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Characteristic fractional step finite difference method for nonlinear section coupled system

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Abstract

For the section coupled system of multilayer dynamics of fluids in porous media, a parallel scheme modified by the characteristic finite difference fractional steps is proposed for a complete point set consisting of coarse and fine partitions. Some techniques, such as calculus of variations, energy method, twofold-quadratic interpolation of product type, multiplicative commutation law of difference operators, decomposition of high order difference operators, and prior estimates, are used in theoretical analysis. Optimal order estimates in l 2 norm are derived to show accuracy of the second order approximation solutions. These methods have been used to simulate the problems of migration-accumulation of oil resources.

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Authors and Affiliations

  1. Institute of Mathematics, Shandong University, Jinan, 250100, P. R. China

    Yi-rang Yuan  (袁益让), Tong-jun Sun  (孙同军) & Yun-xin Liu  (刘允欣)

  2. School of Economics, Shandong University, Jinan, 250100, P. R. China

    Chang-feng Li  (李长峰)

Authors
  1. Yi-rang Yuan  (袁益让)
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  2. Chang-feng Li  (李长峰)
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  3. Tong-jun Sun  (孙同军)
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  4. Yun-xin Liu  (刘允欣)
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Corresponding author

Correspondence to Yi-rang Yuan  (袁益让).

Additional information

Project supported by the Major State Basic Research Program of China (No. 19990328), the National Tackling Key Program (No. 20050200069), the National Natural Science Foundation of China (Nos. 10372052, 10771124, 11101244, and 11271231), and the Doctorate Foundation of the State Education Commission (No. 20030422047)

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Yuan, Yr., Li, Cf., Sun, Tj. et al. Characteristic fractional step finite difference method for nonlinear section coupled system. Appl. Math. Mech.-Engl. Ed. 35, 1311–1330 (2014). https://doi.org/10.1007/s10483-014-1866-9

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  • DOI: https://doi.org/10.1007/s10483-014-1866-9

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