Implementation of new time integration methods in POM

摘要

Instead of the standard leapfrog (SLF) scheme, an alternative leapfrog (ALF) scheme is used to solve the barotropic equations of the external mode in the Princeton Ocean Model (POM). The ALF scheme is modified in this study to deal with the nonlinear finite amplitude surface displacement. ALF has the advantage of improved numerical properties, longer time step relative to SLF, conservation of energy, and elimination of the Asselin filter. The numerical experiments of POM are implemented to show the above advantages. The split time stepping in 3D POM is found in this study to have numerical discrepancy due to the mismatched stepping between external and internal modes, and it results in a splitting error between the external and internal modes. A new split time stepping is therefore proposed. Numerical analysis indicates that there is no discrepancy with this split time stepping. The new split time stepping is implemented in the 3D POM. The numerical experiments demonstrate that the splitting error in POM can be reduced by three orders of magnitude relative to the original formulation, though the numerical error of the original formulation is already quite small.