变温度多相流相场模型及其算法、分析和应用

Multi-phase flows and heat transfer play a key role and have been applied in many fields such as industry, engineering, biology and human health. This project considers modelling, analysis and computational methods for phase-field models of multi-phase flow and heat transfer problems. Since there are not many researches on the phase-field model which allows for temperature variation, this project is aiming to propose more accurate models by taking into account of conservation laws of mass, momentum and energy and of the thermodynamical consistency. Moreover, by applying asymptotic methods, we could relate a phase-field model to the corresponding sharp-interface model. We will also design finite element (or finite difference) schemes preserving the mass conservation and energy law and having the thermodynamical consistency. This will allow us to compute multi-phase flow and heat transfer problems more accurately and more robustly. Based on numerical schemes designed in the project we will develop a piece of software based on adaptive mesh refinement techniques and the Block Structured Adaptive Multigrid method to fulfil numerical simulation more accurately, more effectively and more rapidly. We would like to apply our methods and software to a number of applications related to multi-phase flows and moving interface problems with temperature variation.

多相流流动及传热在工业工程生物医疗等领域拥有广泛的应用和核心地位。本项目考虑一般多相流流动及传热问题的相场（phase-field或diffuse-interface）模型的建模、分析和计算。针对现阶段对变温度非恒定表面张力相场模型研究的不足，本项目从质量动量能量等力学定律出发，建立能够更准确描述物理过程与热力学定律相容的相场模型；通过渐近分析方法分析与sharp-interface模型的关系，设计能够保证质量守恒能量变化律乃至热力学定律的有限元或有限差分计算格式，从而更加精确可靠地计算多相流传热问题；同时，本项目结合所设计的计算格式，开发拓展完善基于自适应网格的块结构多重网格方法的计算软件，从而更精确更有效更快捷地进行数值模拟。本项目设计的计算方法与软件也将用于其他包含移动界面的与多相流流动传热相关的应用问题。

多相流流动及传热在工业工程生物医疗等领域拥有广泛的应用和核心地位。本项目考虑一般多相流流动及传热问题的相场（phase-field或diffuse-interface）模型的建模、分析和计算。我们重点研究了具有移动接触线和变密度的两相流问题的建模和仿真。基于拟不可压缩性概念和能量变分法，建立了具有一般Navier边界条件的与热力学定律相容的相场模型。提出了一种质量守恒的在完全离散的水平上是能量稳定的有限元格式来求解偏微分方程组。此外，我们提出了一个拟不可压缩的Navier–Stokes–Cahn–Hilliard（q-NSCH）扩散界面模型，用于具有可变物理性质的两相流体流动，并保持与热力学定律相容。然后，我们将扩散域方法与该两相流体模型耦合，得到一个新的q-NSCH-DD模型，以模拟具有复杂几何形状的移动接触线的两相流。同时，变密度两相流的时间二阶精度的数值方法的设计仍然是一个挑战。我们发展了几种拟不可压缩两相流Navier-Stokes-Cahn-Hilliard模型的二阶精度数值格式。并且这些数值格式可以保持质量守恒或能量耗散定律。本项目还推导了一种与热力学定律相容的相场模型，用于模拟流动条件下囊泡的运动和形状变化。特别地，一般滑动边界条件用于描述囊泡与流体域壁之间的相互作用。我们也提出了一个时间和空间均为二阶精度的有限元方法来求解模型控制方程。此外，我们也探讨了各类相关的流体模型的渐近解、多解、稳定性以及提出或推广一些新的差分、有限元、格子Boltzmann方法等等。