一种基于成对显式龙格-库塔时间积分的大气平流算法  

An Advection Scheme using Paired Explicit Runge-Kutta Time Integration for Atmospheric Modeling

作　　者：孙朝阳 陈春刚 李兴良[2] 沈学顺[2] SUN Zhaoyang;CHEN Chungang;LI Xingliang;SHEN Xueshun(Department of Mechanics,Xi’an Jiaotong University,Xi’an 710049,Shaanxi,China;Center for Earth System Modelling and Predication,China Meteorological Administration,Beijing 100081,China)

机构地区：[1]西安交通大学力学系,陕西西安710049 [2]中国气象局地球系统数值预报中心,北京100081

出　　处：《高原气象》2024年第2期520-528,共9页Plateau Meteorology

基　　金：国家重点研发计划项目(2017YFC1501901)。

摘　　要：为解决大气输送仿真中保形、正定及计算效率等问题,本研究发展了基于水平-多矩有限体积/垂直-有限差分混合格式和显式成对龙格-库塔方法的高效、高保真平流方程时空离散方案。为去除高阶算法在间断分布附近产生的数值振荡,平流方案在水平和垂直方向分别使用了基于加权本质无振荡(weighted essentially non-oscillatory,WENO)和总变差减小(total variation diminishing,TVD)方法的斜率限制器。在时间积分中,算法使用了二阶成对显式龙格-库塔方法,通过在垂直方向增加内循环中空间离散调用次数增大求解器可用CFL数。成对龙格-库塔时间积分方法能有效缓解大气模式垂直小网格距对积分时间步长的限制,使水平、垂直方向稳定性条件允许的最大时间步长尽可能接近,从而改善模式计算效率。论文中还设计了可用于库朗(Courant-Friedrichs-Lewy,CFL)数大于1情形的迭代正定修正算法,能保证平流方程计算结果严格非负。本文采用二维标准算例对所提出的平流方程算法进行了测试和比较分析。数值试验结果表明:本文提出的算法为解决高分辨、可扩展非静力大气模式中平流输送高保真计算难题提供了一条有效途径。In this paper,a new numerical scheme was proposed to solve the advection equation in a multi-moment nonhydrostatic dynamical core.To guarantee the shape-preserving property,the limiting operations are devised for a hybrid discretization framework adopted by the multi-moment dynamical core,consisting of the multi-moment finite-volume and the conservative finite-difference schemes for the horizontal and vertical discretizations respectively.In the horizontal direction,a nonoscillaory scheme is accomplished by adjusting the slope of the multi-moment reconstruction polynomial at the cell center with the application of a WENO(weighted essentially non-oscillatory)algorithm.The resulting multi-moment scheme can achieve the fourth-order accuracy in the convergence test.In the vertical direction,a TVD(total variation diminishing)slope limiter is applied in the finite-difference discretization to remove the non-physical oscillations around the discontinuities.To accomplish the time marching in the proposed advection model,a second-order paired explicit Runge-Kutta scheme is adopted,which is expected to be an efficient and practical method for the advection solvers in the atmospheric models with very high spatial resolutions.The explicit time marching,without the dimension splitting,is useful to avoid the divergence errors in the advection transport calculations.Two Runge-Kutta schemes,requiring different times of conducting the spatial discretization within a time step,are combined,and used for the time marching in the different directions.The finite-difference discretization is called for six times within a time step in order to increase the maximum available CFL(Courant-Friedrichs-Lewy)number in the vertical direction,while the horizontal multi-moment spatial discretization is conducted for two times as the regular second-order schemes.As a result,the difference between the maximum time steps determined by the horizontal and vertical discretizations,due to the very large aspect ratio of the computational cells in atmosph

关 键 词：平流方程 成对显式龙格-库塔方法 斜率限制器 正定算法 多矩方法 

分 类 号：P456.7[天文地球—大气科学及气象学]