Simulation of the incompressible Navier–Stokes via integrated radial basis function based on finite difference scheme

Integrated radial basis function based on finite difference (IRBF–FD) method is presented in this paper for the solution of incompressible Navier–Stokes equations. A semi-implicit temporal scheme is first used to discretize the time variable of the incompressible Navier–Stokes (NS) equations. We consider the same discrete scheme for the time variable for both pressure–Poisson equation and vorticity stream function formulation. For solving lid-driven cavity flow and backward-facing step flow, we used the vorticity-stream formulation. The proposed method approximates the function derivatives at a knot in terms of the function values on a collection of nodes existing in the support domain of the node. We also utilize an algorithm for finding the optimal shape parameter for each stencil based on the range of condition numbers. It can be seen that no special treatment is needed to impose the essential boundary conditions. The efficiency, accuracy and robustness of the presented method are demonstrated by comparing the current method with existing methods.