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A Simple Smoothing TVD Scheme on Structured and Unstructured Grids

  • M. Sun
  • K. Takayama

Abstract

A symmetric TVD Lax-Wendroff scheme is formulated via conservative smoothing or artificial viscosity. The approach is based on the Richtmyer scheme, a predictor-corrector Lax-Wendroff scheme. The predictor step is conducted at interface to determine the states there by advancing the Euler equations by modified half time step. The corrector step sums fluxes given by the Euler equations, and the smoothing flux given by artificial dissipation. The scheme is a simple central difference, and its artificial dissipation can be as less as the first-order upwind scheme around a discontinuity in solving the scalar equation. The scheme is extended to unstructured grid and applied to a variety of gas-dynamic problems by the finite volume method.

Keywords

Finite Volume Method Unstructured Grid Artificial Viscosity Predictor Step Shock Wave Interaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Davis SF (1987) A simplified TVD finite difference scheme via artificial viscosity, SIAM J. Sci. Stat. Comput. 8 : 1–18.MATHCrossRefGoogle Scholar
  2. Sun M (1998) Numerical and experimental studies of shock wave interaction with bodies, Ph.D. Thesis, Tohoku University, Japan. http: //ceres.ifs.tohoku.ac.jp/ ~ sun/thesis,html Google Scholar
  3. Sun M, Takayama K (1999) Conservative smoothing on an adaptive quadrilateral grid, J. Comput. Phys, 150 : 143–180.MATHCrossRefGoogle Scholar
  4. Yee HC, (1987) Construction of explicit and implicit symmetric TVD schemes and their applications, J. of Comput. Phys. 68 : 151–179.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • M. Sun
    • 1
  • K. Takayama
    • 1
  1. 1.Shock Wave Research Center, Institute of Fluid ScienceTohoku UniversitySendaiJapan

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