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.

牛顿线性化用于Navier-Stokes动量方程中的离散对流项。通过分析如何在线性化中隐式考虑质量守恒，开发了一种改进的牛顿线性化算法。改进牛顿线性化算法的数值性能从解决方案稳定性，收敛性和准确性方面进行了研究。使用以Picard，标准牛顿和改进的牛顿方法线性化的基于压力的以单元为中心的完全耦合有限体积求解器，可以解决一组标准的流体流动测试问题。数值解的准确性是通过与提供的基准解和由本耦合耦合器通过皮卡德方法线性化获得的基准解进行比较来评估的。数值结果表明，改进的牛顿线性化算法收敛到解决方案，其速率比Picard线性化算法高出22倍，从而解决了盖驱动空腔测试问题的稳定流场。改进的牛顿线性化技术还通过计算后向台阶上的稳定流和圆柱体周围的非稳定流来进行评估。所开发的算法可将线性化循环的迭代次数最多减少10次，以解决后向步流问题。此外，与Picard线性化算法相比，非恒定流计算是通过改进的Newton线性化算法进行的，迭代次数更少。