论文标题
Cahn-Hilliard Navier-Stokes System的二阶完全平衡的结构赋予分配方案
A second-order fully-balanced structure-preserving variational discretization scheme for the Cahn-Hilliard Navier-Stokes system
论文作者
论文摘要
我们建议和分析Cahn-Hilliard-Navier-Stokes System的结构性时空变分离散方法。在存在浓度依赖性迁移率和粘度参数的情况下，通过相对能量估计值和订单最佳收敛速率在所有变量的情况下，使用平衡的近似空间以及解决方案上放松的规则条件来确定所有变量的唯一性和稳定性。提出了数值测试以证明所提出的方法是完全实用的，并产生了预测的融合率。本文开发的离散稳定性估计值也可用于分析其他离散方案，该方案在讨论中简要概述。
We propose and analyze a structure-preserving space-time variational discretization method for the Cahn-Hilliard-Navier-Stokes system. Uniqueness and stability for the discrete problem is established in the presence of concentration dependent mobility and viscosity parameters by means of the relative energy estimates and order optimal convergence rates are established for all variables using balanced approximation spaces and relaxed regularity conditions on the solution. Numerical tests are presented to demonstrate the proposed method is fully practical and yields the predicted convergence rates. The discrete stability estimates developed in this paper may also be used to analyse other discretization schemes, which is briefly outlined in the discussion.
