A generalized Eulerian-Lagrangian discontinuous Galerkin method for transport problems
نویسندگان
چکیده
We propose a generalized Eulerian-Lagrangian (GEL) discontinuous Galerkin (DG) method. The method is generalization of the (EL) DG for transport problems proposed in [arXiv preprint arXiv: 2002.02930 (2020)], which tracks solution along approximations to characteristics framework, allowing extra large time stepping size with stability. newly GEL this paper motivated solving linear hyperbolic systems variable coefficients, where velocity field adjoint test functions frozen constant. In paper, simplified scalar setting, we methodology by freezing problems, and formulating semi-discrete scheme over space-time region partitioned lines approximating characteristics. fully-discrete schemes are obtained method-of-lines Runge-Kutta methods. further design flux limiters satisfy discrete geometric conservation law (DGCL) maximum principle preserving (MPP) properties. Numerical results on 1D 2D presented demonstrate great properties These include high order spatial temporal accuracy, stability size, satisfaction DGCL MPP
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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2022
ISSN: ['1090-2716', '0021-9991']
DOI: https://doi.org/10.1016/j.jcp.2022.111160