High-order Alternating Direction Implicit Method Based on Compact Integrated-RBF Approximations for Unsteady/Steady Convection-Diffusion Equations
N. Thai-Quang;  N. Mai-Duy;  C.-D Tran;  T. Tran-Cong

doi:10.3970/cmes.2012.089.189
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.
PDF download PDF