带耗散三维不可压缩流体的数值模拟方法及其应用研究

Numerical simulation of the three-dimensional incompressible fluids is a fascinating subject and important content for the computational fluid mechanics, and it plays an important roles in the water conservancy , marine and the fluid engineering. For the dissipative fluid field, the research method of the numerical simulation in a three-dimensional excited tank is still very limited. The complex and dissipative flow fields, such as the complex laminar flow, vortex flow and the flow around a circular cylinder, have something to do with the boundary and the dissipative flow field in an excited tank, and this research results are still lack. For the three-dimensional，dissipative，incompressible fluids with a free surface in a tank, the algorithms and theories of the finite difference method for the incompressible potential flow equation, incompressible Euler equations and the incompressible Navier-Stokes equations are developed in this project, and the numerical simulations of the inviscid and viscous fluid field, vortex flow and the flow around a circular cylinider in a 3D excited tank are calculated. We can attain the hydrodynamic features of the wave elevation, vortex flow and the flow around a circular cylinder in an inviscid and viscous incompressible tank. The motion effect of the vortex flow and the flow around a circular cylinder will be explored in this research, so the research is of great significance to both the theory method and the practical application of the incompressible fluid with a free surface.

三维不可压缩流体的数值模拟是流体力学数值计算研究的热点和重要内容，在水利、海洋和流体工程等领域有着重要的应用。目前研究带耗散三维不可压缩流体的内部流场的数值模拟方法很少，特别是三维带耗散不可压缩流体的复杂层流、绕流和涡流等运动依赖于边界和内部耗散变化，这方面的研究滞后。针对带自由面的三维水槽不可压缩流体，本项目研究带耗散三维不可压缩流体的势流方程、不可压缩Euler方程与不可压缩Navier-Stokes方程的Crank-Nicolson有限差分方法的理论和算法，数值模拟带耗散三维受激励水槽和来流水道内粘性和无粘流体的内部流场、涡流、绕流等数值解。通过研究三维水槽内部不可压缩流体的流场水动力学性态，可获得在无粘和粘性条件下流体的自由面波高、流体的绕流场、涡场等水动力学性质，进一步获得三维水槽涡流、绕流等复杂流体的水动力学规律，对研究带自由面的不可压缩流体的理论、方法和实际应用具有重要的意义。

带耗散不可压缩流体流场的水动力学变化规律问题一直是流体力学数值计算研究的热点和重要内容，在水利、海洋和流体工程等领域有重要的应用，对水动力学理论及其规律的研究重要的理论与实际意义。本项目研究带耗散不可压缩流体的势流方程、不可压缩Navier-Stokes方程的Crank-Nicolson有限差分方法的理论和算法。数值模拟带耗散激励水槽和内部流场、涡流、绕流等数值解。 通过研究水槽内部不可压缩流体的流场水动力学性态，可获得在无粘和粘性条件下流体的自由面波高、流体的绕流场、涡场等水动力学性质，建立带耗散格林函数下的点源和源分布面板法，进一步获得在来流无界区域下的绕流等复杂流体的压力和波高等水动力学规律，对研究带自由面的不可压缩流体的理论、方法和实际应用具有重要的意义。