دانلود رایگان مقاله روش برای شبیه سازی کشش سطحی مخلوط با تئوری گرادیان رابط سیال

Abstract

Surface tension significantly impacts subsurface flow and transport, and it is the main cause of capillary effect, a major immiscible two-phase flow mechanism for systems with a strong wettability preference. In this paper, we consider the numerical simulation of the surface tension of multi-component mixtures with the gradient theory of fluid interfaces. Major numerical challenges include that the system of the Euler–Lagrange equations is solved on the infinite interval and the coefficient matrix is not positive definite. We construct a linear transformation to reduce the Euler–Lagrange equations, and naturally introduce a path function, which is proven to be a monotonic function of the spatial coordinate variable. By using the linear transformation and the path function, we overcome the above difficulties and develop the efficient methods for calculating the interface and its interior compositions. Moreover, the computation of the surface tension is also simplified. The proposed methods do not need to solve the differential equation system, and they are easy to be implemented in practical applications. Numerical examples are tested to verify the efficiency of the proposed methods.

5. Conclusions

A well-defined path function has been constructed based on a linear transformation, and then the expressions of the Euler–Lagrange equations are reduced. Furthermore, we have proven the monotonicity of the path function, and from this, we develop two efficient methods for calculating the two-phase fluid interface and computing the surface tension. Compared to the known methods, the proposed methods not only eliminate the need of solving a differential equation system, but also are easier to be implemented in practical applications. The numerical examples are also given to verify the proposed theory and demonstrate the efficiency of the proposed methods.