Year: 2007
Communications in Computational Physics, Vol. 2 (2007), Iss. 5 : pp. 933–963
Abstract
This is the continuation of the paper "Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction" by the same authors. The hierarchical reconstruction introduced therein is applied to central schemes on overlapping cells and to finite volume schemes on non-staggered grids. This takes a new finite volume approach for approximating non-smooth solutions. A critical step for high-order finite volume schemes is to reconstruct a non-oscillatory high degree polynomial approximation in each cell out of nearby cell averages. In the paper this procedure is accomplished in two steps: first to reconstruct a high degree polynomial in each cell by using e.g., a central reconstruction, which is easy to do despite the fact that the reconstructed polynomial could be oscillatory; then to apply the hierarchical reconstruction to remove the spurious oscillations while maintaining the high resolution. All numerical computations for systems of conservation laws are performed without characteristic decomposition. In particular, we demonstrate that this new approach can generate essentially non-oscillatory solutions even for 5th-order schemes without characteristic decomposition.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-CiCP-7933
Communications in Computational Physics, Vol. 2 (2007), Iss. 5 : pp. 933–963
Published online: 2007-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 31