A Study into Discontinuous Galerkin Methods for the Second Order Wave Equation

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 2015
Accession Number
ADA632321

Entities

People

  • Benjamin J. Davis

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Acoustic Waves
  • Applied Mathematics
  • Birds
  • Boundaries
  • Differential Equations
  • Dynamics
  • Equations
  • Finite Element Analysis
  • Galerkin Method
  • Geometry
  • Mathematics
  • Numerical Analysis
  • Numerical Integration
  • Partial Differential Equations
  • Two Dimensional
  • Variational Equations
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design

Technology Areas

  • Space