MULTIGRID SOLUTION OF INTERNAL FLOWS USING GENERALIZED SOLUTION ADAPTIVE MESHES

IN THIS PROJECT, WE PROPOSE TO DEVELOP A MULTIGRID SOLVER FOR INTERNAL FLOWS USING GENERALIZED SOLUTION ADAPTIVE MESHES COMPOSED OF TRIANGULAR OR TETRAHEDRAL MESH CELLS. THE RESULTING COMPUTER PROGRAM WILL PERMIT THE SOLUTION OF THREE-DIMENSIONAL TRANSONIC VISCOUS FLOWS IN STATIONARY AND ROTATING DOMAINS, AND WILL HAVE THE ABILITY TO ACCURATELY REPRESENT GEOMETRICALLY COMPLEX CONFIGURATIONS AND TO RESOLVE COMPLEX FLOW FEATURES SUCH AS BOUNDARY LAYERS, ZONES OF RECIRCULATION, AND TIP EFFECTS. THE MULTIGRID PROCEDURE WILL PERMIT VERY FAST CALCULATION OF STEADY SOLUTIONS AND WILL ALLOW TIME-ACCURATE CALCULATIONS TO BE PERFORMED AT EFFECTIVE COURANT NUMBERS MUCH LARGER THAN THOSE PERMITTED BY THE STABILITY CONSTRAINTS OF THE EXPLICITTIME-STEPPING SCHEME ALONE. ADDITIONALLY, THE MULTIGRID PROCEDURE PROVIDES AN EXCELLENT LOCAL ERROR INDICATOR THAT WILL BE USED TO GOVERN LOCAL MESH REFINEMENT. CELL DIVISIONWILL BE REGULATED TO KEEP THE MESH SMOOTH AND THE ASPECT RATIOS OF THE CELLS NEAR UNITY. UNDER THESE CONDITIONS, THE FINITE VOLUME SCHEME CAN PROVIDE SECOND ORDER ACCURACY IN REGIONS OF FLOW AWAY FROM DISCONTINUITIES IN THE SOLUTION. AT DISCONTINUITIES, A FIRST ORDER DISSIPATIVE CONTRIBUTION WILL BE ADDED TO CAPTURE SHOCKS WITHOUT OSCILLATION. IF SUCCESSFUL, THIS EFFORT WILL RESULT IN A FAST, EFFICIENT AND ACCURATE COMPUTER PROGRAM FOR THE COMPUTATION OF INTERNAL FLOWS.