Multirate infinitesimal step methods for atmospheric flow simulation
Multirate infinitesimal step methods for atmospheric flow simulation
复制标题
大气流动模拟的多速率无穷小步法
DOI：
10.1007/s10543-009-0222-3
复制
发表时间：
2009
影响因子：
1.5
通讯作者：
Alexander Galant
中科院分区：
文献类型：
--
作者：
J. Wensch;O. Knoth;Alexander Galant
欧拉方程的数值解需要处理不同时间尺度的过程。声波传播速度比平流过程快。基于交错网格的空间离散，本文提出了一种多速率时间积分方法，推广了分裂显式龙格-库塔方法。平流项采用龙格-库塔法积分，宏步长由CFL数限制。声波条款处理的小时间步长尊重CFL的限制所规定的声速。分裂显式龙格-库塔方法一般包括固定的趋势，以前的阶段。将声学方程的稳定性障碍放宽了一倍，给出了低马赫数情况下的渐近阶条件。讨论了与无扰子指数积分器的关系。分析了线性声波方程的稳定性。对线性声学和非线性欧拉方程进行了数值试验。
The numerical solution of the Euler equations requires the treatment of processes in different temporal scales. Sound waves propagate fast compared to advective processes. Based on a spatial discretisation on staggered grids, a multirate time integration procedure is presented here generalising split-explicit Runge-Kutta methods. The advective terms are integrated by a Runge-Kutta method with a macro stepsize restricted by the CFL number. Sound wave terms are treated by small time steps respecting the CFL restriction dictated by the speed of sound.Split-explicit Runge-Kutta methods are generalised by the inclusion of fixed tendencies of previous stages. The stability barrier for the acoustics equation is relaxed by a factor of two.Asymptotic order conditions for the low Mach case are given. The relation to commutator-free exponential integrators is discussed. Stability is analysed for the linear acoustic equation. Numerical tests are executed for the linear acoustics and the nonlinear Euler equations.