Geodesic
On the solution of linear algebraic systems arising from the semi–implicit DGFE discretization of the compressible Navier–Stokes equations
Kybernetika, Tome 46 (2010) no. 2, pp. 260-280

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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.
Classification : 35Q35, 65L06, 65M22, 76M10, 76N15, 76N99
Keywords: discontinuous Galerkin method; compressible Navier–Stokes equations; linear algebra problems; preconditioning; stopping criterion; choice of the time step 
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     author = {Dolej\v{s}{\'\i}, V{\'\i}t},
     title = {On the solution of linear algebraic systems arising from the semi{\textendash}implicit {DGFE} discretization of the compressible {Navier{\textendash}Stokes} equations},
     journal = {Kybernetika},
     pages = {260--280},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2010},
     mrnumber = {2663600},
     zbl = {pre05773708},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010__46_2_a3/}
}
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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, Tome 46 (2010) no. 2, pp. 260-280. http://geodesic.mathdoc.fr/item/KYB_2010__46_2_a3/