×

zbMATH — the first resource for mathematics

A note on two upwind strategies for RBF-based grid-free schemes to solve steady convection-diffusion equations. (English) Zbl 1252.65195
Summary: Two radial basis function (RBF)-based local grid-free upwind schemes have been discussed for convection-diffusion equations. The schemes have been validated over some convection-diffusion problems with sharp boundary layers. It is found that one of the upwind schemes realizes the boundary layers more accurately than the rest. Comparisons with the analytical solutions demonstrate that the local RBF grid-free upwind schemes based on the exact velocity direction are stable and produce accurate results on domains discretized even with scattered distribution of nodal points.

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
PDF BibTeX Cite
Full Text: DOI
References:
[1] Kansa, Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynamicsII solutions to parabolic, hyperbolic and elliptic partial differential equations, Computers and Mathematics with Applications 19 (89) pp 147– (1990) · Zbl 0850.76048
[2] Wright, Scattered node compact finite difference-type formulas generated from radial basis functions, Journal of Computational Physics 212 (1) pp 99– (2006) · Zbl 1089.65020
[3] Chandhini, Local RBF-FD solutions for steady convection-diffusion problems, International Journal for Numerical Methods in Engineering 72 (3) pp 352– (2007) · Zbl 1194.76174
[4] Sanyasiraju, Local radial basis function based gridfree scheme for unsteady incompressible viscous flows, Journal of Computational Physics 227 pp 8922– (2008) · Zbl 1146.76045
[5] Franke, Scattered data interpolation: test of some methods, Mathematics of Computation 48 pp 181– (1982) · Zbl 0476.65005
[6] Hardy, Multiquadric equations of topography and other irregular surfaces, Journal of Geophysical Research 76 pp 1905– (1971)
[7] Gu, Meshless techniques for convection dominated problems, Computational Mechanics 38 pp 171– (2006) · Zbl 1138.76402
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.