交替蛙跳格式在POM的应用

Application of alternative leapfrog scheme in POM

讨论交替蛙跳格式在二维POM的运用。这个交替蛙跳格式是在z坐标下开发的针对线性浅水波方程的一种新的高效无耗散的格式。首先通过一维问题的试验,给出了σ坐标下非线性浅水波的演化特性及其交替蛙跳格式的数值特性,证实该格式的可行性以及优于传统格式的计算效率、守恒性及稳定性。其次,针对该格式二维问题运用讨论了科氏项相应的数值处理,给出了一套完整的数值计算方法,并应用于正压方程和POM外模的数值计算。研究表明,交替蛙跳格式具有两倍于传统蛙跳格式的计算效率,且不再需要Assenlin时间滤波,由此避开了时间滤波带来的数值衰减,具有良好的数值守恒性能。

The alternative leapfrog scheme is an efficient and non-dissipative scheme developed for liner shallow water equa- tions in z-coordinate. In this study, the scheme is used for non-liner equations in a-coordinate. The application to two-dimensional barotropic equations in the Princeton Ocean Model （POM） is numerically investigated. First, the numerical results of one-dimensional wave are given, and the development of non-linear wave is described in details to show its non-linear character. The results also show that the alternative leapfrog scheme has the advantage of its numerically conserved property and computational stability, which are better than those using the conventional leapfrog scheme. Second, the Coriolis term is numerically dealt with in the two-dimensional barotropic equations in order to match the alternative leapfrog scheme, and the numerical results are investigated in terms of the external mode of POM. The results show that with the alternative leapfrog scheme, the external mode of POM has numerical advantages of high computational efficiency twice as much as the original scheme, simplicity without Assenlin filter, and higher numerical conservation than that in POM due to Assenlin filter＇s damping