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SUPG finite element computation of viscous compressible flows based on the conservation and entropy variables formulations. (English) Zbl 0772.76032
We present the SUPG-stabilized finite element formulations for the computation of viscous compressible flows based on the conservation of entropy variables. This article is a sequel to the one on inviscid compressible flows by Le Beau et al. [G. J. Le Beau, S. E. Ray, S. K. Aliabadi and T. E. Tezduyar, “SUPG finite element computation of compressible flows with the conservation and entropy variables formulations”, Univ. Minnesota Supercomput. Inst. Res. Rep. 92/26 (1992)]. For the conservation variables formulation, we use the SUPG stabilization technique introduced in S. K. Aliabadi and T. E. Tezduyar [“Space-time finite element computation of compressible flows involving moving boundaries and interfaces”, Univ. Minnesota Supercomput. Inst. Res. Rep. 92/95 (1992)], which is a modified version of the one described in Le Beau et al. (1992). The formulation is based on the entropy variables.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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