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.
An efficient high-order immersed interface method （IIM） is proposed to solve two-dimensional （2D） heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in both time and space directions. The space variable is discretized by a high-order compact （HOC） difference scheme with correction terms added at the irregular points. The time derivative is integrated by a Crank-Nicolson and alternative direction implicit （ADI） scheme. In this case, the time accuracy is just second-order. The Richardson extrapolation method is used to improve the time accuracy to fourth-order. The numerical results confirm the convergence order and the efficiency of the method.
