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

  • Authors:

  • Bart De Maerschalck;Marc I. Gerritsma

  • Affiliations:

  • Von Karman Institute for Fluid Dynamics, Sint-Genesius-Rode, Belgium 1640;Aerospace Engineering, Delft University of Technology, Delft, The Netherlands 2629 HS

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2006

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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