Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems

By Michael Dumbser, Martin Käser. Journal of Computational Physics, 2007

483 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/24391aaafd3a49294c6a4c1e8831cf95d74d2918

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014, methodology): “This overdetermined system of reconstruction equations is then solved using a constrained least-squares approach, see [64, 37], where the constraint is the integral conservation of the cell average over the big cell Ti, i.”
Well-Balanced High-Order Centred Schemes for Non-Conservative Hyperbolic Systems. Applications to Shallow Water Equations with Fixed and Mobile Bed (2009, methodology): “If all computations are done in a reference element, then this matrix does neither depend on the problem nor on the mesh, see [12].”
Assessment of high-order finite volume methods on unstructured meshes for RANS solutions of aeronautical configurations (2017, background): “The reader is referred to [3, 23, 44], and references therein, for a comprehensive explanation of the different set of geometrical conditions and WENO characteristic reconstruction.”
FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems (2010, methodology): “For test problems with discontinuities, monotonicity is obtained for the finite volume version of the schemes (P0PM) using the WENO algorithm proposed in [18,19], but any of the other unstructured ENO/WENO algorithms available in literature [1,23,40] can be used as well.”
Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials (2012, methodology): “Several strategies became very popular due to their intrinsic simplicity such that the MUSCL method [3,6,7,20,26,32] or their efficiency to achieve very high-order accuracy such that the ENO/WENO method [1,21,29,30,36,37,46,18,19,35,49,41], the Discontinuous Galerkin method [9– 12], the ADER method ”
Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter (2016, methodology): “In all of our numerical tests, following the practice in [11, 31], we take γ0 = 0.”
Numerical simulations of solute transport in highly heterogeneous formations: A comparison of alternative numerical schemes (2013, methodology): “These methods are also available on general unstructured meshes to deal with complex geometries [9–11].”
High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems (2009, methodology): “For three dimensions, finite volume WENO schemes on unstructured meshes were designed in [44, 45, 195].”
A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes (2008, methodology): “For more details on the computation of the flux matrices in 2D and 3D, see [28] and [29].”