Adaptive Wavelet Collocation Method on the Shallow Water Model

This paper presents an integrated approach for modeling several ocean test problems on adaptive grids using novel boundary techniques. The adaptive wavelet collocation method solves the governing equations on temporally and spatially varying meshes, which allows higher effective resolution to be obtained with less computational cost. It is a general method for the solving a large class of partial differential equations, but is applied to the shallow water equations here. In addition to developing wavelet-based computational models, this work also uses an extension of the Brinkman penalization method to represent irregular and non-uniform continental boundaries. This technique is used to enforce no slip boundary conditions through the addition of a term to the field equations. When coupled with the adaptive wavelet collocation method, the flow near the boundary can be well resolved. It is especially useful for simulations of boundary currents and tsunamis, where flow and the boundary is important, thus, those are the test cases presented here