Patent ID: 7231329

Claim:
A method for generating an elliptic grid of coordinates in two dimensions or in three dimensions, the method comprising: providing defining equations, valid near at least one boundary segment in a generalized coordinate system, of a selected grid system, where each of the defining equations has at least two independent Cartesian coordinate variables, has at least one generalized coordinate as a dependent variable, and comprises a partial differential equation, expressed in at least one generalized coordinate; providing a selected group of boundary constraints for the grid system, valid near the at least one boundary segment, where a decay parameter for at least one of the generalized coordinate dependent variables near the at least one boundary segment is determined as part of a solution for the grid system, rather than being prescribed initially; providing defining equations and selected boundary conditions, having at least two independent coordinate variables and at least one dependent variable, for steady state heat transfer on a long thin fin, and providing a correspondence between the at least two independent coordinate variables for the grid system near the at least one grid boundary segment with the at least two independent coordinate variables for the heat transfer problem; providing a correspondence between a selected power of at least one heat transfer coefficient for the heat transfer problem and at least one decay parameter for the grid system near the at least one grid boundary segment; determining a solution of the grid system near the at least one grid boundary segment that incorporates at least one boundary constraint comprising the at least one decay parameter determined for the grid system; and displaying the solution of the grid system.