Recent Developments in Shock-Capturing Schemes

Abstract

This paper reviews the development of the shock capturing methodology, paying special attention to the increasing nonlinearity in its design and it relation to interpolation. It is well-known that high-order approximations to a discontinuous function generate spurious oscillation near the discontinuity (Gibbs phenomenon). Unlike standard finite difference methods which use a fixed stencil, modern shock-capturing schemes use an adaptive stencil which is selected according to the local smoothness of the solution. Near discontinuities this technique automatically switches to one-sided approximations, thus avoiding the use of discontinuous data which brings about spurious oscillations.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1991
Accession Number
ADA232652

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People

  • Ami Harten

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  • Algorithms
  • Approximation (Mathematics)
  • Coefficients
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  • Differential Equations
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  • Inequalities
  • Interpolation
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  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Theoretical Analysis.