Runge-Kutta IMEX schemes for the Horizontally Explicit/Vertically Implicit (HEVI) solution of wave equations
Runge-Kutta IMEX schemes for the Horizontally Explicit/Vertically Implicit (HEVI) solution of wave equations
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用于波动方程的水平显式/垂直隐式 (HEVI) 解的 Runge-Kutta IMEX 方案
DOI：
10.1016/j.jcp.2013.06.025
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发表时间：
2013
影响因子：
4.1
通讯作者：
Weller H
中科院分区：
文献类型：
--
作者：
Weller H
许多业务天气预报中心使用半隐式时间步进方案，因为它们的效率很高。然而，随着计算机变得越来越并行，大气运动方程的水平显式解可能成为一种有吸引力的替代方案，因为隐式方法的处理器间通信增加了。长期以来，隐式和显式(IMEX)时间步进格式在大气模型中使用半隐式、分裂-显式或HEVI分裂相结合。然而，对IMEX格式的精度和稳定性的研究大多局限于平流扩散方程的抛物型情形。我们演示了一些Runge-Kutta IMEX格式如何用于求解双曲型波动方程，无论是半隐式还是HEVI。提出了一种新的HEVI分裂形式UfPreb，大大提高了层流中重力波模拟的精度和稳定性。结果表明，与半隐式格式相比，HEVI格式具有更好的精度，得到了梯形隐式IMEX格式和某些Runge-Kutta IMEX格式的稳定性极限，并用可压缩的Boussinesq方程组合隐式和显式两种形式对这两种格式进行了测试。一些龙格-库塔格式被发现比梯形格式更有利，特别是因为它们在不降低到一阶精度的情况下抑制了高频。我们测试了对于严格系统但在严格限制(几乎不可压缩)中不是形式上准确的方案，并发现它们可以很好地执行。ARK2(2，3，2)方案在测试中表现最好。
Many operational weather forecasting centres use semi-implicit time-stepping schemes because of their good efficiency. However, as computers become ever more parallel, horizontally explicit solutions of the equations of atmospheric motion might become an attractive alternative due to the additional inter-processor communication of implicit methods. Implicit and explicit (IMEX) time-stepping schemes have long been combined in models of the atmosphere using semi-implicit, split-explicit or HEVI splitting. However, most studies of the accuracy and stability of IMEX schemes have been limited to the parabolic case of advection–diffusion equations. We demonstrate how a number of Runge–Kutta IMEX schemes can be used to solve hyperbolic wave equations either semi-implicitly or HEVI. A new form of HEVI splitting is proposed, UfPreb, which dramatically improves accuracy and stability of simulations of gravity waves in stratified flow. As a consequence it is found that there are HEVI schemes that do not lose accuracy in comparison to semi-implicit ones.The stability limits of a number of variations of trapezoidal implicit and some Runge–Kutta IMEX schemes are found and the schemes are tested on two vertical slice cases using the compressible Boussinesq equations split into various combinations of implicit and explicit terms. Some of the Runge–Kutta schemes are found to be beneficial over trapezoidal, especially since they damp high frequencies without dropping to first-order accuracy. We test schemes that are not formally accurate for stiff systems but in stiff limits (nearly incompressible) and find that they can perform well. The scheme ARK2(2,3,2) performs the best in the tests.
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影响因子：
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作者：
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通讯作者：
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