A Fourth Order Accurate Discretization for the Laplace and Heat Equations on Arbitrary Domains, with Applications to the Stefan Problem

Abstract

In this paper, the authors first describe a fourth order accurate finite difference discretization for both the Laplace equation and the heat equation with Dirichlet boundary conditions on irregular domains. In the case of the heat equation, they use an implicit time discretization to avoid the stringent time step restrictions associated with explicit schemes. They then turn their focus to the Stefan problem and construct a third order accurate method that also includes an implicit time discretization. Multidimensional computational results are presented to demonstrate the order accuracy of these numerical methods.

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Document Details

Document Type
Technical Report
Publication Date
Apr 27, 2004
Accession Number
ADA479464

Entities

People

  • Frédéric Gibou
  • Ronald Fedkiw

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Boundaries
  • Boundary Value Problems
  • Coefficients
  • Computations
  • Computer Science
  • Differential Equations
  • Equations
  • Error Analysis
  • Errors
  • Extrapolation
  • Heat Energy
  • Linear Systems
  • Partial Differential Equations
  • Temperature Gradients
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Computational Fluid Dynamics (CFD)