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Splitting algorithms as applied to the Navier-Stokes equations. (Russian, English) Zbl 1177.76200
Zh. Vychisl. Mat. Mat. Fiz. 49, No. 4, 700-714 (2009); translation in Comput. Math., Math. Phys. 49, No. 4, 676-690 (2009).
Summary: Implicit finite-difference schemes of approximate factorization and predictor-corrector schemes based on a special splitting of operators are proposed for the numerical solution of the Navier-Stokes equations governing a viscous compressible heat-conducting gas. The schemes are based on scalar tridiagonal Gaussian elimination and are unconditionally stable. The accuracy and efficiency of the algorithms are confirmed by computing two-dimensional flows of complex geometry.

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
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