Numerical Simulation of the Linear Advection of Cosine Bell on the Cube Sphere

徐亚博; 常建忠; 王剑; 周运宁

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Numerical Simulation of the Linear Advection of Cosine Bell on the Cube Sphere

更新时间：2026-09-14

- Numerical Simulation of the Linear Advection of Cosine Bell on the Cube Sphere
- 立方球体坐标下余弦钟绕球平流的数值模拟
- Issue 5, (2005)
- 作者机构：
  
  1. 中北大学环境与安全工程系
  2. 山西省农业科学院,山西,太原,030051
  3. ,山西,太原,030051
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2005
- 稿件说明：
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徐亚博, 常建忠, 王剑, et al. Numerical Simulation of the Linear Advection of Cosine Bell on the Cube Sphere[J]. 2005, (5).
DOI：

徐亚博, 常建忠, 王剑, et al. Numerical Simulation of the Linear Advection of Cosine Bell on the Cube Sphere[J]. 2005, (5). DOI：

摘要

在立方球体坐标系下推导出浅水波方程的形式

使用M DQ方法和4阶R ung-K u tta方法求解该方程

计算了余弦钟绕球平流算例的三种情况

并且给出了该算例在立方球体坐标系下6个区间的速度矢量的表达式.为了解决由于边界插值所引起的数值不稳定性

引入了4阶的人工粘性项(-4).通过对测试方案的求解和分析

可以看出该方法的优点:①完全显式格式;②时间上的4阶精度;③仅仅通过改变一个参数就可以获得空间的高阶精度;④该数值方案有较强的适用性.

Abstract

The formulations of the shallow water equations are deduced from the cube sphere coordinate in the paper.Using the modified differential quadrature(MDQ) special difference scheme and fourth order Runge-Kutta scheme to solve the shallow water equations

the vector velocity expressions of six regions in the linear advection of a cosine bell case are given from the cube sphere coordinate.The paper computes the three cases of the linear advection of a cosine bell.An explicit hyperdiffusion term (-

) was used to free the numerical solutions from the noise introduced at the internal boundaries by the interpolation procedure.The method features the following advantages: ① fully explicit;② fourth order of accuracy in time;③ high order of accuracy in space by changing only one parameter;④ robust in proceeding numerical problem.

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references

R onch i C,Iacono R,Pao lucc i P S.A new m ethod for the so lu tion of partia l d ifferen tia l equations in spherica l geom e-try[J].J.Com pu t.Phys.,1996(124):93-114.

W illiam son D L,D rake J B,H ack J J,Jakob R,Sw arztauber P N.A standard test set for num erica l approx im ationsto the sha llow w ater equations in spherica l geom etry[J].J.Com pu t.Phys.,1992(102):211-224.

Jakob ch ien R,H ack J J,W illam son D L.Spetra l transform so lu tion to the sha llow w ater test set[J].J.Com pu t.Phys,1995(119):164-187.

H idetosh i N ish ida,N obuyuk i Satofuka.H igher-order so lu tions of square driven cav ity flow us ing a variab le-orderm u lti-grid m ethod[J].In ternationa l Journa l for N um erica lM ethods in Eng ineering,1992(34):637-653.

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