Abstract
Discontinuous Galerkin (DG) methods are a very powerful numerical techniques, that offer high degree of robustness, accuracy and flexibility, nowadays necessary for the solution of complex fluid flows. The drawback is the relatively high computational cost and storage requirement. This work will focus on two approaches which can be adopted to enhance the computational efficiency of this class of methods: (i) a DG discretization based upon co-located tensor product basis functions, and (ii) a p-multigrid solution strategy. The effectiveness of the proposed approaches has been demonstrated by computing 3D inviscid and turbulent test cases.
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References
Arnold, D.N., Brezzi, F., Cockburn, B., Marini, D.: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39(5), 1749–1779 (2002)
Bassi, F., Crivellini, A., Rebay, S., Savini, M.: Discontinuous Galerkin solution of the Reynolds averaged Navier-Stokes and k − ω turbulence model equations. Computers & Fluids 34, 507–540 (2005)
Bassi, F., Franchina, N., Ghidoni, A., Rebay, S.: Spectral discontinuous Galerkin solution of the Navier-Stokes equations. Int. J. Numer. Meth. Fluids (2009) (submitted)
Bassi, F., Franchina, N., Ghidoni, A., Rebay, S.: Spectral p-multigrid discontinuous Galerkin solution of the Navier-Stokes equations. Int. J. Numer. Meth. Fluids (2009) (submitted)
Bassi, F., Ghidoni, A., Rebay, S., Tesini, P.: High-order accurate p-multigrid discontinuous Galerkin solution of the Euler equations. Int. J. Numer. Meth. Fluids 60(8), 847–865 (2009)
Bassi, F., Rebay, S.: A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier–Stokes equations. J. Comput. Phys. 131, 267–279 (1997)
Bassi, F., Rebay, S.: High-order accurate discontinuous finite element solution of the 2D Euler equations. J. Comput. Phys. 138, 251–285 (1997)
Bassi, F., Rebay, S.: GMRES discontinuous Galerkin solution of the compressible Navier–Stokes equations. In: First International Symposium on Discontinuous Galerkin Methods on Discontinuous Galerkin Methods. Theory, Computation and Applications, Newport, RI, USA, May 24–26. Lecture Notes in Computational Science and Engineering, vol. 11, Springer, Heidelberg (1999)
Bassi, F., Rebay, S.: A high order discontinuous Galerkin method for compressible turbulent flows. In: First International Symposium on Discontinuous Galerkin Methods on Discontinuous Galerkin Methods. Theory, Computation and Applications, Newport, RI, USA, May 24–26. Lecture Notes in Computational Science and Engineering, vol. 11, Springer, Heidelberg (2000)
Bassi, F., Rebay, S.: Numerical solution of the Euler equations with a multiorder discontinuous finite element method. In: Armfield, S., Morgan, P., Srinivas, K. (eds.) Computational Fluid Dynamics 2002: Proceedings of the Second International Conference on Computational Fluid Dynamics, Sydney, pp. 199–204. Springer, Heidelberg (2002)
Bassi, F., Rebay, S., Mariotti, G., Pedinotti, S., Savini, M.: A high-order accurate discontinuous finite element method for inviscid and viscous turbomachinery flows. In: Decuypere, R., Dibelius, G. (eds.) 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, Antwerpen, Belgium, March 5-7, pp. 99–108. Technologisch Instituut. (1997)
Brezzi, F., Manzini, G., Marini, D., Pietra, P., Russo, A.: Discontinuous Galerkin approximations for elliptic problems. Numer. Meth. for Part. Diff. Eq. 16, 365–378 (2000)
Fidkowski, K.J., Oliver, T.A., Lu, J., Darmofal, L.: p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. Journal of Computational Physics 207(1), 92–113 (2005)
Kroll, N.: ADIGMA-A European project on the development of adaptive higher-order varational methods for aerospace applications. AIAA Paper 2009-176, AIAA (2009)
Warburton, T.C., Lomtev, I., Du, Y., Sherwin, S.J., Karniadakis, G.E.: Galerkin and discontinuous Galerkin spectral/hp methods. Computer methods in applied mechanics and engineering 175, 343–359 (1999)
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Bassi, F., Colombo, A., Franchina, N., Ghidoni, A., Rebay, S. (2010). Robust and Efficient Implementation of Very High-Order Discontinuous Galerkin Methods in CFD. In: Kroll, N., Bieler, H., Deconinck, H., Couaillier, V., van der Ven, H., Sørensen, K. (eds) ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03707-8_20
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DOI: https://doi.org/10.1007/978-3-642-03707-8_20
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