Resolution of high order WENO schemes for complicated flow structures

By Jing Shi, Yong-Tao Zhang, Chi-Wang Shu. 2003

296 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/550f246cd629af7bfef4b28f906444ac921a17b8

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws (2011, background): “Additionally, as it was shown in [4], the CPU cost of increasing the order is smaller than the one of increasing the spatial resolution.”
Optimized sixth‐order monotonicity‐preserving scheme by nonlinear spectral analysis (2013, background): “Comparing Figure 11c with the results in [22] (Figure 1), the results obtained by the OMP6 on a 960 240 grid are similar to the classical WENO9 on a 1920 480 grid.”
High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems (2009, methodology): “A careful numerical study is performed in [147] for Euler equations and in [193] for Navier–Stokes equations to demonstrate that for flow problems containing both shocks and complicated smooth region structures, it is more economical to use high order WENO schemes than to use lower order schemes to ”
A family of high-order targeted ENO schemes for compressible-fluid simulations (2016, methodology): “1, the TENO5-opt and TENO5 resolve the finest small structure and the strongest wall jet among all the five-point stencil schemes, and even better than fifth-order WENO-JS scheme at resolution h = 1/960 (see literature Shi et al. (2003)).”
A high-order finite volume method for systems of conservation laws - Multi-dimensional Optimal Order Detection (MOOD) (2011, background): “Usually, the amount of instabilities measures the numerical diffusion influence [22]: large instabilities derive from small numerical diffusion and the number of plane vortexes in the slip line is a qualitative measure of the scheme diffusivity.”
Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes (2006, background): “3)); (5) 5th-order WENO scheme with characteristic decomposition (reprinted from [36], Copyright (2003), with permission from Elsevier).”
A high‐resolution hybrid scheme for hyperbolic conservation laws (2015, background): “The complex structures around slip lines are important to identify the smallness of the inherent numerical viscosities of the numerical schemes [19].”