Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points

By Andrew K. Henrick, Tariq D. Aslam, Joseph M. Powers. 2005

977 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/39f4e2280643ecb3804fac13fbe0fbf32669a68a

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

A high‐resolution hybrid scheme for hyperbolic conservation laws (2015, methodology): “[4], that the weighting procedure (8) actually fails in the achievement of designed order in critical points, a fact that was hidden by the small value ".”
Improvement of the WENO scheme smoothness estimator (2008, methodology): “A mapping function is proposed by Henrick et al[10] to obtain the optimal order near critical points.”
High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems (2009, background): “Examples of such designs include the modified nonlinear weights to enhance accuracy in smooth regions, especially at smooth extrema [68], discussed in Section 2.”
A new smoothness indicator for third‐order WENO scheme (2016, background): “Critical point problem The critical point problem has become a focus of discussions because it was pointed out in [4] that the standard value of ε=10 6 actually conceals the fact that the classical WENO schemes fail to recover design-order at critical points.”
An adaptive central-upwind weighted essentially non-oscillatory scheme (2010, methodology): “[7]) and the WENO-SYMOO and WENO-SYMBO schemes (see Fig.”
High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws (2011, methodology): “In [5], it was shown that if the smoothness indicators βk satisfy βk = 6”
High order Hybrid central-WENO finite difference scheme for conservation laws (2007, methodology): “A good review of the role of ε in the accuracy of the WENO scheme can be found in a recent paper [9].”
A family of high-order targeted ENO schemes for compressible-fluid simulations (2016, methodology): “[19] investigate the effective order of classical WENO schemes and conclude that an overall (2r − 1)-th order accuracy requires the condition wk − dk = O( x3) to be satisfied in smooth regions.”
An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws (2008, methodology): “In [3], truncation error analysis of the finite difference Eq.”