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Derivative Riemann solvers for systems of conservation laws and ader methods. (English) Zbl 1087.65590
Summary: We first briefly review the semi-analytical method of E. F. Toro and V. A. Titarev [Proc. Roy. Soc. London, Ser. A, Math. Phys. Eng. Sci. 458, No. 2018, 271–281 (2002; Zbl 1019.35061)] for solving the derivative Riemann problem for systems of hyperbolic conservation laws with source terms. Next, we generalize it to hyperbolic systems for which the Riemann problem solution is not available. As an application example we implement the new derivative Riemann solver in the high-order finite-volume ADER advection schemes. We provide numerical examples for the compressible Euler equations in two space dimensions which illustrate robustness and high accuracy of the resulting schemes.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
76N15 Gas dynamics (general theory)
76M20 Finite difference methods applied to problems in fluid mechanics
Software:
HE-E1GODF; HLLE
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References:
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