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., 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
Online ISBN: 978-3-642-03707-8
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