Abstract
A new approach for a flux solver is presented which takes source terms into account. The source terms are distributed from the volumes to the volume interfaces, where they define the flux jumps of the Rankine-Hugoniot conditions. Thereby within the cells, homogeneous hyperbolic conditions are obtained. These are used by a linearized Riemann solver to yield the additional relations to determine the left and right states at the cell interfaces. For viscous and multidimensional flows, the viscous flux balance and the flux difference in the other coordinate directions, respectively, are considered as parts of the source terms. Compared with conventional Riemann solvers not taking into account source terms, the new Rankine-Hugoniot-Riemann solver significantly improves the accuracy for a 2D Euler test case without source terms and for 1D and 2D combustion simulations with stiff source terms and viscous terms. The present consideration of source terms by the flux solver can be generalized to hyperbolic systems other than the Euler equations.
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Jenny, P., Müller, B. (1999). A New Approach for a Flux Solver Taking into Account Source Terms, Viscous and Multidimensional Effects. In: Jeltsch, R., Fey, M. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 130. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8724-3_1
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DOI: https://doi.org/10.1007/978-3-0348-8724-3_1
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