Nodal Integral Method Using Quadrilateral Elements for Transport Equations: Part 2-Navier-Stokes Equations

A numerical scheme for the Navier-Stokes equations in an irregular shaped domain using the nodal integral method (NIM) is developed. A mapping similar to the convection-diffusion article (Part 1) is used for the Navier-Stokes equations using the NIM in an arbitrary-shaped domain. Use of a recently developed pressure correction-based iterative scheme for the NIM ensures that the final solution satisfies the continuity condition. Lid-driven and buoyancy-driven flows in a skewed cavity are used as two test cases for comparison and verification. From the detailed comparative study of the results obtained by the NIM and very-fine-grid results (using finite-volume or similar approaches) of previous studies, it is established that this NIM-based scheme for the Navier-Stokes equation retains its capability to produce accurate results in comparatively much coarser grids, even with nonorthogonal grids