Development of a Higher-Order Upwind Algorithm for Discontinuous Compressible Flow

Abstract

A global fourth-order solution method that incorporates compact differencing with Roe's approximate Riemann solver was investigated. This method was incorporated into a one-dimensional numerical simulation of the compressible Euler equations, and applied to a one-dimensional shock tube problem. The method was also extended to two dimensions, and applied to a two-dimensional shock tube problem and an advecting vortical structure problem on both rectilinear and curvilinear meshes. The results were compared to a third-order Roe scheme and a fourth-order compact difference scheme. An order of accuracy determination showed that it has an order of accuracy somewhere near fourth order, with absolute error comparable to that of the standard compact difference scheme. With proper selection of solution parameters, the scheme was also shown to accurately capture a discontinuous solution where unfiltered compact schemes would become unstable.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 2005
Accession Number
ADA434268

Entities

People

  • Barry A. Croker

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Boundary Layer
  • Chemical Oxygen Iodine Lasers
  • Compressible Flow
  • Computational Fluid Dynamics
  • Computational Science
  • Difference Equations
  • Differential Equations
  • Engineering
  • Euler Equations
  • Fluid Dynamics
  • Fluid Flow
  • Numerical Methods And Procedures
  • Partial Differential Equations
  • Pressure Distribution
  • Two Dimensional
  • Wave Equations

Readers

  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)