基于曲线网格高精度格式的不可压缩两相流动快速求解方法

Co-exist of high density-ratio fluid and complex boundary for the two-phase flow problems in naval architecture and ocean engineering brings great challenge for the computational efficiency, numerical accuracy and stability. Compared with other high-order methodologies, the dimension-wise high-order finite difference method is computationally more efficient, together with the curvilinear mesh coordinate transformation, highly accurate discretization for momentum equation can be made. However, the accuracy-degrading and low-numerical-instability may be induced by a non-smooth curvilinear mesh. Since the convergence speed of traditional iterative method is sensitive to the mesh distortion and high density-ratio, the scalability for large scale parallel computation is limited. Following research emphasizes are scheduled to overcome the difficulties of two-phase flow simulation in complex mesh. At first, the highly accurate coordinate transformation satisfying geometric conservation law will be established for discretization of governing equation; then isolating approach for the variation-coefficients induced by both the density difference and curvilinear mesh will be proposed; afterwards, a suite of approaches for solving the two-phase flow problems based on high-order curvilinear finite difference method and fast Fourier transformation will be formulated; after development of the target simulator, numerical accuracy and reliability will be validated by physical experiment of typical two-phase flow problems.

船舶与海洋工程两相流动问题中大密度比流体和复杂边界的存在，对数值模拟的精度、效率、稳定性提出了很大挑战。相比其他高精度方法，逐维推进的高阶差分格式计算量较小，结合曲线网格坐标变换方法可用于动量方程的高精度离散，但该方法在计算网格不光滑时计算稳定性较差，且存在明显的精度降阶；除此之外，传统求解压力方程的迭代方法收敛速度较慢且易受网格畸变、流体密度比等因素的影响，对大规模并行计算的可扩展性欠佳。针对在复杂网格下模拟大密度比两相流动的难题，本项目拟建立满足几何守恒律的高精度坐标变换方法用于离散两相流控制方程；发展兼顾流体大密度比和复杂曲线网格的变系数分离方法用于压力方程的快速求解；形成一套基于曲线网格高阶差分和压力方程快速傅里叶变换求解方法的两相流高性能计算解决方案；开发目标求解器并设计数值实验对典型两相流动问题进行求解精度和可靠性方面的检验。

船舶与海洋工程中存在大量的两相界面流动现象，比如甲板砰击上浪、船首尾兴波破碎等，这些复杂水气界面流动问题对船舶与海洋结构物的水动力学性能等产生重要影响。传统数值方法数值耗散较大，在处理大密度两相流动时仍面临计算稳定性差等问题。本项目以一般结构化网格为研究目标，提出了大密度比两相流质量-动量一致推进格式、两相流新压力梯度计算模式，开发了几何VOF界面捕捉方法等。上述方法可以应用于包括曲线网格、变间距直角网格、自适应直角网格等一般结构化网格。在方法研究的基础上，本项目针对全交错网格变量定义形式、结构化曲线网格的特点设计了高性能数值模拟软件框架，该软件框架提供求解器开发、运行必须的并行支撑环境，实现了串行化编程、并行化应用。在高性能数值模拟软件框架基础上开发了两相流求解器，并设计数值实验对主要求解模块进行求解精度和可靠性方面的检验。最后将求解器用于NACA机翼绕流水跃问题、平板高速拖曳问题、高Froude数方尾船尾流演化问题的精细化模拟，充分验证了求解器模拟大密度比两相流问题的精度和可靠性。本研究创新了基于一般结构化网格的大密度比气液两相流数值模拟方法，为船舶与海洋工程多尺度界面流动分析提供了强有力的研究工具，为后续模拟两相流边界层分离、两相湍流演化等提供了技术支撑。