An Adaptive Mesh-Moving and Local Refinement Method for Time-Dependent Partial Differential Equations

Abstract

We discuss mesh-moving, static mesh regeneration, and local mesh-refinement algorithms that can be used with a finite difference or finite element scheme to solve initial boundary value problems for vector systems of time-dependent partial differential equations in two space dimensions and time. A coarse based mesh of quadrilateral cells is moved by an algebraic mesh-movement function so as to follow and isolate spatially distinct phenomena. The local mesh-refinement method recursively divides the time step and spatial cells of the moving base mesh in regions where error indicators are high until a prescribed tolerance is satisfied. The static mesh-regeneration procedure is used to create a new base mesh when the existing one becomes to distorted. The adaptive methods have been combined with a MacCormack finite difference scheme for hyperbolic systems and an error indicator based upon estimates of the local discretization error obtained by Richardson extrapolation. Results are presented for several computational examples.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1990
Accession Number
ADA235464

Entities

People

  • David C. Arney
  • J. E. Flaherty

Organizations

  • Rensselaer Polytechnic Institute

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Algorithms
  • Boundary Value Problems
  • Computational Complexity
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Computer Science
  • Differential Equations
  • Equations
  • Euler Equations
  • Geometry
  • Mathematical Programming
  • Numerical Analysis
  • Partial Differential Equations
  • United States Military Academy

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space