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Higher-Order Gauss–Lobatto Integration for Non-Linear Hyperbolic Equations

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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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Authors and Affiliations

  1. Von Karman Institute for Fluid Dynamics, Waterloosesteenweg 72, 1640, Sint-Genesius-Rode, Belgium

    Bart De Maerschalck

  2. Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS, Delft, The Netherlands

    Marc I. Gerritsma

Authors
  1. Bart De Maerschalck
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  2. Marc I. Gerritsma
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Correspondence to Bart De Maerschalck.

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Maerschalck, B.D., Gerritsma, M.I. Higher-Order Gauss–Lobatto Integration for Non-Linear Hyperbolic Equations. J Sci Comput 27, 201–214 (2006). https://doi.org/10.1007/s10915-005-9052-x

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  • DOI: https://doi.org/10.1007/s10915-005-9052-x

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