Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations

Abstract

The authors present an adaptive method based on the idea of multiple, component grids for the solution of hyperbolic partial differential equations using finite difference techniques. Based upon Richardson-type estimates of the truncation error, refined grids are created or existing ones removed to attain a given accuracy for a minimum amount of work. Their approach is recursive in that fine grids can themselves contain even finer grids. The grids with finer mesh width in space also have a smaller mesh width in time, making this a mesh refinement algorithm in time and space. This document includes algorithm, data structures and grid generation procedure, and concludes with numerical examples in one and two space dimensions.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1983
Accession Number
ADA130162

Entities

People

  • Joseph Oliger
  • Marsha J. Berger

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Boundary Layer
  • Boundary Value Problems
  • Collision Avoidance
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Programming
  • Computer Science
  • Coordinate Systems
  • Difference Equations
  • Differential Equations
  • Fluid Dynamics
  • Fluid Mechanics
  • Linear Accelerators
  • Partial Differential Equations
  • Pattern Recognition
  • Two Dimensional

Readers

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

Technology Areas

  • Space