The Numerical Solution of the Fluid Dynamical Equations in Curvilinear Coordinates.

Abstract

DIFFICULTIES, ONE MUST TRANSFORM THE GOVERNING EQUATIONS OF MOTION INTO A COORDINATE SYSTEM WHERE THE BOUNDARIES ARE SIMPLE. Among the most useful transformations are those which are constructed from analytic functions and from simple homotopies. In essence, the simplified boundaries are obtained at the expense of having a slightly more complicated system of equations. This slight complication offers very little resistance to a numerical solution. A numerical method is then developed to efficiently solve the transformed equations. The numerical scheme is a hybrid of the methods of Lax-Wendroff and MacCormack which is adapted to accommodate source terms. In particular, this time-dependent procedure has two steps which follow the non-centered pattern of MacCormack's method where the fluxes are adjusted in such a way that second derivatives are handled in the well-centered manner characteristic of the Lax-Wendroff method. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1973
Accession Number
AD0766697

Entities

People

  • Peter R. Eiseman

Organizations

  • Air Force Research Laboratory

Tags

DTIC Thesaurus Topics

  • Analytic Functions
  • Boundaries
  • Coordinate Systems
  • Equations
  • Equations Of Motion
  • Mathematics
  • Resistance

Fields of Study

  • Mathematics

Readers

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