On a high-order Newton linearization method for solving the incompressible Navier-Stokes equations

The present study aims to accelerate the non-linear convergence to incompressible Navier–Stokes solution by developing a high-order Newton linearization method in non-staggered grids. For the sake of accuracy, the linearized convection–diffusion–reaction finite-difference equation is solved line-by-line using the nodally exact one-dimensional scheme. The matrix size is reduced and, at the same time, the CPU time is considerably saved owing to the reduction of stencil points. This Newton linearization method is computationally efficient and is demonstrated to outperform the classical Newton method through computational exercises