Research Projects

High-order entropy stable schemes for systems of conservation laws

Principal investigators

  • Prof. Dr. Siddhartha Mishra, Seminar for Applied Mathematics, ETH Zurich
  • Ulrik S. Fjordholm, NTNU Trondheim
  • Aziz Madrane, Bombardier Aerospace, Montreal
  • Eitan Tadmor, University of Maryland, College Park

Start date: 01.03.2008

Description

Systems of conservation laws modelling physical and engineering systems are equipped with an entropy formulation that provides stability estimates and selects the physically meaningful. We design arbitrarily high-order entropy stable schemes for a general system of conservation laws by combining entropy conservative fluxes with high-order numerical diffusion operators based on the ENO (essentially non-oscillatory) reconstruction. The schemes are applied to the shallow water equations and the Euler equations of gas dynamics. Ongoing work focuses on extension these high-order entropy stable schemes to unstructured grids and to the MHD equations.

Publications

  • U. S. Fjordholm, S. Mishra and E. Tadmor. Energy preserving and energy stable schemes for the shallow water equations, Proc. FoCM, Foundations of Computational Mathematics, Math. Soc. lecture notes 363 (2009), pp. 93-139
  • U. S. Fjordholm, S. Mishra and E. Tadmor. Entropy stable ENO scheme, Proc. 13th Int. Hyperbolic Conf., Beijing (2011), SAM Report 2011-05
  • N. Hancke, J. M. Melenk and Ch. Schwab. A p-FEM approach to solve the Orr-Sommerfeld equation, ZAMM, 79/3 (1999), pp. 685-686

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