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ADER DG and FV Schemes for Shallow Water Flows

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Part of the book series: Mathematics in Industry ((TECMI,volume 12))

We are concern with ADER [3] high-order numerical methods for the timedependent two-dimensional non-linear shallow water equations [2] in the framework of finite volumes (FV) and discontinuous Galerkin (DG) finite elements methods using non-structured triangular meshes.

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References

  1. M. Dumbser and M. Käser. Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems. J. Comp. Phys. (In Press), 00:000-000, 2006.

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  2. E.F. Toro. Shock-Capturing Methods for Free-Surface Shallow Flows. John Wiley and Sons, Chichester, 2001.

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  3. E.F. Toro, R.C. Millington, and L.A.M. Nejad. Towards very high order Godunovs schemes. In E.F. Toro, editor, Godunov Methods. Theory and Appli- cations, pages 907-940. Kluwer/Plenum Academic Publishers, 2001.

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  4. E.F. Toro and V.A. Titarev. Derivative Riemann Solvers for Systems of Conser- vation Laws and ADER Methods. J. Comp. Phys., 212:150-165, 2006.

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Castro, C.E., Toro, E.F. (2008). ADER DG and FV Schemes for Shallow Water Flows. In: Bonilla, L.L., Moscoso, M., Platero, G., Vega, J.M. (eds) Progress in Industrial Mathematics at ECMI 2006. Mathematics in Industry, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71992-2_49

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