Entropy-stable residual distribution methods for system of euler equations
| dc.contributor.author | Hossain Chizari | |
| dc.date.accessioned | 2021-04-13T02:17:47Z | |
| dc.date.available | 2021-04-13T02:17:47Z | |
| dc.date.issued | 2016-09-01 | |
| dc.description.abstract | Residual-distribution (RD) methods have fundamental benefits over finite volume (FV) or finite difference (FD) methods particularly in mimicking multi-dimensional physics, achieving higher order accuracy with much smaller stencils and less sensitivity to grid changes. The aim of this study is to develop a multi-dimensional entropy-stable residual distribution method to solve the hyperbolic system of equations. First, an alternative residual-distribution method is proposed to ensure conservation of primary variables is obtained by default. This is followed by introducing a new signal distribution and multi-dimensional entropy-conserved and entropy-stable RD method starting with the two-dimensional Burgers’ equation. The development is extended to the two-dimensional Euler equations. There will be rigorous mathematical analyses on entropy-stability, multi-dimensional positivity, and truncation error study to determine the formal order-of-accuracy for the entropy stable methods. In addition, it will also be shown that conservation is automatic with the new RD method unlike with the current RD methods where conservation requires a strict set of characteristic-averaging within the elements and different systems of equations would require a different type of averaging. The developments of limited entropy-stable RD methods would also be included herein. Numerical experiments for the Burgers’ equation include an expansion and a shock-tree problem followed by subsonic, transonic and supersonic gas dynamics problem over various geometries for the Euler equations. Moreover, the classical residual-distribution methods such as N, LDA, and PSI methods are studied in this research to provide direct comparisons with the new entropy-stable RD methods. Results of the new RD approach are comparable to the results of classic RD and FV methods, yet are more robust for a variety of test cases. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/12764 | |
| dc.language.iso | en | en_US |
| dc.title | Entropy-stable residual distribution methods for system of euler equations | en_US |
| dc.type | Thesis | en_US |
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