Computational fluid dynamics (CFD) simulations of viscous fluids described by the Navier-Stokes equations are considered. Depending on the Reynolds number of the flow, the Navier-Stokes equations may exhibit a highly nonlinear behavior. The system of nonlinear equations resulting from the discretization of the Navier-Stokes equations can be solved using nonlinear iteration methods, such as Newton's method. However, fast quadratic convergence is typically only obtained in a local neighborhood of the solution, and for many configurations, the classical Newton iteration does not converge at all. In such cases, so-called globalization techniques may help to improve convergence. In this paper, pseudo-transient continuation is employed in order to improve nonlinear convergence. The classical algorithm is enhanced by a neural network model that is trained to predict a local pseudo-time step. Generalization of the novel approach is facilitated by predicting the local pseudo-time step separately on each element using only local information on a patch of adjacent elements as input. Numerical results for standard benchmark problems, including flow through a backward facing step geometry and Couette flow, show the performance of the machine learning-enhanced globalization approach; as the software for the simulations, the CFD module of COMSOL Multiphysics is employed.

翻译：针对由纳维-斯托克斯方程描述的黏性流体计算流体动力学（CFD）模拟问题展开研究。根据流动的雷诺数，纳维-斯托克斯方程可能呈现高度非线性行为。由纳维-斯托克斯方程离散化产生的非线性方程组，可采用牛顿法等高线性的迭代方法求解。然而，经典的牛顿迭代仅在解局部邻域内具有快速二次收敛特性，对于许多配置情形甚至完全不收敛。在此类情况下，全局化技术有助于改善收敛性。本文采用伪瞬态延拓法来改进非线性收敛性，通过训练神经网络模型预测局部伪时间步长，对经典算法进行增强。该创新方法通过利用相邻单元组成的单元块上的局部信息，分别预测每个单元上的局部伪时间步长，从而提升了泛化能力。基于标准基准问题（包括后向台阶几何体绕流和库埃特流动）的数值测试结果表明，该机器学习增强型全局化方法具有优越性能；模拟计算软件采用COMSOL Multiphysics的CFD模块。