Pressure Correction–Based Iterative Scheme for Navier-Stokes Equations using Nodal Integral Method

Abstract

A novel numerical scheme is developed for steady-state, 2-D incompressible Navier-Stokes equations using the nodal integral method (NIM). The NIM-based schemes have been used to solve partial differential equations in different areas of physics and are known to have very high accuracy compared to conventional numerical schemes. The scheme is implemented using a SIMPLE (Semi-Implicit Method for Pressure-Linked Equations)-like algorithm for pressure and velocity correction instead of solving the exact pressure Poisson equation. To verify the results, two well-known test problems, the lid-driven cavity and natural convection of air in a square cavity, are chosen. For both cases, results are in good agreement with the benchmark solutions even for quite coarse grids.