Preconditioning Technique In Slightly Compressible Model

The Slightly Compressible ModeI(SCM)efficient for lOW Mach number flow calculationderived by Deng Xiaogang is veryBut the eigenvalue system ofthe SCM equations shows strong stiffness when the freesteam Mach number is very low,because the same governing equations with the Navier-Stokes equations are introducedin SCM．A preconditioned method proposed for SCM(SCM-P)is not very effective in solving the unsteady flow calculations and critical state,since the continuity equationis only satisfied in the steady state．In this thesis based on SCM．a new preconditioned method has been proposed．This thesis iS composed of six chapters:The first chapter is the preface of this thesis．The background of the simulation forlOW Mach number flows iS introduced jn brief SO as to the popular arithmetic．The characteristic and problems confronted in using SCM and SCM．P to calculate the low and very low Mach number flows are included in the next part．The last part is theresearch work ofthis thesis．In the second chapter,the stiffneSS of SCM iS introduced．Four schemes areproposed based on algebraic preconditioned methods．the results indicate an importantimprovement．In the third chapter,the stability and the convergence characteristics of methodsproposed in chapter 2 are investigated．SCM-APl and SCM-AP2 which exhibitfeasible results are further developed in this thesis．The effects of the approximationsintroduced in the implementations on the stability are analysed．In the fourth chapter,some two．dimensionaJ results calculated by SCM．APl andSCM-AP2 are presented and compared with the results calculated by SCM and SCM-PIn the present work,SCM·AP2 is more excellent in the precision and convergence．In the fifth chapter,flow fields around a delta wing and an ellipsoid are simulatedby the SCM-AP2．Results show that SCM．AP2 is effective in simulating unsteadyseparation flows at high angle of attack．The concluding remarks are given in the sixth chapter,where the summary ofcurrent study work is presented and the job tO be carried on in future is pointed out asweIlIn the end,the references and acknowledgements are presented．...