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Discontinuous Galerkin solution of compressible flow in time-dependent domains. (English) Zbl 1425.76212
Summary: This work is concerned with the simulation of inviscid compressible flow in time-dependent domains. We present an arbitrary Lagrangian-Eulerian (ALE) formulation of the Euler equations describing compressible flow, discretize them in space by the discontinuous Galerkin method and introduce a semi-implicit linearized time stepping for the numerical solution of the complete problem. Special attention is paid to the treatment of boundary conditions and the limiting procedure avoiding the Gibbs phenomenon in the vicinity of discontinuities. The presented computational results show the applicability of the developed method.

MSC:
76N15 Gas dynamics (general theory)
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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[1] Bassi, F.; Rebay, S., High-order accurate discontinuous finite element solution of the 2D Euler equations, J. comput. phys., 138, 251-285, (1997) · Zbl 0902.76056
[2] Baumann, C.E.; Oden, J.T., A discontinuous hp finite element method for the Euler and navier – stokes equations, Int. J. numer. methods fluids, 31, 79-95, (1999) · Zbl 0985.76048
[3] ()
[4] Davis, T.A.; Duff, I.S., A combined unifrontal/multifrontal method for unsymmetric sparse matrices, ACM trans. math. softw., 25, 1-19, (1999) · Zbl 0962.65027
[5] Dolejší, V., Anisotropic mesh adaptation for finite volume and finite element methods on triangular meshes, Comput. vis. sci., 1, 3, 165-178, (1998) · Zbl 0917.68214
[6] Dolejší, V.; Feistauer, M., A semi-implicit discontinuous Galerkin finite element method for the numerical solution of inviscid compressible flow, J. comput. phys., 198, 727-746, (2004) · Zbl 1116.76386
[7] Dolejší, V.; Feistauer, M.; Schwab, C., On some aspects of the discontinuous Galerkin finite element method for conservation laws, Math. comput. simul., 61, 333-346, (2003) · Zbl 1013.65108
[8] Feistauer, M.; Dolejší, V.; Kučera, V., On the discontinuous Galerkin method for the simulation of compressible flow with wide range of Mach numbers, Comput. vis. sci., 10, 17-27, (2007)
[9] Feistauer, M.; Felcman, J.; Straškaraba, I., Mathematical and computational methods for compressible flow, (2003), Clarendon Press Oxford
[10] Feistauer, M.; Kučera, V., On a robust discontinuous Galerkin technique for the solution of compressible flow, J. comput. phys., 224, 208-221, (2007) · Zbl 1114.76042
[11] Krivodonova, L.; Berger, M., High-order accurate implementation of solid wall boundary conditions in curved geometries, J. comput. phys., 211, 492-512, (2006) · Zbl 1138.76403
[12] Nomura, T.; Hughes, T.J.R., An arbitrary lagrangian – eulerian finite element method for interaction of fluid and a rigid body, Comput. methods appl. mech. eng., 95, 115-138, (1992) · Zbl 0756.76047
[13] Sváček, P.; Feistauer, M.; Horáček, J., Numerical simulation of flow induced airfoil vibrations with large amplitudes, J. fluids struct., 23, 391-411, (2007)
[14] van der Vegt, J.J.W.; van der Ven, H., Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flow, J. comput. phys., 182, 546-585, (2002) · Zbl 1057.76553
[15] Vijayasundaram, G., Transonic flow simulation using upstream centered scheme of Godunov type in finite elements, J. comput. phys., 63, 416-433, (1986) · Zbl 0592.76081
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