Multi-Domain Hybrid Spectral-WENO Methods for Hyperbolic Conservation Laws

Abstract

In this article we introduce the multi-domain hybrid Spectral-WENO method aimed at the discontinuous solutions of hyperbolic conservation laws. The main idea is to conjugate the non-oscillatory properties of the high order weighted essentially nonoscillatory (WENO) finite difference schemes with the high computational efficiency and accuracy of spectral methods. Built in a multi-domain framework, subdomain adaptivity in space and time is used in order to maintain the solutions parts exhibiting high gradients and discontinuities always inside WENO subdomains while the smooth parts of the solution are kept in spectral ones. A high order multi-resolution algorithm by Ami Harten is used to determine the smoothness of the solution in each subdomain. Numerical experiments with the simulation of compressible flow in the presence of shock waves are performed.

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Document Details

Document Type
Technical Report
Publication Date
Feb 22, 2006
Accession Number
ADA458975

Entities

People

  • Bruno Costa
  • Wai S. Don

Organizations

  • Brown University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Applied Mathematics
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Differential Equations
  • Equations
  • Euler Equations
  • Flow
  • Fluid Flow
  • Frequency
  • High Resolution
  • Numerical Analysis
  • Polynomials
  • Shock Tubes
  • Shock Waves
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space