Author(s)

B. Šarler , T. Tran-Cong & C. S. Chen

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. 1 Introduction Problems in science and engineering are usually reduced to a set of coupled partial differential equations. It is not easy to obtain their analytical solution, particularly in non-linear and complex-shaped cases, and discrete approximate methods have to be employed accordingly. The finite volume (FVM), the finite

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