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High-Order One-Step Schemes for Non-Conservative PDE: Application to Shallow Water Systems

Author(s): Arturo Hidalgo; Michael Dumbser

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Abstract: We show applications of a new unified family of arbitrary high order accurate path-conservative one--step schemes on unstructured triangular and adaptively refined Cartesian meshes for the solution of hyperbolic PDE with nonconservative products and stiff source terms. The fully discrete one-step schemes are within the general framework of PNPM schemes first proposed in[6]. In this general framework, classical high order finite volume and discontinuous Galerkin schemes are only special cases. The one-step time discretization of high order of accuracy is obtained using a new local space-time Galerkin predictor that is also able to deal with stiff source terms[5]. The centered treatment of the non-conservative products is done using a multi-dimensional generalization of the FORCE scheme, see[2; 6]. We show applications of our new method to shallow water equations.


Year: 2012

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