Abstract
Contemporarily, the dramatic progress that proceeded in astrophysical simulation stems from the computational upgrade. Simultaneously, the relative algorithms are from naive to mature. Some imaginary algorithms spring up like bamboo. The typical methods are Monte-Carlo, Particle-in-Cell, and Magnetohydrodynamic considering the relativistic effect. This paper reviews the typical progress of the above three methods as well as their hybrid method in astrophysics. These results offer a guideline for further research in astrophysics simulation.
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