Numerical Methods for a Multicomponent Two-Phase Interface Model with Geometric Mean Influence Parameters
Type
ArticleAuthors
Kou, Jisheng
Sun, Shuyu

KAUST Department
Computational Transport Phenomena LabEarth Science and Engineering Program
Physical Science and Engineering (PSE) Division
Date
2015-07-16Online Publication Date
2015-07-16Print Publication Date
2015-01Permanent link to this record
http://hdl.handle.net/10754/577322
Metadata
Show full item recordAbstract
In this paper, we consider an interface model for multicomponent two-phase fluids with geometric mean influence parameters, which is popularly used to model and predict surface tension in practical applications. For this model, there are two major challenges in theoretical analysis and numerical simulation: the first one is that the influence parameter matrix is not positive definite; the second one is the complicated structure of the energy function, which requires us to find out a physically consistent treatment. To overcome these two challenging problems, we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density, and furthermore, we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions. From this, we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density. For numerical simulation, we propose a modified Newton's method for solving this nonlinear model and analyze its properties; we also analyze a finite element method with a physical-based adaptive mesh-refinement technique. Numerical examples are tested to verify the theoretical results and the efficiency of the proposed methods.Citation
Numerical Methods for a Multicomponent Two-Phase Interface Model with Geometric Mean Influence Parameters 2015, 37 (4):B543 SIAM Journal on Scientific ComputingAdditional Links
http://epubs.siam.org/doi/10.1137/140969579ae974a485f413a2113503eed53cd6c53
10.1137/140969579