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Duck-Joo Lee

2013-11-11
09:10:00 - 10:20:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

High order finite schemes have low truncation errors, which does not guarantee a good quality of solution for time dependent problems. Taylor series is used to rank the order of schemes. A Fourier analysis provides an effective ways to quantify dissipative error and dispersion(phase) error. Low dispersion error is critical in simulation of unsteady flows and propagating waves. Convection term in the Navier-Stokes equation is important in the generation of nonlinear phenomena of turbulence and in the propagation of wave through a moving medium. Accurate and high resolution schemes for the space derivative in the convection term are introduced and analyzed in details. Most of high resolution finite scheme is central scheme because of zero dissipation error. Direct comparisons of high resolution schemes will be shown in wave number domain. So called DRP(Dispersion-Relation-Preserving) scheme, Spectral-Like scheme and Optimized High Order Compact schemes are compared with conventional 2nd order central scheme and standard Pade scheme. A unified Lomax approach in the stability analysis will be introduced.

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