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An hp-adaptive discontinuous Galerkin method for shallow water flows

Claes Eskilsson (Institutionen för sjöfart och marin teknik, Hydromekanik)
International Journal for Numerical Methods in Fluids (0271-2091). Vol. 67 (2011), 11, p. 1605-1623 .
[Artikel, refereegranskad vetenskaplig]

An adaptive spectral/hp discontinuous Galerkin method for the two-dimensional shallow water equations is presented. The model uses an orthogonal modal basis of arbitrary polynomial order p defined on unstructured, possibly non-conforming, triangular elements for the spatial discretization. Based on a simple error indicator constructed by the solutions of approximation order p and p−1, we allow both for the mesh size, h, and polynomial approximation order to dynamically change during the simulation. For the h-type refinement, the parent element is subdivided into four similar sibling elements. The time-stepping is performed using a third-order Runge–Kutta scheme. The performance of the hp-adaptivity is illustrated for several test cases. It is found that for the case of smooth flows, p-adaptivity is more efficient than h-adaptivity with respect to degrees of freedom and computational time.

Nyckelord: shallow water equations, discontinuous Galerkin method, high-order, adaptivity, non-conforming elements

Denna post skapades 2010-11-10. Senast ändrad 2011-12-22.
CPL Pubid: 128831


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Institutioner (Chalmers)

Institutionen för sjöfart och marin teknik, Hydromekanik (2005-2011)



Chalmers infrastruktur