Radial Basis Function Based Partition of Unity Method for Two-Dimensional Unsteady Convection Diffusion Equations

Abstract

<h2>Abstract</h2>\n<p><strong>Objective:</strong> The present method aims to solve and investigate the efficiency, accuracy, and stability of the 2D unsteady Navier-Stokes equation in stream function vorticity formulation and Taylor’s vortex problem. <strong>Method:</strong> RBF partition of unity method (RBF-PUM) was implemented to solve the twodimensional Navier- Stokes equations in stream function vorticity formulation and Taylor’s vortex problem. <strong>Findings:</strong> RBF-PUM results show good agreement with the exact solutions. The numerical approach is found to be efficient and accurate while maintaining stability even for a Reynolds number as high as 1000. The global RBF method’s high computational cost can be overcome by using the RBF-PUM. <strong>Novelty and applications:</strong> The RBF-PU methodology is extended to solve the two-dimensional Navier- Stokes equations in stream function vorticity formulation and Taylor’s vortex problem, which were not discussed earlier in the literature. The adaptive spatial refinement within the partitions may be performed independently using the RBF-PUM. Then it may be extended to the more complex problems in CFD.</p>\n<p><strong>Keywords:</strong> Mesh Free Methods; RBF- PUM; Navier- Stokes Equations; Taylor’s Vortex Problem; CFD</p>