DEVELOPMENT OF GRADIENT SMOOTHING METHOD (GSM) FOR FLUID FLOW PROBLEMS

Abstract

<P>IN THIS THESIS, A NOVEL GRADIENT SMOOTHING METHOD (GSM) BASED ON STRONG FORM OF GOVERNING EQUATIONS FOR FLUID DYNAMICS PROBLEMS IS PRESENTED. IRREGULAR CELLS ARE FOCUSED TO BE USED IN THE GSM, WHICH MAKES THIS METHOD VIABLE FOR ARBITRARILY COMPLEX GEOMETRIES. IN THE GSM, THE SPATIAL DERIVATIVES AT A LOCATION OF INTEREST ARE APPROXIMATED BY THE GRADIENT SMOOTHING OPERATION. IT RELATES TO A SPATIALLY AVERAGED INTEGRAL OVER A SMOOTHING DOMAIN CONSTRUCTED AROUND THE LOCATION OF INTEREST, WITH THE HELP OF SMOOTHING FUNCTIONS. RESEARCH STUDIES HERE PRIMARILY COVER THE SEARCH FOR FAVORABLE DISCRETIZATION SCHEMES, DIFFERENT TYPES OF SMOOTHING FUNCTIONS, BOTH EXPLICIT AND IMPLICIT SOLVERS AND SOLUTION-BASED ADAPTATION. A MOST FAVORABLE GSM SCHEME HAS BEEN COMPREHENSIVELY APPLIED FOR SOLUTIONS TO CLASSICAL COMPRESSIBLE AND INCOMPRESSIBLE BENCHMARKING PROBLEMS. RESULTS REVEAL THAT THE PROPOSED GSM IS REMARKABLY CONSERVATIVE, ACCURATE, ROBUST, STABLE AND EFFICIENT. </P>