A Coordinate Transformation for the Porous Media Equation that Renders the Free-Boundary Stationary.

Abstract

We consider the one-dimensional porous media problem ut = u square xx' u(0, x) = u0(x) for initial data sub uo which vanishes outside a finite interval. Solutions of this problem contain a free boundary separating points (t,x) with u(t,x) > 0 from those with u(t,x) = 0. We deduce a coordinate transformation x = X(t,p) which renders this free boundary stationary in time. We describe a simple difference scheme based on this transformation and show that, even with a fairly crude mesh, the free boundary is tracked quite accurately.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1983
Accession Number
ADA132839

Entities

People

  • Eduardo A. Socolovsky
  • Morton E. Gurtin
  • Richard C. Maccamy

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Boundaries
  • Continents
  • Continuum Mechanics
  • Contracts
  • Differential Equations
  • Equations
  • Gas Flow
  • Intervals
  • Mathematics
  • Military Research
  • North Carolina
  • Partial Differential Equations
  • Scalar Functions
  • Stationary
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra