Numerical Simulations of Self-Gravitating Systems Through Collision less Boltzmann Equation on Six-Dimensional Phase Space

我们开发了一个自引力系统的数值模拟程序，它直接集成了无碰撞玻尔兹曼方程耦合泊松方程的六维相空间，并执行，第一次，一组数值模拟的自引力系统使用无碰撞玻尔兹曼方程具有科学意义的问题大小。此外，通过比较从我们的数值模拟和传统的N体模拟得到的结果，我们证实了我们的数值方法的有效性，并估计其优点和缺点，比传统的N体方法。我们还将我们的方法推广到宇宙共动框架中，并将其应用于宇宙大尺度结构形成的数值模拟，通过与传统N体模拟结果的比较，再次验证了我们方法的有效性.

We develop a numerical simulation code for self-gravitating systems which directly integrates the collisionless Boltzmann equation coupled with the Poisson equation on the six-dimensional phase space, and perform, for the first time, a set of numerical simulations of self-gravitating systems using the collisionless Boltzmann equation with a scientifically meaningful problem size. Furthermore, by comparing the results obtained from both of our numerical simulations and conventional N-body simulations, we confirm the validity of our numerical method and estimate its advantage and disadvantages over the conventional N-body method. We also adopt our method to numerical simulations of the large-scale structure formation in the universe by extending our implementation into the cosmological comoving frame, and confirm its validity again by comparing the results with those from conventional N-body simulations.