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。

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.