Algorithms to Solve Nonlinear Time Dependent Problems of Engineering and Physics

Abstract

During this last year Osher developed a joint project with James Sethian concerning fronts propagating with curvature dependent speed. They devised new algorithms approximating the equations of motion, which resemble Hamilton-Jacobi equations with parabolic right-hand sides, by using techniques from hyperbolic conservation laws. Essentially non-oscillatory schemes are used. These methods accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, and work in any number of space dimensions. The methods can also be used for more general Hamilton-Jacobi type problems. Applications of the algorithms include crystal growth, solidification of metals and flame propagation.

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Document Details

Document Type
Technical Report
Publication Date
Jun 30, 1989
Accession Number
ADA221463

Entities

People

  • Daniel Cook
  • E. Widder
  • J. Case
  • James Sethian
  • Stanley Osher

Organizations

  • University of California, Los Angeles

Tags

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Availability
  • Blast Waves
  • Cauchy Problem
  • Computations
  • Crystal Growth
  • Discontinuities
  • Equations
  • Equations Of Motion
  • Flame Propagation
  • High Resolution
  • Mathematics
  • Shock
  • Shock Waves
  • Stochastic Control
  • Three Dimensional

Readers

  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Dynamics.

Technology Areas

  • Space