Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier–Stokes equations

By Chi-Wang Shu, Hang Ding, K. S. Yeo. 2003

529 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/7b8147196490d582e8c4de287d9e9d4848a61ae3

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Computation of Incompressible Navier-Stokes Equations by Local RBF-based Differential Quadrature Method (2005, methodology): “[11], the nth order derivative of a smooth function ) , ( y x f with respect to x, ) (n x f , and its mth order derivative with respect to y, ) (m y f , at ) , ( i i y x can be approximated by local MQ-DQ method as ) , ( ) , ( 1 ) ( , ) ( k k N”
Subdomain radial basis collocation method for heterogeneous media (2009, methodology): “[20] introduced RBFs in the direct collocation of PDE by computing derivatives based on a differential quadrature scheme within a local domain of influence.”
Gaussian RBF-FD weights and its corresponding local truncation errors (2012, unknown): “To overcome this drawback a local RBF method was independently proposed by several authors [15–17].”
Meshless local radial basis function collocation method for convective‐diffusive solid‐liquid phase change problems (2006, methodology): “This feature of the developed method represents its principal difference from the other related local approaches, where the resultant matrix is large and sparse (Lee et al., 2003; Shu et al., 2003; Tolstykh and Shirobokov, 2005).”
Solving PDEs with radial basis functions * (2015, background): “(2010) [4] Stemmer et al. (2006) [2] Harder and Hansen (2005) [5] Kameyama et al.”
Error estimates of local multiquadric‐based differential quadrature (LMQDQ) method through numerical experiments (2005, methodology): “It has been proved to be a robust and effective method by solving buoyancy-driven natural convection problem [16].”
A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs (2007, unknown): “To resolve this problem, several attempts to use local RBF approximations ( Shu et al. , 2003”
Machine learning methods for turbulence modeling in subsonic flows around airfoils (2018, methodology): “The radial basis function was proved to be a great approximator [28] and has been applied to the PDEs solution [29], flow field reconstruction [30] and model of nonlinear unsteady aerodynamics [31-32].”
Static analysis of laminated composite curved shells and panels of revolution with a posteriori shear and normal stress recovery using generalized differential quadrature method (2012, methodology): “Furthermore, meshless methods are also available to solve analogous problems such as reported in literature [30–34].”