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Explicit formulations and performance of LSFD method on Cartesian mesh

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Abstract

Performance of the LSFD method is compared with conventional FD schemes. Generally, 9-point stencils for 2D cases and 27-point stencils for 3D cases are used for the approximation of the first and second order derivatives obtained with conventional central difference schemes. When the same stencils are used, explicit LSFD formulations for approximation of the first and second order derivatives are presented. The LSFD formulations are actually a combination of conventional central difference schemes along relevant mesh lines. It has been found that LSFD formulations need much less iteration steps than the conventional FD schemes to converge, and the ratio of mesh spacing in the x and y directions is an important parameter in the LSFD application, with a great impact on stability of LSFD computation.

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Correspondence to Qing-dong Cai  (蔡庆东).

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(Communicated by Zhe-wei ZHOU)

Project supported by the National Natural Science Foundation of China (Nos. 10872005, 10532010)

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Cai, Qd. Explicit formulations and performance of LSFD method on Cartesian mesh. Appl. Math. Mech.-Engl. Ed. 30, 183–196 (2009). https://doi.org/10.1007/s10483-009-0206-z

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  • DOI: https://doi.org/10.1007/s10483-009-0206-z

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Chinese Library Classification

2000 Mathematics Subject Classification

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