Efficient Implementation of High Order Inverse Lax-Wendroff Boundary Treatment for Conservation Laws

Abstract

In [18], two of the authors developed a high order accurate numerical boundary condition procedure for hyperbolic conservation laws on a Cartesian mesh, which allows the computation using high order finite difference schemes on Cartesian meshes to solve problems in arbitrary physical domains whose boundaries do not coincide with grid lines. This procedure is based on the so-called inverse Lax-Wendroff (ILW) procedure for inflow boundary conditions and high order extrapolation for outflow boundary conditions. However, the algebra of the ILW procedure is quite heavy for two dimensional (2D) hyperbolic systems, which makes it difficult to implement the procedure for order of accuracy higher than three. In this paper we first discuss a simplified and improved implementation for this procedure, which uses the relatively complicated ILW procedure only for the evaluation of the first order normal derivatives. Fifth order WENO type extrapolation is used for all other derivatives, regardless of the direction of the local characteristics and the smoothness of the solution. This makes the implementation of a fifth order boundary treatment practical for 2D systems with source terms. For no-penetration boundary condition of compressible inviscid flows, a further simplification is discussed, in which the evaluation of the tangential derivatives involved in the ILW procedure is avoided. We test our simplified and improved boundary treatment for Euler equations with or without source terms representing chemical reactions in detonations. The results demonstrate the designed fifth order accuracy, stability, and good performance for problems involving complicated interactions between detonation/shock waves and solid boundaries.

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Document Details

Document Type
Technical Report
Publication Date
Jul 15, 2011
Accession Number
ADA557713

Entities

People

  • Cheng Wang
  • Chi-Wang Shu
  • Jianguo Ning
  • Sirui Tan

Organizations

  • Brown University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Chemical Reactants
  • Chemical Reactions
  • Computational Fluid Dynamics
  • Computational Science
  • Detonations
  • Differential Equations
  • Equations
  • Euler Equations
  • Extrapolation
  • Geometry
  • Inviscid Flow
  • Mathematics
  • Shock
  • Shock Waves
  • Two Dimensional
  • Waves

Fields of Study

  • Mathematics

Readers

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