热力学一致非等温多相流体系统的计算建模、算法设计与数值分析

非等温条件下的多组分流体对流与扩散在工程应用中发挥着重要的作用，是流体力学和传热过程研究的中心课题之一。本项目旨在探究与外界有能量交换的开放系统中温度场对多相流体产生的影响。首先，基于广义Onsager原理的相场输运Cahn-Hilliard方程、力平衡的Navier-Stokes方程和来源于非平衡态热力学框架导出的能量守恒方程组成热力学一致(熵增)非等温两相不可压缩粘性流体力学模型。在此基础上，根据能量二次化(EQ)以及补充变量法(SVM)对上述新模型提出两类关于时间与空间均为二阶并保持各相液体组分体积守恒和正的熵增率的保结构数值格式。最后，设计快速傅里叶算法对两相流体的Bernard-Convection现象进行精确、高效地数值模拟，揭示温度的变化对多相流体产生的影响。这一研究不仅提高人们对耦合非等温效应的多相流体的认识，而且为促进非平衡态现象的物理研究提供理论和实验依据。

Multi-component fluid convection and diffusion under non-isothermal conditions plays an important role in engineering applications and is one of the central topics in the study of fluid mechanics and heat transfer process. This project aims to explore the influence of temperature field on multiphase fluid in an open system with external energy exchange. Firstly, we proposes the thermodynamically consistent (entropy increase) non-isothermal two-phase incompressible viscous fluid dynamics model which composed of a phase field transport Cahn-Hilliard equation based on the generalized Onsager principle, the Navier-Stokes equation for force balance and the energy conservation equation derived from the non-equilibrium thermodynamics framework; On this basis, according to the entropy quadratization (EQ) and the supplementary variable method (SVM), two types of structure-preserving numerical schemes are proposed for the above-mentioned model, both of which are second-order in time and space, and this schemes maintained the volume conservation and entropy increase rate of the liquid components in each phase are positively maintained; Finally, a fast Fourier transform algorithm is designed to simulate the Bernard-Convection phenomenon of two-phase fluid accurately and efficiently, and the influence of temperature changes on the multi-phase fluid system is revealed through the simulation results.This research not only improves our understanding of non-isothermal multiphase fluid flow, but also provides theoretical and experimental basis for promoting the physical research of non-equilibrium phenomenon.