Automatic Time Stepping with Newton-Raphson Method for Two-phase Fluid Flow in Porous Media

摘要

In the numerical simulations of flow in partially saturated porous media, high computational efficiency is an essential requirement when large scale applications such as the fluid flow field in a CO_2 storage repository, are under consideration. In the present work, our aim is to enhance the computational efficiency by improving numerical algorithms. To this purpose, we apply a theoretically based time stepping method for the partial differential equations of fluid flow in partially saturated porous media. The time stepping method is embedded with automatic control and integrated into the Newton-Raphson linearization. With the time stepping method, the prediction of time step size depends upon the errors of the solutions between two successive nonlinear iterations and the solutions between two successive time steps. A good nonlinear convergence means small error in nonlinear iteration and therefore leads to an adequate time step size prediction. In the present study we linearize the two-phase flow equations with analytical Jacobians for the finite element discretization of their weak forms. The analytical Jacobian is suited for any material model and produces quadratic nonlinear convergence for commonly used models such as van Genuchten and Brooks-Corey. An example of modeling a 3D CO_2 storage model is presented to demonstrate the computational behavior and the efficiency of the time stepping method.