二元流-表面活性剂相场模型与流体流动的数值近似：二阶、线性、能量稳定的方案
Numerical approximations for the binary Fluid-Surfactant Phase Field Model with fluid flow: Second-order, Linear, Energy stable schemes
AI总结：
本文提出二阶线性能量稳定的数值方案，用于求解耦合流体流动的二元流-表面活性剂相场模型，通过不变能量平方化方法、投影法和隐式-显式处理，证明了方案的无条件能量稳定性。
摘要：
本文考虑了耦合流体流动的二元流-表面活性剂相场模型的数值近似，系统高度非线性，耦合了不可压缩纳维-斯托克斯方程和两个卡恩-希尔利德型方程。我们开发了两种线性和二阶时间推进方案，结合不变能量平方化方法处理非线性势能，投影法求解纳维-斯托克斯方程，以及对应力和对流项的巧妙隐式-显式处理。我们严格证明了线性系统的well-posedness及其无条件能量稳定性。进行了各种2D和3D数值实验以验证所提方案的精度和能量稳定性。
英文摘要：
In this paper, we consider numerical approximations of a binary fluid-surfactant phase-field model coupled with the fluid flow, in which the system is highly nonlinear that couples the incompressible Navier-Stokes equations and two Cahn-Hilliard type equations. We develop two, linear and second order time marching schemes for solving this system, by combining the "Invariant Energy Quadratization" approach for the nonlinear potentials, the projection method for the Navier-Stokes equation, and a subtle implicit-explicit treatment for the stress and convective terms. We prove the well-posedness of the linear system and its unconditional energy stability rigorously. Various 2D and 3D numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
