随着对不可压复杂流动研究的不断深入，工程界对准确预测复杂流动提出了更高的要求，大涡模拟是有希望实现复杂流动准确预测和控制的有效途径。有限体积法具有很好的质量、动量和能量守恒性，且对复杂边界的处理比较容易。但现有大多数有限体积法只有二阶精度，限制了真正意义上的大涡模拟的实现，制约了其工程实用价值。因此，本文的目的是建立高精度有限体大涡模拟方法，为了适应复杂边界流动的计算，基本方程和数值计算建立在一般曲线坐标系中。本文主要的研究工作成果包括：一、建立了高精度有限体大涡模拟方法，在非交错网格上离散大涡模拟不可压缩N-S方程组，空间离散采用有限体四阶紧致格式，时间推进用四阶Runge-Kutta格式，压力-速度耦合应用四阶紧致动量插值，亚格子应力采用动力Smagorinsky模式，代数方程组求解运用强隐迭代法。通过求解有精确解的二维驱动方腔流动和振荡平板上方流动，验证了该方法具有近四阶精度；二、应用本文提出的数值方法，对三维顶盖驱动方腔流动、槽道湍流流动和有分离的后台阶流动三个典型算例进行了大涡模拟计算，并用较少的网格得到了与文献上直接数值模拟定量吻合的结果。表明本文方法具有计算精度高、计算网格少、适应能力强和预报准确性高的优点。三、针对大涡模拟的复杂边界处理问题，采用浸没边界法，对弯槽湍流流动和NACA0012翼型绕流流动两个经典问题进行了高精度有限体大涡模拟计算，得到与DNS和实验一致的结果，表明本文方法与浸没边界法结合可有效地模拟曲面边界等复杂流动。说明该方法具有边界处理简单的优点，为准确高效地预测复杂流动打下了基础，对湍流大涡模拟方法在工程领域的应用和发展具有重要意义。四、应用本文建立的高精度有限体大涡模拟数值方法对可逆式水泵水轮机转轮内单流道流动进行了模拟计算，得到了不同工况下的合理结果。总之，算例证明本文的方法可用于流体机械的复杂内流计算。
More accurate prediction of complex flows is demanded in engineering practice as the research of incompressible complex flows has been developed considerably. Large eddy simulation (LES) is believed to be a potential prediction method for complex turbulent flows in foreseeable future. The finite volume method (FVM) possesses good property of mass, momentum and energy conservation and it is also easy to deal with complex boundaries. However, most of the existing finite volume methods for LES are of second order accuracy. Therefore, the purpose of the present study is to construct a finite volume method with high accuracy for LES. For accommodation with complex flow configuration, the governing equations and numerical scheme are established in general curvilinear coordinates. The major achievements of the thesis are:1. A finite volume method with high accuracy for LES is established. The filtered Navier-Stokes equation is solved numerically on non-staggered grids by the finite volume with fourth-order-accurate compact scheme for spatial discretization and fourth-order Runge-Kutta integration for time advancement. The coupling between pressure and velocity is handled by the momentum interpolation method with a fourth-order-accurate compact scheme. The dynamic Smagrorinsky model is used for the subgrid stress and the discretized equations are solved by SIP method. The numerical accuracy is checked by the two-dimensional lid-driven cavity flow and the flow over an oscillating plate. It is evaluated that the proposed method is of fourth-order accuracy approximately.2. The numerical simulations of a three-dimensional lid-driven cavity flow, a turbulent channel flow and a turbulent flow over a backward facing step are performed successfully by the proposed method. Results are in good agreement with DNS data in coarse girds. It is concluded that the proposed method has the advantages of higher accuracy, less grids and lower computing cost.3. To deal with flows with complex configuration the immersed boundary method (IBM) is used to satisfy the boundary condition on the rigid wall. A curved channel flow and a flow around an airfoil of NACA0012 are computed with immersed boundary method. The results are consistent with experiment and DNS data and validate the feasibility of immersed boundary method. It is concluded that the proposed method is a powerful approach to precisely simulate the flow fields with complex configurations.4. The proposed high order accurate finite volume method for LES is applied to simulate the flow in a reversible pump-turbine runner with satisfaction. Based on it, we can perfect the program for fine calculation of inner flow fields of fluid machinery.In summary, the numerical examples performed in the thesis give strong evidence that the proposed method can be used to compute complex inner flows of fluid machinery.
