A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws

Abstract

Homotopy continuation is an efficient tool for solving polynomial systems. Its efficiency relies on utilizing adaptive stepsize and adaptive precision path tracking, and endgames. In this article, we apply homotopy continuation to solve steady state problems of hyperbolic conservation laws. The algorithm is based on discretization of the hyperbolic PDEs by a third order finite difference weighted essentially non-oscillatory (WENO) scheme with Lax-Friedrichs flux splitting. This new approach is free of CFL condition constraint. Extensive numerical examples in both scalar and system test problems in one and two dimensions demonstrate the efficiency and robustness of the new method.

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Document Details

Document Type
Technical Report
Publication Date
Sep 03, 2012
Accession Number
ADA568170

Entities

People

  • Andrew J. Sommese
  • Chi-Wang Shu
  • Jonathan D Hauenstein
  • Wenrui Hao
  • Yong-tao Zhang
  • Zhiliang Xu

Organizations

  • Brown University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Algebraic Geometry
  • Algorithms
  • Applied Mathematics
  • Boundaries
  • Cauchy Problem
  • Complex Numbers
  • Differential Equations
  • Equations
  • Euler Equations
  • Geometry
  • Mathematics
  • Polynomials
  • Precision
  • Statistics
  • Steady State
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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