Michael Dumbser

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In [20], Qiu and Shu investigated using weighted essentially non-oscillatory (WENO) finite volume methodology as limiters for the Runge-Kutta discontinuous Galerkin (RKDG) methods for solving nonlinear hyperbolic conservation law systems on structured meshes. In this continuation paper, we extend the method to solve two dimensional problems on unstructured(More)
In this paper we propose a new high order accurate centered path-conservative method on unstructured triangular and tetrahedral meshes for the solution of multidimensional non-conservative hyperbolic systems, as they typically arise in the context of compressible multi-phase flows. Our path-conservative centered scheme is an extension of the centered method(More)
In this article a conservative least-squares polynomial reconstruction operator is applied to the discontinuous Galerkin method. In a first instance, piecewise polynomials of degree N are used as test functions as well as to represent the data in each element at the beginning of a time step. The time evolution of these data and the flux computation,(More)
The purpose of this work is to propose a novel a posteriori finite volume subcell limiter technique for the Discontinuous Galerkin finite element method for nonlinear systems of hyperbolic conservation laws in multiple space dimensions that works well for arbitrary high order of accuracy in space and time and that does not destroy the natural subcell(More)
In this paper we apply the ADER one step time discretization to the Discontinuous Galerkin framework for hyperbolic conservation laws. In the case of linear hyperbolic systems we obtain a quadrature-free explicit single-step scheme of arbitrary order of accuracy in space and time on Cartesian and triangular meshes. The ADERDG scheme does not need more(More)