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Discontinuous Galerkin Finite Element Method for Inviscid Compressible Flows
| Content Provider | Semantic Scholar |
|---|---|
| Author | Stoia-Djeska, Marius |
| Copyright Year | 2004 |
| Abstract | This paper presents the development of an algorithm based on the discontinuous Galerkin finite element method (DGFEM) for the Euler equations of gas dynamics. The DGFEM is a mixture of a finite volume and finite element method. In the DGFEM the unknowns in each element are locally expanded in a polynomial series and thus the information about the flow state at the element faces can be directly obtained. The use of separate equations for the flow gradients in the DGFEM eliminates the classical reconstruction that is usually necessary in the finite volume method (FVM) to determine the flow gradients from data in neighboring elements. Another significant benefit of the cell based DGFEM in comparison with node based finite element methods is that the mass matrix of each element is uncoupled from other elements and it is not necessary to invert a large mass matrix for the complete finite element system. In our paper the DGFEM is first used to discretize the Euler equations of gas dynamics in an Arbitrary Lagrangian-Eulerian formulation. The method is combined with a four-stage Runge–Kutta time-stepping scheme for the advancement in time of the solution. The numerical fluxes between the elements are calculated with an improved variant of Roe’s fluxdifference scheme. Numerical results for steady and unsteady internal and external flows illustrate the possibilities of the method. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://mmut.mec.upt.ro/mh/Conferinta_MH/817_Stoia.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
