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An hp ‐adaptive discontinuous Galerkin method for shallow water flows
Author(s) -
Eskilsson C.
Publication year - 2010
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2434
Subject(s) - discontinuous galerkin method , discretization , shallow water equations , degree of a polynomial , mathematics , polynomial , galerkin method , degrees of freedom (physics and chemistry) , basis function , finite element method , mathematical analysis , physics , quantum mechanics , thermodynamics
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.