Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes

Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes

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

Keywords: