Numerical Simulation of Convection-Diffusion Phenomena by Four Inverse-Quadratic-RBF Domain-Meshfree Schemes

S Kaennakham, N Chuathong


The convection-diffusion type of PDEs is numerically solved by four numerical methods in this work. These four comparatively young numerical approaches are categorized as ‘domain-meshfree’ as they require no internal meshing but rely only on the collocation process amongst nodes via. the inverse-quadratic radial basis function (IQ-RBF). They are; the well-known Kansa Collocation Method (KCM), the Hermite Collocation Method (HCM), the Radial Point Interpolation Method (RPIM), and the Dual Reciprocity Boundary Element Method (DRBEM). The work aims to demonstrate the use of IQ-RBF as well as to compare the practical use of the methods. Moreover, engineering senses of criteria judging the quality of the methods are considered. It is found in this work that while KCM is the simplest to construct and deploys, it is highly sensitive to the number of nodes and the IQ-RBF shape parameter. The unsymmetric and populated matrix problem are alleviated when HCM or DRBEM are in use yet more CPU-time and storage seem to be the price to pay, particularly HCM.  However, it is actually RPIM that has appeared to be an optimal choice under all the criteria imposed.

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