Numerical Modelling of Crystal Growth

Abstract

A code which solves the two-dimensional Euler equations for inviscid incompressible fluid flow was developed. It is based on a) adaptive triangulation of initial data, b) fast summation of the velocity field induced by a piecewise linear vorticity distribution, and (c) Delaunay triangulation of the vortices at-each step. The Euler equations were chosen as a model.problem for crystal growth because they share the numerical structure of moving points without the added difficulties of finding curvature and normal; instead, the velocity field is simply found from the Biot-Savart law. The code was tested on multiple rotating patches of constant and smooth vorticity. It is-second-order in space and fourth order in time, even on piecewise constant solutions. The error are much smaller that standard blob-based vortex methods with the same number of degrees of freedom.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Sep 30, 1992
Accession Number
ADA271206

Entities

People

  • John Strain

Organizations

  • Princeton University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Crystal Growth
  • Crystals
  • Equations
  • Equations Of State
  • Euler Equations
  • Flow
  • Fluid Flow
  • Geometry
  • Integral Equations
  • Mathematics
  • Potential Theory
  • Standards
  • Stratified Fluids
  • Triangulation
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space