Navier–Stokes equations

Vít Dolejší

Kybernetika (2010)

  • Volume: 46, Issue: 2, page 260-280
  • ISSN: 0023-5954

Abstract

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We deal with the numerical simulation of a motion of viscous compressible fluids. We discretize the governing Navier–Stokes equations by the backward difference formula – discontinuous Galerkin finite element (BDF-DGFE) method, which exhibits a sufficiently stable, efficient and accurate numerical scheme. The BDF-DGFE method requires a solution of one linear algebra system at each time step. In this paper, we deal with these linear algebra systems with the aid of an iterative solver. We discuss the choice of the preconditioner, stopping criterion and the choice of the time step and propose a new strategy which leads to an efficient and accurate numerical scheme.

How to cite

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Dolejší, Vít. "On the solution of linear algebraic systems arising from the semi–implicit DGFE discretization of the compressible Navier–Stokes equations." Kybernetika 46.2 (2010): 260-280. <http://eudml.org/doc/196789>.

@article{Dolejší2010,
abstract = {We deal with the numerical simulation of a motion of viscous compressible fluids. We discretize the governing Navier–Stokes equations by the backward difference formula – discontinuous Galerkin finite element (BDF-DGFE) method, which exhibits a sufficiently stable, efficient and accurate numerical scheme. The BDF-DGFE method requires a solution of one linear algebra system at each time step. In this paper, we deal with these linear algebra systems with the aid of an iterative solver. We discuss the choice of the preconditioner, stopping criterion and the choice of the time step and propose a new strategy which leads to an efficient and accurate numerical scheme.},
author = {Dolejší, Vít},
journal = {Kybernetika},
keywords = {discontinuous Galerkin method; compressible Navier–Stokes equations; linear algebra problems; preconditioning; stopping criterion; choice of the time step; discontinuous Galerkin method; compressible Navier-Stokes equations; linear algebra problems; preconditioning; stopping criterion; choice of the time step},
language = {eng},
number = {2},
pages = {260-280},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the solution of linear algebraic systems arising from the semi–implicit DGFE discretization of the compressible Navier–Stokes equations},
url = {http://eudml.org/doc/196789},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Dolejší, Vít
TI - On the solution of linear algebraic systems arising from the semi–implicit DGFE discretization of the compressible Navier–Stokes equations
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 2
SP - 260
EP - 280
AB - We deal with the numerical simulation of a motion of viscous compressible fluids. We discretize the governing Navier–Stokes equations by the backward difference formula – discontinuous Galerkin finite element (BDF-DGFE) method, which exhibits a sufficiently stable, efficient and accurate numerical scheme. The BDF-DGFE method requires a solution of one linear algebra system at each time step. In this paper, we deal with these linear algebra systems with the aid of an iterative solver. We discuss the choice of the preconditioner, stopping criterion and the choice of the time step and propose a new strategy which leads to an efficient and accurate numerical scheme.
LA - eng
KW - discontinuous Galerkin method; compressible Navier–Stokes equations; linear algebra problems; preconditioning; stopping criterion; choice of the time step; discontinuous Galerkin method; compressible Navier-Stokes equations; linear algebra problems; preconditioning; stopping criterion; choice of the time step
UR - http://eudml.org/doc/196789
ER -

References

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