非线性多相多体流固耦合的粘性水弹性数值方法研究

By developing the approach of multiphase in CFD and the theory modelling multibody, the proposal attempts to break through the nonlinear dissipation method for two-phase flow and a moving mesh technique in the fluid-solid interaction within the traditional framework, according to problems involving viscous hydroelasticity in multiphase-multibody interaction. A novel sharp interface method for two-phase flow in this proposal is put forward, that is used to reveal the mechanism of viscous hydroelasticity for gas-liquid-solid multiphase flow under various environments in deep sea, and a multibody cut-cell finite volume method is also developed. Firstly, the cut-cell grid finite volume method over fixed Cartesian grids is focused, which helps to capture the complex movements of multibody at high Reynolds number. A major character is not necessary to reconstruct grid but to maintain the conservation of mass and geometry. Secondly, the sharp interface method proposed can effectively solve a nonlinear two-phase flow with a large ratio of liquid to air, by satisfying the jump conditions at the interface over virtual grids. Based on the radial basic function, finally, an approach of level set for constructing implicit interface with multibody is designed, including interpolation technique about a boundary data, the code for dynamic response in structure and the 3D model for super-thin flexible structures. The relevant theory and numerical method developed will enhance the CFD platform with self-core technology and open a new method for the solution of the Navier-Stokes equation.

针对多相多体的粘性水弹性问题，本项目旨在突破传统框架下求解非线性两相流的耗散法及流固耦合的动网格技术，通过发展现代CFD技术及复杂多体运动的建模理论，提出一种尖锐界面两相流法及多体切割网格有限体积法，揭示多种深远海环境下气液固多相流的粘性水弹性机理。首先，强调固定笛卡尔网格下的多体切割网格有限体积法，描述高雷诺数下复杂多体运动，网格无需重构，维持质量与几何守恒。其次，以尖锐界面法，借助于传递边界跳跃条件的虚拟网格，求解大密度比非线性两相流。最后，开发基于径向基函数的Level Set多体隐式界面构造法与边界数据插值技术，以及结构动力响应的计算程序和超细长柔性3D计算模型。相关理论及数值方法，形成自主创新核心技术CFD平台，开发了一种新的求解Navier-Stokes方程的数值方法。

本课题按照项目申报书的相关研究内容，以尖锐界面建模与数值方法、分区双向耦合粘性水弹性方法为研究对象，重点围绕“尖锐界面气液固多相耦合建模与方法”，“粘性水弹性理论与方法”两个关键科学基础问题开展研究，在CFD/CSD前沿技术的框架下，通过发展现代代数类型VOF算法、尖锐界面多相流法，创建了尖锐界面气液固多相流数学模型，提出了虚拟模式尖锐界面VOF多相流法，开发了绝对节点坐标下有限元法，形成具有自主原创、自主核心技术的多相流大涡模拟CFD平台，具有自主知识产权的粘性水弹性CFD/CSD平台，突破传统框架下基于连续耗散法研究气液/固液两相流问题、基于动网格技术研究流固耦合问题，解决多数著名NVD系列算法内在的局部极值消减局限性，完成了项目任务书预期的研究目标，为研究海洋环境下多体多相粘性水弹性问题，提供新的理论、方法和模拟手段。.针对构建多相流大涡模拟CFD平台，以虚拟流体方法、尖锐界面方法、TVD/NVD限制器的交叉理论为基础，结合发展现代代数类型VOF算法、人工数值耗散技术、TVD/NVD格式通量限制器等，提出高分辨率格式虚拟模式尖锐界面两相流法，发展气液两相流间断解含局部极值的自适应加权修正下风高精度格式。.针对开发粘性水弹性平台，以虚拟网格法、绝对节点坐标有限元法的交叉理论为基础，引入径向基函数技术、梯度增量Level-set方法，开发了径向基函数重构虚拟网格动边界条件技术。.通过试验及标模，结果分析表明，本项目建立数学模型、提出数值方法是可行及精确的。在本项目支撑下，重要国际会议上发表7篇论文，重要国内会议上发表1篇论文，国内外期刊上发表5篇论文，软件著作权6项，培养硕博研究生共计13名。.本项目主要工作内容包括：.①建立含多切割体动质量力模型的尖锐界面气液固多相流五方程数学模型；.②发展基于TVD通量限制器的高效切割网格高精度格式；.③提出高分辨率格式虚拟模式尖锐界面气液两相流方法；.④开发基于绝对坐标有限元法CFD/CSD平台。