Download or read book Hp Discontinuous Galerkin (DG) Methods for Coastal Ocean Circulation and Transport written by Colton J. Conroy and published by . This book was released on 2014 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we present the development and implementation of a high-order, discontinuous Galerkin (DG), three-dimensional coastal ocean circulation and transport model. The model solves the three-dimensional shallow water equations (SWE) using a DG spatial discretization coupled with explicit Runge-Kutta (RK) time stepping. All the primary variables, including the free surface elevation, are discretized via discontinuous polynomial spaces of arbitrary order. The difficulty of mismatched lateral boundaries that accompanies a discontinuous free surface is overcome through the use of a novel, well-balanced, sigma coordinate system in the vertical, which transforms the bottom boundary and free surface into coordinate surfaces. Novel techniques incorporated by the new model include: a high-order coupling method that evaluates the discrete depth-integrated velocity exactly, the use of a compact convolution kernel made-up of B-splines that filters out errors in the DG discretization and enhances the accuracy and convergence properties of the numerical solution, as well as a so-called modified basis method, which calculates the vertical velocity and the baroclinic pressure force in a high order fashion. Model verification is presented for a number of three-dimensional analytic test cases including flow and transport problems, displaying up to fourth-order convergence for smooth solutions.