Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy

By Dinshaw S. Balsara, Chi-Wang Shu. 2000

1,326 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d08b5b8e656d022727360157d559c91ef6679bf6

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In Computational Mechanics

Citations in the corpus

A further study of numerical errors in large-eddy simulations (2003, background): “There have also recently been several studies which have developed improved higher-order finite difference schemes with the aim of reducing numerical errors in LES (see for example [1,8]).”
Resolution of high order WENO schemes for complicated flow structures (2003, methodology): “The ‘‘monotonicity preserving limiters’’ in [1] is not used in this paper.”
High order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD (2001, methodology): “Very high order nite di erence WENO schemes (for orders between 7 and 11) have been developed in [2].”
ADER schemes for three-dimensional non-linear hyperbolic systems (2005, methodology): “circumvent the Godunov theorem [5] and design non-oscillatory schemes we use the nonlinear (solution-adaptive) weighted essentially non-oscillatory (WENO) reconstruction, see [10, 1 , 22] and references therein.”
High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems (2009, methodology): “Higher order versions of this WENO reconstruction were discussed in [4].”
An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws (2008, methodology): “Following [1], the hyperbolicity of the Euler equations admits a complete set of right and left eigenvectors for the Jacobian of the system.”
A technique of treating negative weights in WENO schemes (2000, background): “We remark that negative linear weights do not appear in nite di erence WENO schemes in any spatial dimensions for conservation laws for any order of accuracy [10], [1], and they do not appear in one dimensional as well as some multi-dimensional nite volume WENO schemes for conservation laws.”
Eulerian-Lagrangian modelling of detonative combustion in two-phase gas-droplet mixtures with OpenFOAM: Validations and verifications (2020, methodology): “[37], in which 7th-order WENO (Weighted Essentially Non-Oscillatory) scheme [52] and a mechanism of 9 species and 18 elementary reactions for hydrogen [53] are used.”
High order one-step monotonicity-preserving schemes for unsteady compressible flow calculations (2004, methodology): “Using the argument developed in [2] that the flow features should be simulated with at least 1% accuracy for the purpose of LES calculations, we can see that the OSMP7 scheme achieves this level of error on the coarsest 25 × 25 grid (all flow variables are of the order of unity).”