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Optimization And Application Of A Global Seventh-Order Dissipative Compact Finite-difference Scheme Based On A Genetic Algorithm

Posted on:2019-03-13Degree:MasterType:Thesis
Country:ChinaCandidate:Y LinFull Text:PDF
GTID:2370330611993387Subject:Computer Science and Technology
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Finite-difference methods are widely used in the field of computational fluid dynamics due to their high efficiency and simple implementation.It is easy to construct a highorder interior scheme for finite-difference methods.However,it may become challenging to derive proper boundary closures to keep the scheme both time stable and global high accurate.This thesis studies a global seventh-order dissipative compact finite-difference scheme,and optimizes its boundary closures to enhance time stability of the scheme.Then,the optimized scheme is applied to calculate Euler equations and Navier-Stokes equations to verify its global accuracy and time stability.In this thesis,the global seventh-order dissipative compact finite-difference scheme is recalled firstly.Then the optimization problem is put forward,which is solved by a genetic algorithm,resulting in two sets of optimization coefficients.Therefore,two optimized schemes are established.Time stability of the optimized schemes is analyzed by using ?-pseudospectra.The result shows that the optimized schemes are time stable and have better time stability than the old one.After that,Fourier analysis of the optimized schemes is employed to demonstrate good dispersion and dissipation properties of the optimized schemes.Then,the optimized scheme is used to solve one-and two-dimensional Euler equations.The results show that the optimized scheme can achieve global seventhorder accuracy.Finally,one-and two-dimensional Navier-Stokes equations with source terms are calculated,showing that global seventh-order accuracy is also achieved.
Keywords/Search Tags:high order, global seventh-order, finite difference, time stable, ?-pseudospectra, Euler equations, Navier-Stokes equations
PDF Full Text Request
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