Fast Implicit Methods for Stiff Moving Interfaces

Abstract

The research supported by this grant aimed to solve moving interface problems with two flexible computational modules: semi-Lagrangian contouring (SLC) methods which evolved an interface with a given velocity field, and problem-dependent evaluation of the velocity of a given interface. These modules, with associated engines for fast computational geometry, constituted a highly effective toolbox for evolving an implicitly represented interface through arbitrary topology under a given velocity functional. The first module was extended with linearly-implicit SLC methods which evolved stiff interfaces under geometric velocities such as mean curvature and surface diffusion, and fourth-order SLC methods which delivered greatly improved accuracy. The second module was extended with fast solvers for elliptic systems which evaluated interface velocities determined by quasistationary physical interactions off the interface, and enabled the solution of key models such as Ostwald ripening, elastic membranes in Stokes flow, and crystal growth.

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Document Details

Document Type
Technical Report
Publication Date
Mar 16, 2011
Accession Number
ADA563709

Entities

People

  • John Strain

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Asymptotic Series
  • Boundary Value Problems
  • Cell Movement
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Differential Equations
  • Equations
  • Fast Fourier Transforms
  • Fluid Dynamics
  • Fourier Series
  • Geometry
  • Integral Equations
  • Integrals
  • Materials Science
  • Mathematics
  • Two Dimensional

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