An adaptive discretization of shallow-water equations based on discontinuous Galerkin methods

Remacle, Jean-François;Soares Frazao, Sandra;Li, Xiangrong;Shephard, Mark S.
(2006) International Journal for Numerical Methods in Fluids — Vol. 52, n° 8, p. 903-923 (2006)

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In this paper, we present a discontinuous Galerkin formulation of the shallow-water equations. An orthogonal basis is used for the spatial discretization and an explicit Runge-Kutta scheme is used for time discretization. Some results of second-order anisotropic adaptive calculations are presented for dam breaking problems. The adaptive procedure uses an error indicator that concentrates the computational effort near discontinuities like hydraulic jumps. Copyright (c) 2006 John Wiley & Sons, Ltd.
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Remacle, J.-F., Soares Frazao, S., Li, X., & Shephard, M. S. (2006). An adaptive discretization of shallow-water equations based on discontinuous Galerkin methods. International Journal for Numerical Methods in Fluids, 52(8), 903-923. https://doi.org/10.1002/fld.1204 (Original work published 2006)