考虑自引力的欧拉流体动力学模拟的一种新的能量守恒方法
A New Way to Conserve Total Energy for Eulerian Hydrodynamic Simulations with Self-Gravity
摘要：
提出了一种新的方法，以节省总能量舍入误差的网格为基础的代码与自重力流体动力学模拟。给出了由于自引力做功而引起的能流公式，从而总能量的变化可以用守恒形式表示。用Athena程序进行的数值实验表明，新算法确实是能量守恒的，而且具有二阶精度。我们已经进行了一组测试，显示在传统的，非保守的算法的数值误差会影响系统的动态。与传统的包含自引力源项的算法相比，新算法只需要增加一个泊松方程的解。如果泊松求解器占用总仿真时间的一小部分，例如使用FFT时，则新算法几乎与原始方法一样有效。该算法适用于具有自重力的欧拉流体动力学模拟，特别是当计算结果对小的能量误差敏感时，如辐射压力主导的流动。
英文摘要：
We propose a new method to conserve the total energy to round-off error in grid-based codes for hydrodynamic simulations with self-gravity. A formula for the energy flux due to the work done by the the self-gravitational force is given, so the change in total energy can be written in conservative form. Numerical experiments with the code Athena show that the total energy is indeed conserved with our new algorithm and the new algorithm is second order accurate. We have performed a set of tests that show the numerical errors in the traditional, non-conservative algorithm can affect the dynamics of the system. The new algorithm only requires one extra solution of the Poisson equation, as compared to the traditional algorithm which includes self-gravity as a source term. If the Poisson solver takes a negligible fraction of the total simulation time, such as when FFTs are used, the new algorithm is almost as efficient as the original method. This new algorithm is useful in Eulerian hydrodynamic simulations with self-gravity, especially when results are sensitive to small energy errors, as for radiation pressure dominated flow.
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