Newton linearization of the Navier–Stokes equations for flow computations using a fully coupled finite volume method

Newton linearization is implemented for the discretized advection terms in the Navier-Stokes momentum equations. A modified Newton linearization algorithm is developed by analyzing how to properly account for mass conservation implicitly in the linearization. The numerical performance of the modified Newton linearization algorithm is investigated in terms of solution stability, convergence behaviour, and accuracy. A set of standard fluid flow test problems is solved using a pressure-based cell-centered fully coupled finite volume solver linearized by Picard, standard Newton, and modified Newton methods. The accuracy of numerical solutions is assessed by comparisons with provided benchmark solutions and those obtained by the present coupled solver linearized by the Picard method. The numerical results showed the modified Newton linearization algorithm converged to a solution with a rate up to 22 times higher than that of Picard linearization algorithm for the steady flow fields for lid-driven cavity test problems. The modified Newton linearization technique is also evaluated by computations of steady flow over a backward facing step and unsteady flow around a circular cylinder. The developed algorithm reduces the iteration number of the linearization cycle required up to 10 times for the backward facing step flow problem. Also, the unsteady flow computations are performed by modified Newton linearization algorithm with a lower number of iterations in comparison with the Picard linearization algorithm. The numerical experiments indicate that the modified Newton linearization algorithm maintains the solution accuracy with respect to the Picard linearization algorithm.