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Computation of discontinuous solutions of fluid dynamics equations with entropy nondecrease guarantee. (Russian, English) Zbl 1313.35238

Zh. Vychisl. Mat. Mat. Fiz. 54, No. 6, 1008-1921 (2014); translation in Comput. Math. Math. Phys. 54, No. 6, 1012-1024 (2014).
Summary: A new formulation of the Godunov scheme with linear Riemann problems is proposed that guarantees a nondecrease in entropy. The new version of the method is described for the simplest example of one-dimensional gas dynamics in Lagrangian coordinates.

MSC:

35Q15 Riemann-Hilbert problems in context of PDEs
30E25 Boundary value problems in the complex plane
31A25 Boundary value and inverse problems for harmonic functions in two dimensions
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
76M20 Finite difference methods applied to problems in fluid mechanics

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References:

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