A DG HWENO scheme for hyperbolic equations
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 deve...
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| Language: | English |
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Massachusetts Institute of Technology
2005
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| Online Access: | http://hdl.handle.net/1721.1/17819 |
| Summary: | 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. |
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