A lattice Boltzmann model with an amending function forsimulating nonlinear partial differential equations |
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| Authors: | Chen Lin-Jie and Ma Chang-Feng |
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| Affiliation: | School of Mathematics and Computer Sciences, Fujian Normal University, Fuzhou 350007, China |
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| Abstract: | ![]()
This paper proposes a lattice Boltzmann model with anamending function for one-dimensional nonlinear partialdifferential equations (NPDEs) in the form $ u_t+alpha uu_x+betau^nu_x+gamma u_{xx}+delta u_{xxx}+zeta u_{xxxx}=0.$ This model isdifferent from existing models because it lets the time stepbe equivalent to the square of the space step and derives higheraccuracy and nonlinear terms in NPDEs. With the Chapman--Enskogexpansion, the governing evolution equation is recovered correctlyfrom the continuous Boltzmann equation. The numerical resultsagree well with the analytical solutions. |
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| Keywords: | nonlinear partial differential equation lattice Boltzmannmethod Chapman--Enskog expansion Taylor expansion |
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