数值计算方法在海洋模型中的开发和运用

New numerical schemes/methods are difficulty to apply in ocean models due to the complexity of parallel code and demands for practical usage. During long time of study on ocean models, however, we have had many experiences and several accomplishments on numerical methods and their applications in models with bench mark test. We have developed several methods, like the Alternative Leapfrog Scheme, and Split Time Stepping. We also applied them in models, like our model TOM, and also famous model POM. We also have developed an open boundary method, which keeps the conservation of mass, salinity and heat, and succeeded in its application in the SCS. Furthermore, we discovered a new explicit scheme, which has no limitation of CFL on time step, though it was only found to be available for the Coriolis term. .We will focus on the further application of our schemes in models, specifically, the application of the Alternative Leapfrog Scheme, and Split Time Stepping in LICOM, and a parallel coding version of POM. Then we will use our Conserved Open Boundary method in those models on the SCS’s regional model. Furthermore, we will continue our study of the new scheme and its development in the advection term.

由于并行编程及实用要求带来的苛刻，海洋模型中新格式/方法的开发和运用并非容易。但我们在海洋模型和数值方法研究上有长期积累并取得了一些进展：如交替蛙跳格式和正斜压分裂积分方案。这些新方法已经在海洋模型，如自主开发的TOM和著名的POM标量版中有应用并经过bench mark检验。我们还开发了具有质、盐和热量守恒/收支平衡的新的开边界方法，并在南海的TOM中有应用。此外，针对科氏项，有了理论突破性的进展，发现一类不受CFL条件限制的显式格式。本项目将展开上述新积分方案在LICOM和POM并行版的运用，改善LICOM的数值稳定性和积分效率，并探讨这些方法在其它海洋模型如ROMS运用的可能性；在南海，展开守恒性开边界在LICOM和POM的运用。此外，我们将继续展开新显式格式在科氏项以外（如平流项）的开发研究，并拓广该格式，如与浅水重力波或平流项的联合应用。