A NEW APPROACH FOR SOLVING NAVIER-STOKES EQUATIONS ON UNSTRUCTURED GRIDS BASED ON ADAPTIVE METHODS AND OPERATOR-SPLITTING

TODAY AN OVERWHELMING MAJORITY OF CFD CALCULATIONS ARE DONE WITH STANDARD FIXED GRID FINITE DIFFERENCE METHODS. HOWEVER, A SIMPLE CALCULATION CAN ESTABLISH THAT SUCH METHODS CANNOT POSSIBLY EXPLOIT THE FULL COMPUTING POWER OF TODAY'S COMPUTING EQUIPMENT NOR CAN THEY DELIVER HIGHLY ACCURATE SIMULATIONS OF FINE SCALE FLOW PHENOMENA IN COMPLEXFLOW DOMAINS. TO FULLY EXPLOIT CONTEMPORARY COMPUTING CAPABILITIES, NEW AND INNOVATIVE COMPUTATIONAL PROCEDURES MUST BE DEVELOPED THAT ARE BASED ON CONCEPTS WHICH REPRESENT A SIGNIFICANT DEPARTURES FROM CONVENTIONAL FD FLOW SOLVERS. IN THE PRESENT PROPOSAL, A PROJECT IS OUTLINED WHICH WILL HAVE AS ITS ULTIMATE GOAL THE DEVELOPMENT OF A NEW FAMILY OF CFD CODES THAT CAN BE USED TO EFFECTIVELY ADDRESS A VARIETY OF VERY COMPLEX FLOW PROBLEMS THAT ARE NOT TREATED SATISFACTORILY WITH EXISTING METHODS. THESE NEW METHODS ARE BUILT AROUND TWO BASIC IDEAS: 1) THE USE OF NEW OPERATOR-SPLITTING TECHNIQUES THAT PROVIDE SPECIAL HIGH-ORDER SCHEMES FOR THE CONVECTION AND DIFFUSION STEPS IN AN UNSTEADY NAVIER-STOKES CALCULATION AND2) THE USE OF SPECIAL H-P ADAPTIVE SCHEMES ON UNSTRUCTURED GRIDS. THE PHASE I PROJECT IS TO FOCUS ON DEVELOPING OPERATOR-SPLITTING METHODS FOR EULER EQUATIONS ON UNSTRUCTURED GRIDS WITH PARTICULAR ATTENTION GIVEN TO EXPLICIT METHODS SECOND-ORDER ACCURATE IN TIME. RELIABLE A-POSTERIORI ERROR ESTIMATORS WILL BE DEVELOPED THAT WILL PROVIDE A BASIS FOR H-P ADAPTIVITY, I.E. A SOLUTION ADAPTIVESCHEME WILL BE DEVISED WHICH WILL ATTEMPT TO PROVIDE AN OPTIMAL APPROXIMATION BY SIMULTANEOUSLY INCREASING A LOCAL SPECTRAL ORDER OF THE APPROXIMATION AS WELL AS DECREASING THE MESH SIZE.