Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 334, Issue -, Pages 102-124Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2016.12.031
Keywords
Transport equation; Advection remap; Flux corrected transport; Bernstein basis finite elements; Maximum principle; High-order discontinuous finite elements
Funding
- U.S. Department of Energy by Lawrence Livermore National Laboratory [DE-AC52-07NA27344, LLNL-JRNL-684083]
- German Research Association (DFG) [KU 1530/15-1]
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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.
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