2026-09-19T09:26:01Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/178192022-01-13T07:54:10Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Jamie Peraire.
Serrano, Matthieu, 1978-
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
2005-06-02T18:47:54Z
2005-06-02T18:47:54Z
2004
2004
http://hdl.handle.net/1721.1/17819
56558587
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.
62 p.
2356472 bytes
2361137 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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.
http://dspace.mit.edu/handle/1721.1/7582
Aeronautics and Astronautics
A DG HWENO scheme for hyperbolic equations
Discontinuous Galerkin Hermite Weighted Essentially Non-Oscillatory scheme for hyperbolic equations
Thesis
application/pdf
false
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="4968311c-c40a-485f-beae-5d653e63d50a">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Language>eng</Language>
<Title>A DG HWENO scheme for hyperbolic equations</Title>
<Subtitle>Discontinuous Galerkin Hermite Weighted Essentially Non-Oscillatory scheme for hyperbolic equations</Subtitle>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2004</PublicationDate>
<Authors>
<Author>
<DisplayName>Serrano, Matthieu, 1978-</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://dspace.mit.edu/handle/1721.1/7582</License>
<Keyword>Aeronautics and Astronautics</Keyword>
<Abstract>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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>