本文由两大部分组成。 第一部分是对潮汐流动中垂向排放近区的数值模拟，这是水环境污染问题中的前沿研究课题，并具有重大实际应用价值，本文选用K-ε双方程紊流模型，以Spalding 和Patankar 提出的SIMPLE方法为基础，对自由水面采用“准”刚盖假设，建立了潮汐流动中垂向排放近区的数值模型。根据潮汐流往复回荡的特点，提出了代数方程组的“跟踪”扫描逐行求解方法。对不同周期情况下的射流流场、浓度场的变化过程进行了数值计算；对回流区的形成、浓度极值线位置、紊动动能K、紊动耗散率ε及紊动粘性系数Νt的分布和主回流区相对高度Hc/H、主回流区形态α(=Hc/Lc)等随潮汐流速或动量比参数(Vj/Uin)2B/H的变化规律进行了系统分析，讨论了非恒定性的影响，获得了一些有益的结果。 本文第二部分对优化差分方法进行了探讨，具有较高的理论研究和应用价值。本文在该部分提出了一维含源抛物型方程、对流扩散方程及二维泊松方程、Navier-Stokes方程的优化差分方法，其精度均可达o(h4)，泊松方程的可高达o(h6)。文中对这些方程优化差分格式精度匹配问题、源项优化差分系数的确定方法及源项处理对计算精度及收敛性的影响等问题进行了研究。数值实践表明，本文提出这些方程的优化差分方法具有精度高、计算省时和收敛速度快等特点。
The thesis consists of two parts:A. The first is on numerical simulation for the near field fo vertical disarranges into tidal flows, which is the frontier research subject in water environment and has great value in its practical application. Based on STMPLE method proposed by Spalding and Patanka. The mathematical model for the problem is established, in which a K-εtwo equation turbulent model is used and quasi-rigid-lip approximation of free surface is made. According to the oscillation features of tidal flows, a trake-sweep line by line method for solution of a set of algebraic equations corresponding to the problem is presented in the paper. Numerical calculations are done on the process of velocity fields and concentration fields under different periodical conditions. With the change of tidal flows or momentum ratio parameter (Vj/Uin)2B/H, a systematic analysis is carried out of evolution of recalculation regions, position of maximum concentration line, distributions of turbulent Kinetic energy K, turbulent dissipation rate εand turbulent viscosity νt, relative height Hc/H and shap parameterα(=Hc/Lc) of main recalculation region, etc. The effects of unsteadiness is also discussed, and some profitable results are obtained in this part.B. The second is on the optimal difference method, which are of particular value in therotical research and their application. In this part, the optimal difference methods for 1-D parabolic equations with source terms, advection-diffusion equations, 2-D poison equations and Navier-Stokes equations are put forward. All the solutions can achieve the forth order accuracy o(h4), among them the solution of Poison equation can be particularly as accurate as o(h6). The mathematical deductions arte given in detail to set for the optimal difference schemes for the above equations. The accuracy match between the schemes of boundary notes and inner notes, the method determine the optimal difference coefficients as well as the effects of treatment will source terms on calculation accuracy and convergecy are all studied. The mathematical analysis and numerical tests indicate that the method mentioned in this part have some advantages, such as higher accuracy, shorter computing time and faster convergecy.
