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- W3034650320 abstract "May, SandraWhen solving time-dependent conservation laws on cut cell meshes, one has to face the small cell problem: standard explicit schemes are not stable if the time step is chosen based on the size of the background cells. Therefore, special schemes must be developed. The first part of this contribution discusses the small cell problem in detail and summarizes several existing solution approaches in the context of both finite volume (FV) schemes and discontinuous Galerkin (DG) schemes. In the second part, we present our two fundamentally different solution approaches for overcoming the small cell problem: the FV based mixed explicit implicit scheme, developed in collaboration with Berger (J. Sci. Comput. 71, pp. 919–943, 2017), and the DG based Domain-of-Dependence (DoD) stabilization, joint work with Engwer, Nüßing, and Streitbürger ( ArXiv:1906.05642 )." @default.
- W3034650320 created "2020-06-19" @default.
- W3034650320 creator A5073463914 @default.
- W3034650320 date "2020-01-01" @default.
- W3034650320 modified "2023-09-23" @default.
- W3034650320 title "Time-Dependent Conservation Laws on Cut Cell Meshes and the Small Cell Problem" @default.
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- W3034650320 doi "https://doi.org/10.1007/978-3-030-43651-3_3" @default.
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