用于Cahn-Hilliard-Navier-Stokes方程的一族二阶线性无条件稳定方法
A family of second order, linear, unconditionally stable methods for the Cahn-Hilliard-Navier-Stokes equations
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中文总结 AI 辅助
针对匹配密度两相流的Cahn-Hilliard-Navier-Stokes方程，本文提出一族二阶线性无条件稳定IMEX方法，该方法每时间步仅需线性求解，经数值实验验证具有约二阶时间收敛性，可有效模拟多种典型界面流问题。
中文摘要 AI 辅助
针对模拟匹配密度两相流的Cahn-Hilliard-Navier-Stokes（CHNS）方程，本文提出了一族二阶线性无条件稳定的隐式-显式（IMEX）方法。所提半离散格式结合了非线性项的外推、非线性自由能项的辅助变量形式，以及由参数ε控制的时间曲率正则化。我们建立了离散能量估计，证明当θ∈(1/2,1]且ε≥0时，该方法具有无条件长时间稳定性。所得格式每时间步仅需线性求解。数值实验表明其具有约二阶时间收敛性，并检验了质量守恒、能量耗散、数值鲁棒性，以及旋节线分解、液滴形状松弛、两相顶盖驱动空腔流、瑞利-泰勒不稳定性等多个典型界面流问题。
英文摘要
We present a family of second-order, linear, unconditionally stable implicit-explicit (IMEX) methods for the Cahn-Hilliard-Navier-Stokes (CHNS) equations modeling matched-density two-phase flows. The proposed semi-discrete scheme combines extrapolation of the nonlinear terms with an auxiliary-variable formulation of the nonlinear free-energy term and a temporal-curvature regularization controlled by a parameter $ε$. We establish a discrete energy estimate showing unconditional long-time stability of the method for $θ\in(1/2,1]$ and $ε\geq0$. The resulting scheme requires only linear solves at each time step. Numerical experiments demonstrate approximately second-order temporal convergence and examine mass conservation, energy dissipation, numerical robustness, and several representative interfacial-flow problems, including spinodal decomposition, droplet shape relaxation, two-phase lid-driven cavity flow, and Rayleigh-Taylor instability.
