Abstract
In this paper we consider the very high order approximation of solutions of the Euler equations. We present a systematic generalization of the Residual Distribution method of [8] to very high order of accuracy, by extending the preliminary work discussed in [17]. We present extensive numerical validation for the third and fourth order cases with Lagrange finite elements. In particular, we demonstrate that we an both have a non oscillatory behavior, even for very strong shocks and complex flow patterns, and the expected accuracy on smooth problems. We also extend the scheme to laminar viscous problems.
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Abgrall, R., Marpeau, F.: Residual distribution schemes on quadrilateral meshes. J. Sci. Comput. 30(1), 131–175 (2007)
Struijs, R., Deconinck, H., Roe, P.L.: Fluctuation splitting schemes for the 2D Euler equations. VKI-LS 1991-01, Computational Fluid Dynamics (1991)
Deconinck, H., Roe, P.L., Struijs, R.: A multidimensional generalization of Roe’s difference splitter for the Euler equations. Computer and Fluids 22(2/3), 215–222 (1993)
van der Weide, E., Deconinck, H.: Positive matrix distribution schemes for hyperbolic systems. In: Computational Fluid Dynamics, pp. 747–753. Wiley, New York (1996)
Abgrall, R.: Toward the ultimate conservative scheme: Following the quest. J. Comput. Phys. 167(2), 277–315 (2001)
De Palma, P., Pascazio, G., Rossiello, G., Napolitano, M.: A second-order-accurate monotone implicit fluctuation splitting scheme for unsteady problems. J. Comput. Phys. 208(1), 1–33 (2005)
Rossiello, G., De Palma, P., Pascazio, G., Napolitano, M.: Third-order-accurate fluctuation splitting schemes for unsteady hyperbolic problems. J. Comput. Phys. 222(1), 332–352 (2007)
Abgrall, R.: Essentially non-oscillatory residual distribution schemes for hyperbolic problems. J. Comput. Phys. 214(2), 773–808 (2006)
Corre, C., Hanss, G., Lerat, A.: A residual-based compact scheme for the unsteady compressible Navier-Stokes equations. Comput. Fluids 34(4-5), 561–580 (2005)
Abgrall, R., Tavé, C.: Construction of very high order residual distribution schemes. In: Deconinck, H., Dick, E. (eds.) Preceedings of the ICCFD6, Ghent, Belgium, July 2006. Springer, Heidelberg (2006)
Larat, A., Abgrall, R., Ricchiuto, M.: Very high order residual distribution schemes for steady flow problems. In: Proceedings of the ICCDF8, Seoul, July 2008. Springer, Heidelberg (2008)
Caraeni, D., Fuchs, L.: Compact third–order multidimensional upwind scheme for Navier Stokes simulations. Theoretical and Computational Fluid Dynamics 15, 373–401 (2002)
Abgrall, R., Roe, P.L.: High-order fluctuation schemes on triangular meshes. J. Sci. Comput. 19(1-3), 3–36 (2003)
Abgrall, R., Mezine, M.: Construction of second-order accurate monotone and stable residual distribution schemes for steady problems. J. Comput. Phys. 195(2), 474–507 (2004)
Roe, P.L.: Fluctuations and signals - a framework for numerical evolution problems. In: Proc. Conf., Numerical methods for fluid dynamics, Reading, U.K., pp. 219–257 (1982)
Csík, Á., Ricchiuto, M., Deconinck, H.: A conservative formulation of the multidimensional upwind residual distribution schemes for general nonlinear conservation laws. J. Comput. Phys. 179(2), 286–312 (2002)
Abgrall, R., Ricchiutto, M., Larat, A.: A simple construction of very high order non oscillatory compact schemes on unstructured meshes. In: Computers and Fluids (2008) (in press)
Csík, Á., Ricchiuto, M., Deconinck, H.: A conservative formulation of the multidimensional upwind residual distribution schemes for general nonlinear conservation laws. J. Comput. Phys. 179(1), 286–312 (2002)
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Abgrall, R., Larat, A., Ricchiuto, M. (2010). Construction of High-Order Non Upwind Distribution Schemes. 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_9
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DOI: https://doi.org/10.1007/978-3-642-03707-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03706-1
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