# Meshfree direct and indirect local radial basis function collocation formulations for transport phenomena

Sarler, Bozidar and Tran-Cong, Thanh and Chen, Ching S. (2005) Meshfree direct and indirect local radial basis function collocation formulations for transport phenomena. In: 27th World Conference on Boundary Elements and Other Mesh reduction Methods Incorporating Engineering and Electromagnetics (BEM XXVII), 15-18 Mar 2005, Orlando, FL. United States.

## Abstract

This paper formulates an upgrade of the classical meshless Kansa method. It overcomes the principal large-scale bottleneck problem of this method. The formulation copes with the non-linear transport equation, applicable in solutions of a broad spectrum of mass, momentum, energy and species transfer problems. The domain and boundary of interest are divided into overlapping influence areas. On each of them, the fields (direct version) or second partial derivatives (indirect version) are represented by the multiquadrics radial basis function collocation on a related sub-set of nodes. Time-stepping is performed in an explicit way. The governing equation is solved in its strong form, i.e. no integrations are performed. The polygonisation is not present and the method is practically independent of the problem dimension. The complicated geometry is easy to cope with. The method is simple to learn and to code. The method can be straightforwardly extended to tackle other types of partial differential equations. Statistics for this ePrint Item
Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper) No Live Archive c. 2005 WIT Press. Historic - Faculty of Engineering and Surveying - No Department (Up to 30 Jun 2013) Historic - Faculty of Engineering and Surveying - No Department (Up to 30 Jun 2013) 12 Jan 2021 03:20 12 Jan 2021 03:20 radial basis function (RBF); Kansa method; collocation; mesh free; meshless; non-linear transport equation; bottleneck 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations01 Mathematical Sciences > 0101 Pure Mathematics > 010111 Real and Complex Functions (incl. Several Variables)01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation 49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490303 Numerical solution of differential and integral equations49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490411 Real and complex functions (incl. several variables)49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490101 Approximation theory and asymptotic methods40 ENGINEERING > 4017 Mechanical engineering > 401706 Numerical modelling and mechanical characterisation http://eprints.usq.edu.au/id/eprint/299 Archive Repository Staff Only