An hp‐adaptive discontinuous Galerkin method for shallow water flows |
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Authors: | C. Eskilsson |
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Affiliation: | Department of Shipping and Marine Technology, Chalmers University of Technology, Gothenburg, Sweden |
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Abstract: | 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. Copyright © 2010 John Wiley & Sons, Ltd. |
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Keywords: | shallow water equations discontinuous Galerkin method high‐order adaptivity non‐conforming elements |
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