STUDIES OF FINITE DIFFERENCE TECHNIQUES FOR CONTINUUM MECHANICS.

Abstract

Solutions to hyperbolic equations typically have discontinuous first or second space and time derivatives. This limits the rate of convergence of time-marching numerical procedures for solving hyperbolic problems. With N zones on a finite one-dimensional region of space, the truncation error tends to zero no faster than N-3/2 for large N. Truncation error estimates based on Taylor's Series expansions are usually incorrect. The truncation error can be decreased by using higherorder differences if the equations are written in characteristic coordinates. These conclusions are reached by solving finite difference equations analytically, e.g., the Richtmyer-von Neumann equations are solved with infinitesimal time-step for a pulse in an elastic medium. Supporting numerical results are shown. Artificial viscosities--particularly linear viscosities--significantly degrade pulses in elastic media. Numerical results are given for various viscosity coefficients. A procedure is given for uniquely determining finite strain in finite zones of material.

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1964
Accession Number
AD0613351

Entities

People

  • John G. Trulio

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Continuum Mechanics
  • Convergence
  • Difference Equations
  • Equations
  • Materials
  • Mathematical Analysis
  • Mathematics
  • Mechanical Properties
  • Mechanics
  • Truncation
  • Viscosity

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space