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An offline-online Riemann solver for one-dimensional systems of conservation laws. (English) Zbl 1356.65220

Summary: In this paper, we present an exact Riemann solver for one-dimensional systems of conservation laws. The method is based on an offline-online computational decomposition. During the offline stage, we generate an accurate surrogate model for the solution to the Riemann problem for arbitrary left and right states. Then, during the online stage, we employ the surrogate model to generate accurate initial conditions for an iterative Newton solver. We present a mathematical analysis of the Riemann problem to justify the proposed approach. Finally, we illustrate its effectiveness by means of two numerical examples.

MSC:

65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
76N15 Gas dynamics (general theory)
76M12 Finite volume methods applied to problems in fluid mechanics

Software:

HE-E1GODF; PMTK; redbKIT
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Full Text: DOI Link

References:

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