A study into discontinuous Galerkin methods for the second order wave equation
Davis, Benjamin J.
Kozdon, Jeremy E.
Wilcox, Lucas C.
MetadataShow full item record
There are numerous numerical methods for solving different types of partial differential equations (PDEs) that describe the physical dynamics of the world. For instance, PDEs are used to understand fluid flow for aerodynamics, wave dynamics for seismic exploration, and orbital mechanics. The goal of these numerical methods is to approximate the solution to a continuous PDE with an accurate discrete representation. The focus of this thesis is to explore a new Discontinuous Galerkin (DG) method for approximating the second order wave equation in complex geometries with curved elements. We begin by briefly highlighting some of the numerical methods used to solve PDEs and discuss the necessary concepts to understand DG methods. These concepts are used to develop a one- and two-dimensional DG method with an upwind flux, boundary conditions, and curved elements. We demonstrate convergence numerically and prove discrete stability of the method through an energy analysis.
Approved for public release; distribution is unlimited
Showing items related by title, author, creator and subject.
Kelly, J.F.; Giraldo, Francis X.; Constantinescu, E.M. (2013);We derive an implicit-explicit (IMEX) formalism for the three-dimensional Euler equations that allow a unified representation of various nonhydrostatic flow regimes, including cloud-resolving and mesoscale (flow in a 3D ...
Arnason, G.; Haltiner, G.J.; Frawley, M.J. (1962-05);Two iterative methods are described for obtaining horizontal winds from the pressure-height field by means of higher-order geostrophic approximations for the purpose of improving upon the geostrophic wind. The convergence ...
Exponential leap-forward gradient scheme for determining the isothermal layer depth from profile data Chu, P.C.; Fan, C.W. (Springer, 2017);Two distinct layers usually exist in the upper ocean. The rst has a near-zero vertical gradient in temperature (or density) from the surface and is called the iso-thermal layer (or mixed layer). Beneath that is a layer ...