Non-Oberbeck-Boussinesq效应下两相自然对流问题的建模及高效算法研究

两相流中的自然对流广泛存在于自然界和工业生产中。大温差条件下，流体物性参数随温度的变化不可忽略，需要考虑non-Oberbeck-Boussinesq(NOB)效应。因此，为了更加准确、高效地认识两相自然对流，需要建立有效的数学模型并设计高效的数值算法探讨NOB效应对该问题的影响。项目拟采用交错时间离散思想，针对单相NOB自然对流，建立改善时间步长限制、精确、高效的隐式方法及并行格式；考虑物性参数随温度的非线性变化，耦合相场模型，建立NOB假设下的两相自然对流模型；将求解单相问题的隐式算法拓展到两相系统，设计稳定、高精度、高效并能精确捕捉变化的数值方法及并行格式；拓展两相NOB自然对流算法到三维问题，探究NOB效应对不同两相流体系统流动、传热、相界面变化的影响。该项目是数学、热力学等领域的深刻交叉，拓宽了非等温两相流问题的研究思路，对准确、高效地模拟非等温两相流的流动和传热具有重要意义。

Two-phase natural convection not only occurs in natural science and many chemical engineering applications but also is the key issue of scientific problems (e.g., nuclear reactor and nanofluid technology). For the cases with relatively large temperature difference, the physical parameters of two phases may strongly depend on the temperature, and non-Oberbeck-Boussinesq (NOB) effects should be involved. Therefore, it will be a new and valuable topic to investigate the NOB effects on two-phase natural convection problems. Firstly, inspired by our previous work, for single-phase natural convection with NOB effects, the staggered time discretization technique is introduced to propose a stable, accurate, and efficient projection-method-based implicit numerical scheme. Secondly, by considering the nonlinear temperature-dependence of physical properties (e.g., fluid density, viscosity, thermal conductivity, and specific heat capacity) and phase-field model (Cahn-Hilliard equation), a reasonable mathematical model can be designed for describing the two-phase natural convection problems with NOB effects. Based on this mathematical model, a new method can be developed based on the proposed scheme for single-phase natural convection. It is expected that the method is able to not only maintain the high stability, excellent accuracy, and efficiency but also capture the interface movement accurately. Two- and three-dimensional two-phase natural convection problems will be simulated by considering the NOB effects using the parallelized version of the proposed algorithms. Moreover, the NOB effects on fluid motion, heat transfer, and interface movement will be investigated and analyzed in detail. The present work is a kind of mathematics-based multidisciplinary area and will expand the research areas of two-phase natural convection problems.