太阳表面对流数值模拟方法的效率分析
Achievable Efficiency of Numerical Methods for Simulations of Solar Surface Convection
摘要：
我们调查的时间和空间的离散化方法在混合抛物-双曲问题的Anglomerate可实现的效率。我们表明，五阶变体的WENO结合二阶Runge-Kutta格式不仅比标准的一阶和二阶格式更准确，但也更有效地考虑到计算时间。然后，我们计算了WENO的误差衰减率与几个显式Runge-Kutta格式的对流和扩散问题的光滑和非光滑的初始条件。利用这些数据，我们估计了恒星表面对流三维模拟的计算成本，并表明SSP RK（3，2）是最有效的方案，在这种比较中考虑。
英文摘要：
We investigate the achievable efficiency of both the time and the space discretisation methods used in Antares for mixed parabolic-hyperbolic problems. We show that the fifth order variant of WENO combined with a second order Runge-Kutta scheme is not only more accurate than standard first and second order schemes, but also more efficient taking the computation time into account. Then, we calculate the error decay rates of WENO with several explicit Runge-Kutta schemes for advective and diffusive problems with smooth and non-smooth initial conditions. With this data, we estimate the computational costs of three-dimensional simulations of stellar surface convection and show that SSP RK(3,2) is the most efficient scheme considered in this comparison.
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