Hybridisable discontinuous Galerkin formulation of compressible flows

Author (s): Vila-Pérez, J.; Giacomini, M.; Sevilla, R. and Huerta, A.
Journal: Archives of Computational Methods in Engineering

Volume: 28, Issue 2
Pages: 753 – 784
Date: 2021

Abstract:
This work presents a review of high-order hybridisable discontinuous Galerkin (HDG) methods in the context of compressible flows. Moreover, an original unified framework for the derivation of Riemann solvers in hybridised formulations is proposed. This framework includes, for the first time in an HDG context, the HLL and HLLEM Riemann solvers as well as the traditional Lax-Friedrichs and Roe solvers. HLL-type Riemann solvers demonstrate their superiority with respect to Roe in supersonic cases due to their positivity preserving properties. In addition, HLLEM specifically outstands in the approximation of boundary layers because of its shear preservation, which confers it an increased accuracy with respect to HLL and Lax-Friedrichs. A comprehensive set of relevant numerical benchmarks of viscous and inviscid compressible flows is presented. The test cases are used to evaluate the competitiveness of the resulting high-order HDG scheme with the aforementioned Riemann solvers and equipped with a shock treatment technique based on artificial viscosity.

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Bibtex:

@article{JVP-VGSH-21,
        author = {Jordi Vila-P\'{e}rez and Matteo Giacomini 
		  and Ruben Sevilla and Antonio Huerta},
        title = {Hybridisable discontinuous {G}alerkin formulation 
		 of compressible flows},
        fjournal = {Archives of Computational Methods in Engineering},
        journal = {Arch. Comput. Methods Eng.},
        volume = {28},
	number = {2},
        pages = {753--784},
        year = {2021},
	doi = {10.1007/s11831-020-09508-z}
}