A DG HWENO scheme for hyperbolic equations

• Main Author: Serrano, Matthieu, 1978-
• Other Authors: Jamie Peraire.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2005
• Subjects: Aeronautics and Astronautics
• Online Access: http://hdl.handle.net/1721.1/17819

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004. === Includes bibliographical references (p. 61-62). === 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. === by Matthieu Serrano. === S.M.