Wavelet Analysis and Ocean Modeling: A Dynamically Adaptive Numerical Method “WOFD-AHO”

Abstract

Wavelet analysis provides information on the energy present at various scales and locations throughout a computational domain. This information is precisely the information that is needed to define the appropriate gridpoint densities and the appropriate numerical order to resolve the physics at hand in the computationally most efficient manner. Here a two-dimensional version of the numerical method known as the Wavelet Optimized Finite Difference Method (WOFD) is introduced to a model problem in oceanography. WOFD is a completely dynamically adaptive numerical method that has the ability to focus on small-scale physics throughout the computational domain as the scale of the physics gets smaller and as structures are transported across the domain. In this manner, WOFD applies the computational effort where it is needed without overcomputing in the regions of the domain where the physics is somewhat smooth and perhaps more linear. The version of WOFD used here is such that both the spatial and temporal orders will be fixed at four. In the areas of oceanography and climate modeling, order four can be considered high order and therefore this two-dimensional version will be called the Adaptive High Order (AHO) version of WOFD, or simply WOFD-AHO.