Meshfree Direct And Indirect Local Radial
Basis Function Collocation Formulations
For Transport Phenomena
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
Keywords
Related Book
Other papers in this volume
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