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W2284606989 abstract "Finite difference schemes used in the field of computational fluid dynamics isgenerally only of second-order accurate in representing the spatial derivatives.Numerical algorithms based on higher order finite difference schemes that canachieve fourth-order accuracy in space have been developed. Higher order schemeswill enable a larger grid size with fewer grid points to sufficiently give fine results. Acompact scheme, which preserves the smaller stencil size, is preferred due to itssimplicity and computational efficiency, as opposed to the normal approach toexpand the stencil to achieve higher accuracy. Two approaches are used to obtain thefourth-order accurate compact scheme. In Lax-Wendroff approach, the governingdifferential equations are used to approximate the leading truncation error in thesecond-order central difference of the governing equations. In Hermitian scheme, thefourth-order approximations to the derivatives are treated as unknowns. Theseunknowns are solved explicitly with Hermitian relations that relate the variables andits spatial derivatives. The numerical algorithms are first developed for viscousBurgers' equation on uniform and clustered grids. The fourth-order accuracy and convergence rate is demonstrated. The performance of the two different approachesare compared and found on par with each other. Second, the numerical algorithmsare used to solve the quasi-one-dimensional subsonic-supersonic nozzle flow. TheHermitian scheme shows excellent agreement with the analytical result but the Lax-Wendroffapproach failed to do so due to instability problem. Third, only thenumerical algorithm based on Hermitian scheme is used to solve the flow past abackward-facing step. The reattachment lengths of the first separation bubblecompare favourably with previously published results in the literature. The successof the fourth-order compact finite difference schemes in solving the viscous Burgers'equation is not repeated in the isentropic nozzle flow and the flow past a backward-facingstep. Further efforts have to be made to improve the convergence rate of thenumerical solution of the isentropic nozzle flow using the Hermitian scheme and toovercome the instability in the numerical solution of the same problem using theLax-Wendroff approach." @default.
W2284606989 created "2016-06-24" @default.
W2284606989 creator A5054937899 @default.
W2284606989 date "2003-02-01" @default.
W2284606989 modified "2023-09-24" @default.
W2284606989 title "Application Of Higher Order Compact Finite Difference Methods To Problems In Fluid Dynamics" @default.
W2284606989 hasPublicationYear "2003" @default.
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