Modified preconditioned Newton-Krylov approaches for Navier-Stokes equations using nodal integral method

Nodal integral methods (NIMs) have been proven effective in solving a wide range of scientific and engineering problems by providing accurate solutions with coarser grids. Despite notable advantages, these methods have encountered limited acceptance within the fluid flow community, primarily due to the lack of robust and efficient nonlinear solvers for the algebraic equations arising from discretization using NIM. A preconditioned Jacobian-free Newton-Krylov approach has been recently developed to solve Navier-Stokes equations to overcome this limitation. The developed approach has extended the acceptability of NIM and demonstrated considerable gains in computational time. However, a challenge persists in the efficiency of the proposed approach, particularly in solving the pressure Poisson equation. Addressing this, we offer novel strategies and algorithms to solve the pressure Poisson equation. These strategies aim to improve the computational efficiency of NIMs, making them more effective in solving complex problems in scientific and engineering applications.