AN EFFICIENT PATCHED GRID NAVIER-STOKES SOLUTION PROCEDURE FOR MULTIPLE BODIES

AN EFFICIENT PROCEDURE IS PROPOSED TO SOLVE THE TIME-DEPENDENT, MULTIDIMENSIONAL NAVIER-STOKES EQUATIONS ABOUT MULTIPLE BODY CONFIGURATIONS WHICH MAY BE IN MOTION RELATIVE TO ONE ANOTHER. FOR SUCH APPLICATIONS, THE GEOMETRIC CONSTRAINTS OF THE COMPONENT ELEMENTS OFTEN REQUIRE THAT PATCHED GRIDS BE EMPLOYED. EXISTING PATCHED GRID APPROACHES FIRST OBTAIN SOLUTIONS ON EACH OF THE COMPONENT GRIDS AND THEN ENSURE COMPATABILITY VIA AN ITERATION PROCEDURE. IN CONTRAST TO SUCH APPROACHES THE PROPOSED METHOD CALCULATES THE ENTIRE FLOW FIELD OVER BOTH GRIDS SIMULTANEOUSLY WITHOUT ITERATION. BY ELIMINATTING ITERATION WITHIN A TIME STEP, AND ALLOWING TIME STEPS TO BE CHOSEN BY ACCURACY CONSIDERATIONS RATHER THAN BY STABILITY LIMITS, THIS INNOVATIVE PROCEDURE WOULD LEAD TO A SUBSTANTIAL SAVINGS IN COMPUTER RUN TIME. IN ADDITION, FOR STEADY STATE PROBLEMS, IMPROVED CONVERGENCE RATES COULD BE EXPECTED. THE PROPOSED METHOD IS QUITE GENERAL AND COULD BE APPLIED TO A WIDE CLASS OF PROBLEMS IN WHICH PATCHED GRIDS ARE REQUIRED. HOWEVER, TO DEMONSTRATE THE CAPABILITIES AND ADVANTAGES OF THE NEW PROCEDURE, A PROBLEM OF CURRENT INTEREST IN TURBOMACHINERY WOULD BE INVESTIGATED, THE FLOW FIELD IN A ROTOR STATOR STAGE.