Solving the stationary Navier–Stokes equations by using Taylor meshless method

Abstract

The numerical implementation of the Taylor Meshless Method (TMM) for solving the two-dimensional Navier–Stokes equations is considered in this paper, where the TMM is a true meshless integration-free method based on Taylor series. The performance of the proposed numerical technique is evaluated by three benchmark tests. In the first case, the exact solution ia a high degree polynomial that permits to check the consistency and high accuracy of the proposed numerical method. Then the comparison with the analytical solution of the Kovasznay flow for the Reynolds number in the range [0,1000] is considered. It turns out that the TMM works well for large values of Reynolds number and it converges rapidly with the degree of Taylor series (p-convergence) and the number of sub-domains (h-convergence). Finally the square lid-driven cavity flow problems for the Reynolds number up to Re=1000 are solved and excellent agreements with corresponding benchmark solutions are found.