Higher-Order Gauss–Lobatto Integration for Non-Linear Hyperbolic Equations |
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Authors: | Bart De Maerschalck Marc I Gerritsma |
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Affiliation: | (1) Von Karman Institute for Fluid Dynamics, Waterloosesteenweg 72, 1640 Sint-Genesius-Rode, Belgium;(2) Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands |
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Abstract: | Least-squares spectral elements are capable of solving non-linear hyperbolic equations, in which discontinuities develop in finite time. In recent publications De Maerschalck, B., 2003, http://www.aero.lr.tudelft.nl/∼bart; De Maerschalck, B., and Gerritsma, M. I., 2003, AIAA; De Maerschalck, B., and Gerritsma, M. I., 2005, Num. Algorithms, 38(1–3); 173–196], it was noted that the ability to obtain the correct solution depends on the type of linearization, Picard’s method or Newton linearization. In addition, severe under-relaxation was necessary to reach a converged solution. In this paper the use of higher-order Gauss–Lobatto integration will be addressed. When a sufficiently fine GL-grid is used to approximate the integrals involved, the discrepancies between the various linearization methods are considerably reduced and under-relaxation is no longer necessary |
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Keywords: | Least-squares spectral elements Gauss– Lobatto integration Newton’ s method Picard linearization |
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