Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes

By Yingjie Liu, Eitan Tadmor. Communications in Computational Physics, 2006

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This is the continuation of the paper "Central discontinuous Galerkin meth- ods 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 de- gree 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 approachcangenerate essentially non-oscillatory solutions evenfor 5th-order schemes without characteristic decomposition. AMS subject classfications: 65M06, 65M60

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/89e6bab5e2ddf8948e908e75dd1a990081bca9c7

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In Computational Mechanics

  1. Henry G. Weller
  2. J. Reese
  3. Luca Gasparini
  4. C. J. Greenshields

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