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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Institution: | 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 an
amending function for one-dimensional nonlinear partial
differential equations (NPDEs) in the form $ u_t+\alpha uu_x+\beta
u^nu_x+\gamma u_{xx}+\delta u_{xxx}+\zeta u_{xxxx}=0.$ This model is
different from existing models because it lets the time step
be equivalent to the square of the space step and derives higher
accuracy and nonlinear terms in NPDEs. With the Chapman--Enskog
expansion, the governing evolution equation is recovered correctly
from the continuous Boltzmann equation. The numerical results
agree well with the analytical solutions. |
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Keywords: | nonlinear partial differential equation lattice Boltzmann
method Chapman--Enskog expansion Taylor expansion |
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