Date of Award
12-2003
Degree Type
Thesis
Degree Name
M.S.
Degree Program
Engineering
Department
Mechanical Engineering
Major Professor
Guillot, Martin
Second Advisor
Hall, Carsie
Third Advisor
Akyuzlu, Kazim
Fourth Advisor
Herrington, Paul
Abstract
The main objective of this research work is to apply the discontinuous Galerkin method to a classical partial differential equation to investigate the properties of the numerical solution and compare the numerical solution to the analytical solution by using discontinuous Galerkin method. This scheme is applied to 1-D non-linear conservation equation (Burgers equation) in which the governing differential equation is simplified model of the inviscid Navier-stokes equations. In this work three cases are studied. They are sinusoidal wave profile, initial shock discontinuity and initial linear distribution. A grid and time step refinement is performed. Riemann fluxes at each element interfaces are calculated. This scheme is applied to forward differentiation method (Euler's method) and to second order Runge-kutta method of this work.
Recommended Citation
Voonna, Kiran, "Development of Discontinuous Galerkin Method for 1-D Inviscid Burgers Equation" (2003). University of New Orleans Theses and Dissertations. 58.
https://scholarworks.uno.edu/td/58
Rights
The University of New Orleans and its agents retain the non-exclusive license to archive and make accessible this dissertation or thesis in whole or in part in all forms of media, now or hereafter known. The author retains all other ownership rights to the copyright of the thesis or dissertation.