A DG HWENO scheme for hyperbolic equations

In an effort to build a higher order discontinuous Galerkin (DG) finite element solver for the nonlinear Euler equations of gas dynamics, we develop a shock capturing scheme for hyperbolic equations. The Hermite Weighted Essentially Non-Oscillatory (HWENO) methodology introduced by Qiu [10, 14] is used as the starting point for the proposed limiter. We present a general approach for building a limiter for Runge-Kutta time marching schemes which reconstructs the higher order moments of troubled cells using only information of neighboring cells. This technique is used to develop a limiter in 1-D for P₂ to P₅ interpolants on non-uniform grids and in 2-D for P₂ interpolants on triangular unstructured grids. Numerical results for this limiter are presented for Burgers equation.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2004

Author dc:creator

• Serrano, Matthieu, 1978-

Advisor dc:contributor.advisor

• Jamie Peraire.

• Aeronautics and Astronautics

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/17819

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/17819