六维相空间中无碰撞Boltzmann方程的直接积分：自引力系统
Direct Integration of the Collisionless Boltzmann Equation in Six-dimensional Phase Space: Self-gravitating Systems
摘要：
本文提出了一种数值模拟无碰撞自引力系统的方案，它直接将Vlasov-Poisson方程组积分到六维相空间中。一系列大规模数值模拟的结果表明，该方法可以很好地模拟无碰撞自引力系统。积分方案是基于最近在等离子体物理中发展起来的正通量守恒方法。我们测试的准确性，我们的代码进行几个测试计算，包括国王球的稳定性，引力不稳定性和朗道阻尼。我们表明，我们研究的所有测试用例的质量和能量准确地保存。结果与线性理论预测和/或解析解吻合良好。分布函数保持正性，且无振荡。最大的模拟在64^6网格上运行。计算速度与处理器的数量密切相关，因此我们的代码在大规模并行超级计算机上有效地执行。
英文摘要：
We present a scheme for numerical simulations of collisionless self-gravitating systems which directly integrates the Vlasov--Poisson equations in six-dimensional phase space. By the results from a suite of large-scale numerical simulations, we demonstrate that the present scheme can simulate collisionless self-gravitating systems properly. The integration scheme is based on the positive flux conservation method recently developed in plasma physics. We test the accuracy of our code by performing several test calculations including the stability of King spheres, the gravitational instability and the Landau damping. We show that the mass and the energy are accurately conserved for all the test cases we study. The results are in good agreement with linear theory predictions and/or analytic solutions. The distribution function keeps the property of positivity and remains non-oscillatory. The largest simulations are run on 64^6 grids. The computation speed scales well with the number of processors, and thus our code performs efficiently on massively parallel supercomputers.
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