【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.更多还原

【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 (-~4) 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.更多还原