East Asian J. Appl. Math., 11 (2021), pp. 435-467.
Published online: 2021-05
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In this paper the first dedicated study on high-order non-conservative numerical schemes for hyperbolic moment models is presented. The implementation uses a new formulation that allows for explicit evaluation of the model while satisfying conservation of mass, momentum, and energy. The high-order numerical schemes use a path-conservative treatment of the non-conservative terms and a new consistent evaluation of the eigenvalues. The numerical results of two initial value problems, one stationary test case and a boundary value problem, yield stable and accurate solutions with convergence towards the reference solution despite the presence of a non-conservative term. A large speedup or accuracy gain in comparison to existing first-order codes could be demonstrated.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.090920.130121}, url = {http://global-sci.org/intro/article_detail/eajam/19136.html} }In this paper the first dedicated study on high-order non-conservative numerical schemes for hyperbolic moment models is presented. The implementation uses a new formulation that allows for explicit evaluation of the model while satisfying conservation of mass, momentum, and energy. The high-order numerical schemes use a path-conservative treatment of the non-conservative terms and a new consistent evaluation of the eigenvalues. The numerical results of two initial value problems, one stationary test case and a boundary value problem, yield stable and accurate solutions with convergence towards the reference solution despite the presence of a non-conservative term. A large speedup or accuracy gain in comparison to existing first-order codes could be demonstrated.