Generalized Square Conservative Multistep Finite Difference Scheme Incorporating Historical Observations |
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| Authors: | GONG Jing WANG Bin and JI Zhong-Zhen State |
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| Affiliation: | Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics(LASG),Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing 100029,China 2 Mathematics and Physics Department,North China Electric Power University,Beijing 102206,China |
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| Abstract: | In this paper,a multistep finite difference scheme has been proposed,whose coefficients are determined taking into consideration compatibility and generalized quadratic conservation,as well as incorporating historical observation data.The schemes have three advantages:high-order accuracy in time,generalized square conservation,and smart use of historical observations.Numerical tests based on the one-dimensional linear advection equations suggest that reasonable consideration of accuracy,square conservation,and inclusion of historical observations is critical for good performance of a finite difference scheme. |
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| Keywords: | multistep difference scheme generalized square conservation accuracy historical observations |
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