A semi-implicit discontinuous Galerkin finite element method for the numerical solution of inviscid compressible flow. (English) Zbl 1116.76386
Summary: The paper is concerned with the numerical solution of an inviscid compressible flow with the aid of the discontinuous Galerkin finite element method. Since the explicit time discretization requires a high restriction of the time step, we propose semi-implicit numerical schemes based on the homogeneity of inviscid fluxes, allowing a simple linearization of the Euler equations which leads to a linear algebraic system on each time level. Numerical experiments performed for the Ringleb flow problem verify a higher order of accuracy of the presented method and demonstrate lower CPU-time costs in comparison with an explicit method. Then the method is tested on more complex unsteady Euler flows.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
Software:
HE-E1GODFReferences:
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