Abstract
Compressible Euler equations describing the motion of compressible inviscid fluids are typically solved by means of low-order finite volume (FVM) or finite element (FEM) methods. A promising recent alternative to these low-order methods is the higher-order discontinuous Galerkin (\(hp\)-DG) method (Schnepp and Weiland, J Comput Appl Math 236:4909–4924, 2012; Schnepp and Weiland, Radio Science, vol 46, RS0E03, 2011) that combines the stability of FVM with excellent approximation properties of higher-order FEM. This paper presents a novel \(hp\)-adaptive algorithm for the \(hp\)-DG method which is based on meshes that change dynamically in time. The algorithm reduces the order of the approximation on shocks and keeps higher-order elements where the approximation is smooth, which leads to an efficient discretization of the time-dependent problem. The method is described and numerical examples are presented.
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Acknowledgments
This research was supported by the following sources: 1. The European Regional Development Fund and the Ministry of Education, Youth and Sports of the Czech Republic under the Regional Innovation Centre for Electrical Engineering (RICE), project No. CZ.1.05/2.1.00/03.0094 2. Grant No. P105/10/1682 of the Grant Agency of the Czech Republic 3. Subcontract No. 00089911 of Battelle Energy Alliance (U.S. Department of Energy intermediary) 4. SGS (Studentska Grantova Soutez) grant number SGS-2012-039
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Korous, L., Solin, P. An adaptive \(hp\)-DG method with dynamically-changing meshes for non-stationary compressible Euler equations. Computing 95 (Suppl 1), 425–444 (2013). https://doi.org/10.1007/s00607-012-0257-1
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DOI: https://doi.org/10.1007/s00607-012-0257-1
Keywords
- Numerical simulation
- Finite element method
- Euler equations
- \(hp\)-adaptivity
- Discontinuous Galerkin method
- Automatic adaptivity
- Dynamically changing meshes