Efficient Implementation of Essentially Non-Oscillatory Shock Capturing Schemes.

Abstract

In the computation of discontinuous solutions of hyperbolic conservation laws, TVD (total variation diminishing), TVB (total variation bounded) and the recently developed ENO (essentially non-oscillatory) schemes have proven to be very useful. In this paper two improvements are discussed: a simple TVD Runge-Kutta type time discretization, and an ENO construction procedure based on fluxes rather than on cell averages. These improvements simplify the schemes considerably--especially for multi dimensional problems or problems with forcing terms. Preliminary numerical results are also given. Keywords: Construction laws; Essentially non oscillatory; TVD; Runge Kutta method; Numerical analysis.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1987
Accession Number
ADA189392

Entities

People

  • Chi-Wang Shu

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Cauchy Problem
  • Computations
  • Construction
  • Convergence
  • Differential Equations
  • Discontinuities
  • Eigenvalues
  • Equations
  • Errors
  • High Resolution
  • Mathematics
  • Numerical Analysis
  • Polynomials
  • Runge Kutta Method
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)