Volume 1, Issue 2
Cubic Spline Meshless Method for Numerical Analysis of the Two-Dimensional Navier-Stokes Equations

Lindsey M. Westover and Samer M. Adeeb

Int. J. Numer. Anal. Mod. B, 1 (2010), pp. 172-196

Full Article 82 121
  • Abstract

The solution for the Navier-Stokes equations for incompressible steady state flow is presented using cubic spline (C2) continuous interpolation functions for the primary variables (velocities and pressure) on rectangular domains. The solution was explored for laminar flows with low, intermediate and high inertia effects. Two problems (Fluid squeezed between two plates and Wall-driven 2-D cavity flow) were solved using the presented scheme. Trial functions for velocities and pressure were chosen with cubic spline continuous interpolation functions on a rectangular grid that also satisfied the essential boundary conditions. The Galerkin weighted residual integrals were evaluated for the continuity and momentum equations. Using interpolation functions that satisfy the essential boundary conditions enabled the vanishing of any unknown boundary stress terms in the developed equations. The nonlinear equations were solved using an iterative technique. For low Reynolds number flows, coarse meshes were suffcient to reach convergence with very few iterations. For higher Reynolds number flows, a relatively finer mesh was necessary to reach a solution. The results show that cubic spline interpolation functions are suitable for solving the incompressible steady state flow Navier-Stokes equations using the Galerkin weighted residuals method. The chosen interpolation functions produced smooth continuous and differentiable results with relatively coarse meshes.

  • History

Published online: 2010-01

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