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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 08, 1986
- Accession Number
- ADA253675
Entities
People
- Patrick J. Roache