High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:334

Article

关键词: Transport equation;    Advection remap;    Flux corrected transport;    Bernstein basis finite elements;    Maximum principle;    High-order discontinuous finite elements;   

DOI  :  10.1016/j.jcp.2016.12.031

来源: Elsevier

【 摘 要 】

In this work we present aFCT-like Maximum-Principle Preserving (MPP) method to solve the transport equation. We use high-order polynomial spaces; in particular, we consider up to 5th order spaces in two and three dimensions and 23rd order spaces in one dimension. The method combines the concepts of positive basis functions for discontinuous Galerkin finite element spatial discretization, locally defined solution bounds, element-based flux correction, and non-linear local mass redistribution. We consider a simple 1D problem with non-smooth initial data to explain and understand the behavior of different parts of the method. Convergence tests in space indicate that high-order accuracy is achieved. Numerical results from several benchmarks in two and three dimensions are also reported. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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