An Improved Weighted Essentially Non-Oscillatory Scheme for Hyperbolic Conservation Laws

Abstract

We develop in this article an improved version of the fifth-order weighted essentially non-oscillatory (WENO) scheme. Through the novel use of higher order information already present in the framework of the classical scheme, new smoothness indicators are devised and we obtain a new WENO scheme with less dissipation than the classical WENO of Jiang and Shu, with the same computational cost, and a slightly better performance than the improved mapped version of Henrick et al. We show that the enhancements of the new scheme come from its ability to assign substantially larger weights to discontinuous stencils than the previous versions of WENO. Numerical experiments with the linear advection of discontinuous functions and the one-dimensional Euler system of equations are conducted to demonstrate the benefit of using this improved version of the WENO scheme for hyperbolic conservation laws.

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Document Details

Document Type
Technical Report
Publication Date
Jun 23, 2006
Accession Number
ADA458949

Entities

People

  • Bruno Costa
  • Rafael Brandão de Rezende Borges
  • Wai S. Don

Organizations

  • Brown University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Advection
  • Applied Mathematics
  • Boltzmann Equation
  • Boundaries
  • Computational Fluid Dynamics
  • Computational Science
  • Convergence
  • Difference Equations
  • Differential Equations
  • Discontinuities
  • Electronic Mail
  • Equations
  • Errors
  • Euler Equations
  • Polynomials
  • Wave Equations
  • Waves

Fields of Study

  • Mathematics

Readers

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