|Source||CMES: Computer Modeling in Engineering & Sciences, Vol. 89, No. 3, pp. 189-220, 2012|
|Download||Full length paper in PDF format. Size = 1,206,278 bytes|
|Keywords||compact integrated-RBF stencils, high-order approximations, alternating direction implicit (ADI), convection-diffusion equation.|
|Abstract||In this paper, the alternating direction implicit (ADI) method reported in [ ` 12 `
12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *You2006] for the convection-diffusion equation is implemented in the context of compact integrated radial basis function (CIRBF) approximations. The CIRBF approximations are constructed over 3-point stencils, where extra information is incorporated via two forms: only nodal second-order derivative values (Scheme 1), and both nodal first- and second-order derivative values (Scheme 2). The resultant algebraic systems are sparse, especially for Scheme 2 (tridiagonal matrices). Several steady and non-steady problems are considered to verify the present schemes and to compare their accuracy with some other ADI schemes. Numerical results show that highly accurate results are obtained with the proposed methods.