利用非结构化网格方法对翼型绕流的数值研究

利用同位非结构化网格上的压力加权修正算法 ,对翼型湍流绕流进行了数值分析。详细地给出了一孤立翼型在不同攻角下的分离流结构及翼型表面压力分布 ,为了显示非结构化网格方法在求解多连通流动区域的优越性 ,对双翼型绕流进行了数值计算。在数值分析中 ,对阵面推进法进行改进来生成三角形网格 ,采用有限控制体方法直接在物理空间中的非结构化网格单元上离散 Navier- Stokes方程及 k- ε方程 ,形成的代数方程组通过预条件矩阵共轭梯度平方法求解。计算结果表明 :当流动为附着流时 ,计算结果与实验值吻合程度令人相当满意 ;而在分离区内 ,计算结果与实验值存在一定的误差 ,需对分离区内的湍流模型做进一步的改进。     

An Approach to Transport in Heterogeneous Porous Media Using the Truncated Temporal Moment Equations: Theory and Numerical Validation

In the last decade, the characterization of transport in porous media has benefited largely from numerical advances in applied mathematics and from the increasing power of computers. However, the resolution of a transport problem often remains cumbersome, mostly because of the time-dependence of the equations and the numerical stability constraints imposed by their discretization. To avoid these difficulties, another approach is proposed based on the calculation of the temporal moments of a curve of concentration versus time. The transformation into the Laplace domain of the transport equations makes it possible to develop partial derivative equations for the calculation of complete moments or truncated moments between two finite times, and for any point of a bounded domain. The temporal moment equations are stationary equations, independent of time, and with weaker constraints on their stability and diffusion errors compared to the classical advection–dispersion equation, even with simple discrete numerical schemes. Following the complete theoretical development of these equations, they are compared firstly with analytical solutions for simple cases of transport and secondly with a well-performing transport model for advective–dispersive transport in a heterogeneous medium with rate-limited mass transfer between the free water and an immobile phase. Temporal moment equations have a common parametrization with transport equations in terms of their parameters and their spatial distribution on a grid of discretization. Therefore, they can be used to replace the transport equations and thus accelerate the achievement of studies in which a large number of simulations must be carried out, such as the inverse problem conditioned with transport data or for forecasting pollution hazards.