Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems

By Michael Dumbser, Martin Käser, Vladimir A. Titarev, Eleuterio F. Toro. Journal of Computational Physics, 2007

358 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/19a55dd906a2b318484235b1e537731134a66f4b

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials (2012, methodology): “However according to reference [16] the MOOD method is competitive when compared to truly unstructured methods of the same order.”
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): “The convergence studies of the two-dimensional version of our PNPM schemes are carried out solving the Euler equations of compressible gas dynamics, with conservative variables up = (ρ, ρvj, ρE) T and the flux tensor defined as ~Fp = Fpi = ρvi ρvivj + p δij vi(ρE + p)”
Solving Irregular and Data-enriched Differential Equations using Deep Neural Networks (2019, background): “Similarly when FVM is evaluated at higher than first order accuracy, the absence of flux-limiting leads to unstable solutions [39, 40].”
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.”
Numerical Methods for High-Speed Flows (2011, background): “An important step in the direction of improving the computational efficiency of high-order FV schemes was accomplished by Dumbser et al. (2007), who succeeded in designing one-step non-oscillatory FV schemes for unstructured tetrahedral meshes with arbitrary order of accuracy, without the need of…”
On Universal Osher-Type Schemes for General Nonlinear Hyperbolic Conservation Laws (2011, methodology): “To enforce monotonicity, we use the WENO scheme proposed in [13, 14].”
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014, methodology): “9 in [38]) and with the numerical solution provided in [84].”
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].”
Well-Balanced High-Order Centred Schemes for Non-Conservative Hyperbolic Systems. Applications to Shallow Water Equations with Fixed and Mobile Bed (2009, methodology): “For nonlinear hyperbolic systems, the reconstruction should be done in characteristic variables [19,13] in order to avoid spurious oscillations that may appear when applying ENO or WENO reconstruction operators component-wise to nonlinear hyperbolic systems.”