Application and Improvement of Preconditioning in Solution of Low Mach Number Flow, Using Compressible Flow Equation

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Motaghedolhagh, Kamyar | 2009

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 39411 (45)
University: Sharif University of Technology
Department: Aerospace Engineering
Advisor(s): Mazaheri, Karim
Abstract:
Upwind methods for forward time marching integration of compressible flow equations, suffer low accuracy and convergence rate for very low mach numbers. Here we have used a preconditioning scheme to address this challenge. A preconditioner matrix is multiplied in the Euler flow equations. First we investigate subsonic flow around an airfoil to validate the numerical scheme used here, and to show grid independence of our solutions. Then very low mach numbers between 0.1 and 0.001 is solved and increase in accuracy and convergence rate is demonstrated. The proposed algorithm has flow parameters, which are studied here to find their effect on accuracy and convergence rate. The found results are very satisfactory in accuracy, and the convergence rate is decreased up to 70%. Similar results are observed for solution of viscous flow (Navier Stokes Equation)
Keywords:
Convergence Rate ; Euler Equation ; Low Reynolds Number ; Precondition Algorithm ; Compressible Method ; Low Mach Number

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