Abstract In this work, we first propose a new hydrodynamically-coupled phase-field model for the diblock copolymer melt that is derived based on the Allen-Cahn dynamics where the volume fraction of two composing monomers is conserved by using a nonlocal Lagrange multiplier. Formally, the system is a highly nonlinear system that consists of the incompressible Navier–Stokes equations and a nonlocal-type Allen-Cahn type equation. Then, to solve the model, we develop a linear and second-order time-marching scheme via the Invariant Energy Quadratization approach with the stabilization technique for the nonlinear potentials, as well as the projection method for the Navier–Stokes equations. The unconditional energy stability of the numerical method is proved, and several experiments of 2D and 3D are performed to validate the accuracy and energy stability of the developed numerical scheme.

中文翻译：

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双嵌段共聚物熔体的新流体动力学耦合守恒 Allen-Cahn 型 Ohta-Kawaski 相场模型的有效数值方案

摘要 在这项工作中，我们首先提出了一种新的双嵌段共聚物熔体的流体动力学耦合相场模型，该模型基于 Allen-Cahn 动力学，其中两个组成单体的体积分数通过使用非局部拉格朗日乘数守恒。从形式上讲，该系统是一个高度非线性的系统，由不可压缩的 Navier-Stokes 方程和一个非局部型 Allen-Cahn 型方程组成。然后，为了求解模型，我们通过具有非线性势稳定技术的不变能量二次方化方法以及 Navier-Stokes 方程的投影方法开发了线性和二阶时间推进方案。证明了数值方法的无条件能量稳定性，