Towards Very High Order Godunov Schemes

By Eleuterio F. Toro, R. Millington, L. Nejad. 2001

281 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7a018cc6e5d4a25afaf5775fc9fb79e62adcc421

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In Computational Mechanics

Citations in the corpus

Numerical Methods for High-Speed Flows (2011, methodology): “In the ADER (Arbitrary accuracy DERivative Riemann problem) approach (Toro et al., 2001), the numerical flux is evaluated by solving the generalized Riemann problem using a semi-analytical method.”
Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems (2007, methodology): “on ENO schemes [27] and furthermore in the family of ADER-FV and ADER-DG schemes [17,21,33,47,49,51], the use of the Cauchy–Kovalewski procedure to avoid numerical quadrature in space and time is new.”
Solution of the generalized Riemann problem for advection–reaction equations (2002, methodology): “…be used to construct numerical methods of very high order of accuracy in space and time to solve the general initial-boundary-value problem; results reported in Toro et al. (2001), Toro & Titarev (2001a,b), Titarev (2001), Titarev & Toro (2002) and Schwartzkopff et al. (2001) look very promising.”
Godunov-type methods for free-surface shallow flows: A review (2007, methodology): “The ADER approach (Toro et al., 2001) also allows the construction of Godunov-type schemes of arbitrary order of accuracy in space and time.”
A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes (2008, methodology): “This effort resulted in what they called ADER schemes [72] (for Arbitrary Accuracy DERivative Riemann problem).”
ADER schemes for three-dimensional non-linear hyperbolic systems (2005, methodology): “The extension of original ADER schemes [31] to the one-dimensional nonlinear systems, using the method [32] has been reported in [26, 33].”
Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems (2007, background): “in a finite volume framework for linear equations on Cartesian grids [42,35,34].”