Numerical solution of multiscale problems in atmospheric modeling
Numerical solution of multiscale problems in atmospheric modeling
复制标题
大气模拟中多尺度问题的数值求解
DOI：
10.1016/j.apnum.2012.06.023
复制
发表时间：
2012
影响因子：
2.8
通讯作者：
R. Wolke
中科院分区：
文献类型：
--
作者：
M. Schlegel;O. Knoth;M. Arnold;R. Wolke
显式时间积分方法的特点是每个时间步的数值工作量较小。在大气建模中的多尺度问题的应用中，这种好处通常可以通过稳定性问题和步长限制来补偿，这些问题和步长限制是由刚性化学反应项和平流项的局部变化的库朗-弗里德里希-路易 (CFL) 条件引起的。在本文中，我们通过一种可以递归应用的相当通用的分裂技术来解决这个问题。该技术允许隐式和显式方法（IMEX 分裂）的组合，以及在平流项的显式多速率离散化中时间步长局部适应非均匀空间网格的网格宽度。使用形式表示作为分区龙格-库塔方法，如果满足一些附加阶次条件，则可以显示阶数 p⩽3 的收敛。在一系列数值测试中，验证了收敛结果，并分析了不同分裂策略（如通量分裂和细胞分裂）的后果。
Explicit time integration methods are characterized by a small numerical effort per time step. In the application to multiscale problems in atmospheric modeling, this benefit is often more than compensated by stability problems and stepsize restrictions resulting from stiff chemical reaction terms and from a locally varying Courant–Friedrichs–Lewy (CFL) condition for the advection terms. In the present paper, we address this problem by a rather general splitting technique that may be applied recursively. This technique allows the combination of implicit and explicit methods (IMEX splitting) as well as the local adaptation of the time stepsize to the meshwidth of non-uniform space grids in an explicit multirate discretization of the advection terms. Using a formal representation as partitioned Runge–Kutta method, convergence of order p⩽3 may be shown if some additional order conditions are satisfied. In a series of numerical tests, the convergence results are verified and the consequences of different splitting strategies like flux splitting and cell splitting are analysed.