标题： 密近双星洛希瓣溢流驱动的质量转移数值稳定性 显示英文标题

标题： Numerical stability of mass transfer driven by Roche lobe overflow in close binaries

摘要： 密近双星中物质转移率的时间演化数值计算是一项挑战，尤其是在某些情况下。 通过使用一个简单的物理模型来计算物质转移率，我们证明了对于一个简单的显式迭代方案，除非时间步长足够小，否则物质转移率在数值上是不稳定的。 一般来说，更复杂的显式算法并没有提供显著的改进，因为这种不稳定性是时间离散化的直接结果。 对于典型的双星演化，将物质转移率作为时间的平滑函数进行计算限制了可容忍的最大时间步长，从而设定了演化计算所需的最小总计算工作量。 通过“控制混沌”的方法可以证明，一种基于牛顿法的特定隐式迭代方案是解决该问题最有希望的方法。 显示英文摘要

摘要： Numerical computation of the time evolution of the mass transfer rate in a close binary can be and, in particular, has been a computational challenge. Using a simple physical model to calculate the mass transfer rate, we show that for a simple explicit iteration scheme the mass transfer rate is numerically unstable unless the time steps are sufficiently small. In general, more sophisticated explicit algorithms do not provide any significant improvement since this instability is a direct result of time discretization. For a typical binary evolution, computation of the mass transfer rate as a smooth function of time limits the maximum tolerable time step and thereby sets the minimum total computational effort required for an evolutionary computation. By methods of ``Controlling Chaos'' it can be shown that a specific implicit iteration scheme, based on Newton's method, is the most promising solution for the problem.