A meshless multiple-scale polynomial method for numerical solution of 3D convection–diffusion problems with variable coefficients

Abstract

In this paper numerical solution of 3D convection–diffusion problems both with high Reynolds (Re) numbers and variable coefficients are investigated via a meshless method based on polynomial basis. It is well known that using polynomial basis directly for solving partial differential equations may be unsafe due to ill-conditioned resultant coefficients matrix that formed after discretization process. Therefore to get rid of highly ill-conditioned coefficient matrix we took advantage of multiple-scale method which is essentially based on the idea of equating norm of each column of resultant coefficients matrix. Through this approach we can reduce the condition number greatly. The proposed method is a truly meshless method since there is no need for meshing or any node connectivity and implementation of the method is simple and straightforward. The performance of the proposed method is measured by four test problems in both regular and irregular computational domains. Numerical results corroborate efficiency of meshless multiple-scale polynomial method for 3D convection–diffusion problems as well show its stability in case of large noise effect.