In this paper, we consider a one-dimensional nonlinear partial differential equation that has the form ut + αuux + βunux - γuxx + δuxxx = F(u). A higher order lattice Bhatnager-Gross-Krook (BGK) model with an amen...In this paper, we consider a one-dimensional nonlinear partial differential equation that has the form ut + αuux + βunux - γuxx + δuxxx = F(u). A higher order lattice Bhatnager-Gross-Krook (BGK) model with an amending-function is proposed. With the Chapman-Enskog expansion, different kinds of nonlinear partial differential equations are recovered correctly from the continuous Boltzmann equation. The numerical results show that this method is very effective.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No 10661005) the Science and Technology Plan Item of Fujian Province (Grant No 2008F5019)
文摘In this paper, we consider a one-dimensional nonlinear partial differential equation that has the form ut + αuux + βunux - γuxx + δuxxx = F(u). A higher order lattice Bhatnager-Gross-Krook (BGK) model with an amending-function is proposed. With the Chapman-Enskog expansion, different kinds of nonlinear partial differential equations are recovered correctly from the continuous Boltzmann equation. The numerical results show that this method is very effective.
