In this paper, in order to extend the lattice Boltzmann method to deal with more nonlinear equations, a one-dimensional (1D) lattice Boltzmann scheme with an amending function for the nonlinear Klein-Gordon equation i...In this paper, in order to extend the lattice Boltzmann method to deal with more nonlinear equations, a one-dimensional (1D) lattice Boltzmann scheme with an amending function for the nonlinear Klein-Gordon equation is proposed. With the Taylor and Chapman-Enskog expansion, the nonlinear Klein-Gordon equation is recovered correctly from the lattice Boltzmann equation. The method is applied on some test examples, and the numerical results have been compared with the analytical solutions or the numerical solutions reported in previous studies. The L2, L∞ and Root-Mean-Square (RMS) errors in the solutions show the efficiency of the method computationally.展开更多
This work presents a numerical study on the dynamic high velocity compaction of the metal powder. The analysis of the process is based on a mesoscopic approach using multi-speed lattice Boltzmann method. The boundary ...This work presents a numerical study on the dynamic high velocity compaction of the metal powder. The analysis of the process is based on a mesoscopic approach using multi-speed lattice Boltzmann method. The boundary condition and the relaxation time are tailored to the situation. The dynamic compaction process is vividly presented and the shock wave can be easily found in the simulation. The density is analyzed in order to explore the mechanism of the high velocity compaction.展开更多
文摘In this paper, in order to extend the lattice Boltzmann method to deal with more nonlinear equations, a one-dimensional (1D) lattice Boltzmann scheme with an amending function for the nonlinear Klein-Gordon equation is proposed. With the Taylor and Chapman-Enskog expansion, the nonlinear Klein-Gordon equation is recovered correctly from the lattice Boltzmann equation. The method is applied on some test examples, and the numerical results have been compared with the analytical solutions or the numerical solutions reported in previous studies. The L2, L∞ and Root-Mean-Square (RMS) errors in the solutions show the efficiency of the method computationally.
基金supported by the National Natural Science Foundation of China(Nos. 50874123 and 51174236)National Basic Research Program of China(No. 2011CB606306)
文摘This work presents a numerical study on the dynamic high velocity compaction of the metal powder. The analysis of the process is based on a mesoscopic approach using multi-speed lattice Boltzmann method. The boundary condition and the relaxation time are tailored to the situation. The dynamic compaction process is vividly presented and the shock wave can be easily found in the simulation. The density is analyzed in order to explore the mechanism of the high velocity compaction.
