A Method of Characteristics Solution in Three Independent Variables

Abstract

An improved method for the solution of hyperbolic partial differential equations in three independent variables is presented, with application to supersonic steady flow of an inviscid ideal gas. A finite difference method of characteristics is used. New approaches which improve accuracy and efficiency in a three dimensional numerical solution are discussed for solving the shock singularities, for controlling finite difference meshes in three dimensional space so that stability conditions are satisfied, and for interpolation. A major departure from previous approaches to this problem is the choice of local coordinates and base point configurations with reference to directions of maximum variation of the dependent variables on the initial value surface. While this condition is automatically satisfied in methods of characteristics solutions in two independent variables it has apparently been ignored in previous approaches to the problem in three variables. It is of sufficient importance to make the difference between meaningless and accurate results. Results illustrating the behavior of the numerical solutions are presented.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1965
Accession Number
AD0623405

Entities

People

  • B.n. Pridmore Brown
  • W. J. Franks

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Air Force
  • California
  • Cartesian Coordinates
  • Coordinate Systems
  • Corporations
  • Difference Equations
  • Differential Equations
  • Equations
  • Flow
  • Flow Fields
  • Geometry
  • Method Of Characteristics
  • Partial Differential Equations
  • Shock Waves
  • Supersonic Flow
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Hypersonics
  • Space