Unsplit schemes for multi-dimensional systems of hyperbolic conservation laws with source terms
(1997) APS 50th Annual Meeting of the Division of Fluid Dynamic — Location: San Francisco (23.November.1997)
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- Abstract
- This work describes an unsplit scheme for multi-dimensional systems of hyperbolic conservation laws with source terms, such as the compressible Euler equations for reacting flows. The scheme is an extension of the algorithm for 1-D problems (Papalexandris M.V., Leonard A., and Dimotakis P.E., J. Comp. Phys.), 134, pp. 31-61. It is a MUSCL-type, shock-capturing scheme that integrates all terms of the governing equations simultaneously. Appropriate families of space-time manifolds are introduced, along which the conservation equations decouple to the characteristic equations of the corresponding 1-D homogeneous system. Numerical integration of the characteristic equations is performed on these manifolds in the upwinding part of the algorithm. Numerical studies of 2-D detonations in channel flows will be presented. The proposed scheme appears capable of capturing many of the important details of the flow-fields. No explicit artificial-viscosity mechanisms or other fixes need to be employed with the proposed scheme.
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Papalexandris, M., Leonard, A., & Dimotakis, P. (1997). Unsplit schemes for multi-dimensional systems of hyperbolic conservation laws with source terms. APS 50th Annual Meeting of the Division of Fluid Dynamic, San Francisco. https://hdl.handle.net/2078.5/193875