AN INVESTIGATION IS PROPOSED HEREIN TO FORMALIZE, TEST AND EVALUATE NEW TECHNIQUES FOR IMPROVING THE TRANSIENT ACCURACYOF IMPLICIT FINITE-DIFFERENCE ALGORITHMS FOR THE TWO AND THREE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS.

AN INVESTIGATION IS PROPOSED HEREIN TO FORMALIZE, TEST AND EVALUATE NEW TECHNIQUES FOR IMPROVING THE TRANSIENT ACCURACYOF IMPLICIT FINITE-DIFFERENCE ALGORITHMS FOR THE TWO AND THREE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS. THEPROPOSED INVESTIGATION IS MOTIVATED BY THE NEED FOR COMPUTATIONAL METHODS OF IMPROVED ACCURACY AND EFFICIENCY FOR APPLICATION TO TRANSIENT MULTIDIMENSIONAL FLOWS IN ROCKET ENGINES, WHICH MAY CONTAIN SHOCKS, CHEMICAL REACTIONS, MULTIPLE PHASES, TURBULENCE, AND DEFORMING BOUNDARIES. THE TECHNIQUES TO BE INVESTIGATED WOULD REDUCE SPLITTING ERRORS ASSOCIATED WITH ADI FACTORIZATIONS AND WOULD BE EXAMINED FOR STABILITY, TRANSIENT ACCURACY, TREATMENT OF BOUNDARY CONDITIONS, AND APPLICABILITY TO PRACTICAL FLOW PROBLEMS. THE INVESTIGATION WOULD FOCUS ON THE REMOVAL OF DIFFICULTIES WHICH HAVE ARISEN IN THE SOLUTION OF PRACTICAL UNSTEADY FLOW PROBLEMS IN WHICH MULTIPLE TIME AND LENGTH SCALES ARE PRESENT. THE GOAL WOULDBE TO IDENTIFY A COMPUTATIONAL APPROACH WHICH WOULD REPRESENT A SIGNIFICANT IMPROVEMENT IN ACCURACY AND EFFICIENCY FOR THE TRANSIENT MULTIDIMENSIONAL CATEGORY OF FLOWS CONSIDERED.