Abstract
The subject of the paper is the numerical simulation of inviscid and viscous compressible flow in time dependent domains. The motion of the boundary of the domain occupied by the fluid is taken into account with the aid of the ALE (Arbitrary Lagrangian-Eulerian) formulation of the Euler and Navier-Stokes equations describing compressible flow. They are discretized in space by the discontinuous Galerkin (DG) finite element method using piecewise polynomial discontinuous approximations. For the time discretization the BDF method or DG in time is used. Moreover, we use a special treatment of boundary conditions and shock capturing, allowing the solution of flow with a wide range of Mach numbers. As a result we get an efficient and robust numerical process. We show that the method allows to solve numerically the flow with a wide range of Mach numbers and it is applicable to the solution of practically relevant problems of flow induced airfoil vibrations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bassi, F., Rebay, S.: High-order accurate discontinuous finite element solution of the 2D Euler equations. J. Comput. Phys. 138, 251–285 (1997)
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)
Bisplinghoff, R.L., Ashley, H., Halfman, R.L.: Aeroelasticity. Dover, New York (1996)
Česenek, J.: Discontinuous Galerkin method for the solution of compressible viscous flow. Charles University in Prague, Faculty of Mathematics and Physics (2011) (in Czech)
Davis, T.A., Duff, I.S.: A combined unifrontal/multifrontal method for unsymmetric sparse matrices. ACM Transactions on Mathematical Software 25, 1–19 (1999)
Dolejší, V.: Semi-implicit interior penalty discontinuous Galerkin methods for viscous compressible flows. Commun. Comput. Phys. 4, 231–274 (2008)
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)
Dowell, E.H.: A Modern Course in Aeroelasticity. Kluwer, Dodrecht (1995)
Dubcová, L., Feistauer, M., Horáček, J., Sváček, P.: Numerical simulation of interaction between turbulent flow and a vibrating airfoil. Computing and Visualization in Science 12, 207–225 (2009)
Feistauer, M.: Mathematical Methods in Fluid Dynamics. Longman, Harlow (1993)
Feistauer, M., Česenek, J., Horáček, J., Kučera, V., Prokopová, J.: DGFEM for the numerical solution of compressible flow in time dependent domains and applications to fluid-structure interaction. In: Pereira, J.C.F., Sequeira, A. (eds.) Proceedings of the 5th European Conference on Computational Fluid Dynamics ECCOMAS CFD, Lisbon, Portugal (published ellectronically) (2010) ISBN 978-989-96778-1-4
Feistauer, M., Felcman, J., Straškraba, I.: Mathematical and Computational Methods for Compressible Flow. Clarendon Press, Oxford (2003)
Feistauer, M., Horáček, J., Kučera, V., Prokopová, J.: On numerical solution of compressible flow in time-dependent domains. Mathematica Bohemica 137, 1–16 (2012)
Feistauer, M., Kučera, V.: On a robust discontinuous Galerkin technique for the solution of compressible flow. J. Comput. Phys. 224, 208–221 (2007)
Naudasher, E., Rockwell, D.: Flow-Induced Vibrations. A.A. Balkema, Rotterdam (1994)
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. Engrg. 95, 115–138 (1992)
Sváček, P., Feistauer, M., Horáček, J.: Numerical simulation of flow induced airfoil vibrations with large amplitudes. J. of Fluids and Structures 23, 391–411 (2007)
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)
Vijayasundaram, G.: Transonic flow simulation using upstream centered scheme of Godunov type in finite elements. J. Comput. Phys. 63, 416–433 (1986)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Feistauer, M., Česenek, J., Kučera, V. (2013). Discontinuous Galerkin Method – A Robust Solver for Compressible Flow. In: Ansorge, R., Bijl, H., Meister, A., Sonar, T. (eds) Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33221-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-33221-0_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33220-3
Online ISBN: 978-3-642-33221-0
eBook Packages: EngineeringEngineering (R0)