@Article{IJNAM-18-3,
author = {Yuzhe, Qin and Wang, Cheng and Zhengru, Zhang},
title = {A Positivity-Preserving and Convergent Numerical Scheme for the Binary Fluid-Surfactant System},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2021},
volume = {18},
number = {3},
pages = {399--425},
abstract = {<p style="text-align: justify;">In this paper, we develop a first order (in time) numerical scheme for the binary fluid
surfactant phase field model. The free energy contains a double-well potential, a nonlinear coupling
entropy and a Flory-Huggins potential. The resulting coupled system consists of two Cahn-Hilliard
type equations. This system is solved numerically by finite difference spatial approximation, in
combination with convex splitting temporal discretization. We prove the proposed scheme is
unique solvable, positivity-preserving and unconditionally energy stable. In addition, an optimal
rate convergence analysis is provided for the proposed numerical scheme, which will be the first
such result for the binary fluid-surfactant system. Newton iteration is used to solve the discrete
system. Some numerical experiments are performed to validate the accuracy and energy stability
of the proposed scheme.<br/></p>},
issn = {2617-8710},
doi = {https://doi.org/2021-IJNAM-18727},
url = {https://global-sci.com/article/82983/a-positivity-preserving-and-convergent-numerical-scheme-for-the-binary-fluid-surfactant-system}
}