PRE- AND POST-PROCESSING TECHNIQUES FOR DETERMINING "GOODNESS" OF COMPUTATIONAL MESHES.

IN CONTEMPORARY COMPUTATIONAL FLUID DYNAMICS, FINITE DIFFERENCE OR FINITE ELEMENT GRIDS ARE OFTEN GENERATED USINGSTANDARD MESH GENERATION TECHNIQUES. THE BETTER MESH GENERATION PACKAGES ARE CAPABLE OF DEFINING VERY FINE MESHESIN AREAS WHERE THE ANALYST EXPECTS FINE FEATURES OF THE FLOWNEED TO BE SIMULATED. IN RECENT TIMES, SOME MESH GENERATIONSCHEMES HAVE A MEASURE OF ADAPTIVITY IN THEM ALLOWING FOR SMOOTH ORTHOGONAL MESHES WITH A MINIMUM OF MESH DISTORTION. NEVERTHELESS, THE FINAL MESH THE ANALYST SELECTS TO PROVIDE SOLUTIONS FOR THE FLOW SIMULATION ARE TYPICALLY BASED ON SPECULATION AS TO THE APPROPRIATE MESH DENSITIES AND CONFIGURATIONS. CONCRETE TESTED CRITERIA DOES NOT EXIST THAT CAN GIVE AN INDICATION TO THE ANALYST OF THE QUALITY ("GOODNESS") OF THE MESH PRIOR TO AN EXPENSIVE CALCULATION, AND NO METHODS APPEAR TO BE AVAILABLE FOR DETERMING THE QUALITY OF THE FINAL SOLUTION. IN THE PROPOSED PROJECT, DETAILED STUDY WILL BE MADE OF SEVERAL PRE- AND POST-PROCESSING TECHNIQUES WHICH ARE DESIGNED TO DETERMINE THE OVERALL GOODNESS OF THE COMPUTATIONAL MESH. THESE TECHNIQUES ARE BASED ON SIMPLE A-POSTERIORI ERROR ESTIMATIONAND INTERPOLATION THEORY. IN THE PRE-PROCESSOR, GUIDELINES FOR DETERMINING AN ACCEPTABLE MESH WILL BE PROVIDED IN SUBROUTINES WHICH DO AN EFFICIENT AND MATHEMATICALLY SOUND A-POSTERIORI ESTIMATION OF THE ERROR THAT CAN POTENTIALLY BEDEVELOPED IN A GIVEN MESH. AN ADAPTIVE TECHNIQUE WILL THEN BE CALLED UPON TO PRE- PROCESS THE MESH BEFORE EXPENSIVE CALCULATION IS PERFORMED. POST-PROCESSING UNITS WILL USE DATA FROM A COMPUTED SOLUTION AND RIGOROUS A-POSTERIORI ERROR ESTIMATES TO PROVIDE ESTIMATES OF THE OVERALL QUALITY OF THE SOLUTION, AND BY USING EXTRACTION AND EXTRAPOLATION ROUTINES PROVIDE ENHANCEMENT OF SOLUTIONS OF IMPORTANT FLOW PROBLEMS. INITIAL STUDIES WILL FOCUS ON STEADY 2D EULER ANDNAVIER-STOKES EQUATIONS.