A DG HWENO scheme for hyperbolic equations
Author(s)Serrano, Matthieu, 1978-
Discontinuous Galerkin Hermite Weighted Essentially Non-Oscillatory scheme for hyperbolic equations
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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.
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.Includes bibliographical references (p. 61-62).
DepartmentMassachusetts Institute of Technology. Dept. of Aeronautics and Astronautics
Massachusetts Institute of Technology
Aeronautics and Astronautics