Developing high-order weighted compact nonlinear schemes

By Xiaogang Deng, Hanxin Zhang. 2000

493 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a79fe3b2c5e62eaa49a2580c814876cdaa83442c

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In Computational Mechanics

In Numerical Analysis

Citations in the corpus

High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems (2009, methodology): “In [41], the WENO procedure is used to build nonlinear WENO compact schemes.”
Computational aeroacoustics: progress on nonlinear problems of sound generation (2004, methodology): “WENO schemes with compact (Padé) stencils can be used to achieve higher-orderaccuracy [263,264], and optimized schemes can be used to trade-off formal order-of-accuracy for better performance at high wavenumbers [265,266].”
Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves (2010, methodology): “, based on the weighted essentially non-oscillatory (WENO) schemes of Jiang and Shu [21], possibly with improved wavenumber properties [10,33].”
An efficient class of WENO schemes with adaptive order (2016, methodology): “The finite difference WENO methods have also been adapted to handle complex geometry by Hu and Shu [16] and Liu and Zhang [24].”
Numerical Methods for High-Speed Flows (2011, methodology): “Ducros et al. (2000) showed that the skew-symmetric forms (18) and (19) give rise to locally conservative schemes, when the derivative operators are discretized with explicit central formulas (with order up to six).”
Hybrid finite compact‐WENO schemes for shock calculation (2007, background): “Deng and Zhang [15] developed an algorithm whereby the resolution properties of WENO schemes are improved by introducing compact approximations for pointwise derivatives rather than explicit ones.”
A high-wavenumber viscosity for high-resolution numerical methods (2004, unknown): “[4,5] introduced compact stencils and interpolants into the ENO/WENO framework in an effort to improve the modified wavenumber compared to explicit upwinding.”
Derivation of high-order compact finite difference schemes for non-uniform grid using polynomial interpolation (2005, background): “Deng and Maekawa [23] and Deng and Zhang [22] developed non-linear and weighted non-linear compact schemes, respectively, for capturing discontinuities.”