ADAPTIVE SCHEMES FOR COMPLEX SUBSONIC 3D-FLOW PROBLEMS IN ARBITRARY DOMAINS

THIS PROJECT IS DEVOTED TO THE DEVELOPMENT OF A UNIQUE COLLECTION OF ALGORITHMS DESIGNED TO RESOLVE SOME OF THE MOST DIFFICULT PROBLEMS OF MODERN COMPUTATIONAL FLUID DYNAMICS: (1) THE ANALYSIS OF COMPLEX INCOMPRESSIBLE FLOWS IN ARBITRARY THREE-DIMENSIONAL DOMAINS; (2) THE ANALYSIS OF COMPLEX FLOW-INTERACTION PHENOMENA ASSOCIATED WITH THE MOTION OF ONE OR MORE RIGID BODIES MOVING RELATIVE TO ONE ANOTHER THROUGH A FLOW DOMAIN; (3) THE DEVELOPMENT OF QUANTIFIABLE ESTIMATES OF THE ACCURACY OF COMPUTED SOLUTIONS; AND (4) THE DEVELOPMENT OF NEAR-OPTIMAL CFD SCHEMES WHICH ATTEMPT TO PRODUCE THE BEST POSSIBLE RESULTS FOR A GIVEN, FIXED COMPUTATIONAL EFFORT. TO ACCOMPLISH THESE OBJECTIVES, FULLY-ADAPTIVE COMPUTATIONAL SCHEMES ARE TO BE DEVELOPED WHICH ARE EFFECTIVELY GEOMETRY-INDEPENDENT, WHICH EMPLOY UNSTRUCTURED MESHES, AND WHICH SIMULTANEOUSLY REFINE THE MESH SO AS TO KEEP LOCAL ERRORS WITHIN PREASSIGNED TOLERANCES. FLOW INTERACTION PROBLEMS ARE TO BE HANDLED USING NEW SLIDING MESH ALGORITHMS WHICH FULLY CONSERVE FLOW VARIABLES ACROSS MESH INTERFACES. THE RELIABILITY OF ALL CALCULATIONS IS DETERMINED THROUGH RIGOROUS A-POSTERIORI ERROR ESTIMATES WHICH ALSO PROVIDE THE BASIS FOR THE ADAPTIVE REFINEMENT SCHEMES.