An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws

By Rafael Borges, Monique Carmona, Bruno Costa, Wai Sun Don. Journal of Computational Physics, 2008

1,425 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/84e17864257f4a33bd045df500e93cbad44e8f49

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

A family of high-order targeted ENO schemes for compressible-fluid simulations (2016, background): “[20] find that the improved results of WENO-M for shock capturing problems are due to the non-linear adaptation, i.”
A high‐resolution hybrid scheme for hyperbolic conservation laws (2015, methodology): “For WENO-JS3 and WENO-JS5, the parameter " in Equation (8) is chosen to be " D 10 6, and for WENO-N3 and WENO-Z5, the parameter " in Equation (11) is chosen to be " D 10 40.”
A new smoothness indicator for third‐order WENO scheme (2016, methodology): “[5] succeeded in achieving fifth-order accuracy by combining a modified weighting procedure with a higher-order smoothness indicator.”
An efficient class of WENO schemes with adaptive order (2016, methodology): “[3], we can obtain the un-normalized weights as”
An adaptive central-upwind weighted essentially non-oscillatory scheme (2010, methodology): “We examine the numerical solution on 400 and 800 grid points, and the reference ‘‘exact” solution is a high-resolution numerical solution on 3200 grid points calculated by the WENO-Z scheme [4].”
High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws (2011, methodology): “Thus, the WENO-Z sharper results that were obtained in [10] were due to the assignment of weights to discontinuous substencils that were larger than the ones of WENO-M.”
Improvement of the WENO scheme smoothness estimator (2008, methodology): “Borges et al[11] devised a new set of WENO weights that satisfies the necessary and sufficient conditions for fifth-order convergence proposed by Henrick et al[10] and enhances the accuracy at critical points.”