Author(s)

JURAJ MUŽÍK, ROMAN BULKO

Abstract

In this paper, a numerical algorithm is developed for the solution of two-dimensional isothermal laminar viscous flow. The proposed numerical method implementation, which is quadrature-free, is based on the stream-velocity formulation of Navier–Stokes equations, the method of the particular solutions and the singular boundary method (SBM). The steady stream-velocity formulation of NS equation is 4th order biharmonic non-homogeneous nonlinear equation type which is solved using the proposed method with the non-homogeneous and nonlinear terms approximated using the method of particular solutions with multiquadrics RBF function. The accuracy of the method is proven using 2D backward-facing step and lid-driven cavity test cases.

Keywords

singular boundary method, dual reciprocity, Navier–Stokes equation, biharmonic equations