A triangular spectral/hp discontinuous Galerkin method for modelling 2D shallow water equations

By Claes Eskilsson, Spencer J. Sherwin. 2004

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We present a spectral/hp element discontinuous Galerkin model for simulating shallow water flows on unstructured triangular meshes. The model uses an orthogonal modal expansion basis of arbitrary order for the spatial discretization and a third‐order Runge–Kutta scheme to advance in time. The local elements are coupled together by numerical fluxes, evaluated using the HLLC Riemann solver. We apply the model to test cases involving smooth flows and demonstrate the exponentially fast convergence with regard to polynomial order. We also illustrate that even for results of ‘engineering accuracy’ the computational efficiency increases with increasing order of the model and time of integration. The model is found to be robust in the presence of shocks where Gibbs oscillations can be suppressed by slope limiting. Copyright 2004 John Wiley & Sons, Ltd.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a272bac28a85f9c4f0daa08313ebdc10ef773962

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Citations in the corpus

High‐order semi‐implicit time‐integrators for a triangular discontinuous Galerkin oceanic shallow water model (2009, methodology): “5.1.2. Linear Kelvin Wave This problem involves the transient solution of the linearized inviscid equations with rotation. From [ 13 ] we use the analytic solution”
A Survey of High Order Schemes for the Shallow Water Equations (2014, background): “Several advantages of the DGmethod, including its high order accuracy, high parallel efficiency, flexibility for hp-adaptivity and arbitrary geometry and meshes, make it suited for the SWEs, see [16, 19, 23, 38, 51].”
A well‐balanced Runge–Kutta discontinuous Galerkin method for the shallow‐water equations with flooding and drying (2008, methodology): “In §2, the SWE and the main features of the Runge–Kutta Discontinuous Galerkin (RKDG) scheme introduced in [21] to approximate the SWE are restated.”
A wetting and drying treatment for the Runge-Kutta discontinuous Galerkin solution to the shallow water equations (2009, background): “…Notre Dame, Notre Dame, IN 46556, United States d The University of Texas at Austin, Austin, TX 78712, United States a r t i c l e i n f o Article history: Received 31 July 2008 Received in revised form 26 December 2008 Accepted 8 January 2009 Available online 23 January 2009 Keywords: Shallow…”