Adaptive Grid Generation Using Elliptic Generating Equations with Precise Coordinate Controls

Abstract

Significant contributions in algorithms and codes for automatic grid generation were made in the following specific areas: automatic generation of multidimensional Fortran code via Symbolic Manipulation (Artificial Intelligence), requiring user input of only the governing partial differential equations or the governing variational principles; rigorous techniques for verification of codes, algorithms, and discretization methods; a new and effective formulation for variational methods; analysis of mathematical properties (ellipticity, convexity) of PDE and variational methods including volume, orthogonality, smoothness and other controls; identification and explanations of previously unreported anomalies in common grid generation algorithms, including non-uniqueness due to solution bifurcation and grid folding; identification and explanation of previously unreported ambiguities in common discrete evaluations of transformation Jacobians; use of a reference grid to control target grid properties; development of a solution adaptive method for surface grid generation; development of a hybrid method of solution adaptive grid generation which properly isolates the multigrid methods to elliptic grid generation; development of an algorithm for economically generating sub-grid grid generation discretizations required for multigrid solution techniques; correct interpretation of the "smoothness" property of elliptic grid generation.

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Document Details

Document Type
Technical Report
Publication Date
Jul 08, 1986
Accession Number
ADA253675

Entities

People

  • Patrick J. Roache

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Programming
  • Computer Programs
  • Computers
  • Differential Equations
  • Equations
  • Fluid Dynamics
  • Mathematical Analysis
  • Mechanical Engineering
  • Military Research
  • Partial Differential Equations
  • Three Dimensional
  • Two Dimensional

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms