运动界面模拟技术及在环境分层流问题中的应用
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摘要
自然环境水体中的分层流动通常是由温度、主动输运物质(如盐度、泥沙等)或者它们的组合作用诱导产生的。由于各组分对水体密度的贡献以及其自身的扩散特性的差异使得该类分层流动更为复杂。本文从两流体的角度，采用Level Set方法追踪两流体分层界面的运动，对每相流体分别求解，并考虑界面处两流体间的相互作用，模拟了污水排海等分层流问题，详细阐述了海水入侵过程和机理。本文研究的主要成果包括：
(1)采用Level Set方法追踪界面的时空变化。本文基于快速行进法和源点扫描法的思想，提出了非结构同位网格下Level Set的实现策略。并通过实例，对Level Set法与VOF法作了比较分析。
(2)界面附近网格点密度、扩散系数等物理参数处理，二维三维采用了不同的策略。对二维情形，根据符号距离函数精确计算各网格单元的相体积分布，而后可计算网格单元的密度和扩散系数；对三维情形，直接采用正弦函数光滑处理。对于界面物理量的扩展采用一阶的isobaric fix ghost处理。
(3)将密度方程和动量方程统一成一个积分方程，采用梯度重构策略，结合限制器，改进了两流体的SIMPLE(SIMPLEC)算法和人工压缩算法，建立了非结构网格下N-S方程的求解系统。改进了出口边界的处理策略，能有效地处理“无反射”出口边界问题。对不同的密度比的两流体系统进行了验证分析。
(4)建立了κ-ε紊流模型，壁面采用对数率壁函数处理技术。
(5)从两流体角度对污水排海问题建立了二维和三维数学模型，详细探讨了污水排海工程中海水入侵的机理。
Stratified flows are often induced by single component (e.g. temperature, active scalars) or multi-components in natural water body. Multi-components caused complicated flow characteristics of stratified flows due to the difference of their own diffusion and component's contribution to water density. In the paper, the Level Set Method is applied to track the moving interface between two fluids and every phase is calculated respectively combined the interface effects. Finally, Sewage outfall problem is simulated by 2D and 3D system based the paper, and the process and mechanism of the saline intrusion is explained. The main works of the paper include as follows:
(1) To track the moving interface,the Level Set Method is applied in the paper. Under the unstructured grids system, the method is studed and established based the idea of Fast Marching Method and Source Point Scanning Method, and then the Level Set Method is compared with the VOF Method based a given example.
(2) On the paremeters of the cell near the interface between the two fluids, such as the density and diffusion coefficient, etc. in the paper, two different methods is studied. To the 2D problem, the volume of phase fluids can be calculated from sign distance function,and then the paremeters can be acquired also; To the 3D problem, the paremeters are dealed smothly using sinusoid. Finally ,the method of isobaric fix ghost is applied to extend the variable of the cell near the interface.
(3) In the paper, the density-equation and momentum-equation are unified as a integral style by transforming the momentum-equation, and then the equations are dispersed under unstructured grids with the use of reconstruction of grads and superbee limiter. SIMPLE(SIMPLEC) Method and Artificiale Compressibility Method are improved to solve the pressure-velocity coupling . The problem of outlet boundary is studied in the paper, and some technique are put forward to deal the free boundary. Finally , some example are given to test the technique.
(4) In the paper, the standard k-εturbulence model is established with Wall Functions dealing the flow near walls.
(5) Finally, Sewage outfall problem is simulated by 2D and 3D system based the paper, and the process and mechanism of the saline intrusion is explained.
(1)采用Level Set方法追踪界面的时空变化。本文基于快速行进法和源点扫描法的思想，提出了非结构同位网格下Level Set的实现策略。并通过实例，对Level Set法与VOF法作了比较分析。
(2)界面附近网格点密度、扩散系数等物理参数处理，二维三维采用了不同的策略。对二维情形，根据符号距离函数精确计算各网格单元的相体积分布，而后可计算网格单元的密度和扩散系数；对三维情形，直接采用正弦函数光滑处理。对于界面物理量的扩展采用一阶的isobaric fix ghost处理。
(3)将密度方程和动量方程统一成一个积分方程，采用梯度重构策略，结合限制器，改进了两流体的SIMPLE(SIMPLEC)算法和人工压缩算法，建立了非结构网格下N-S方程的求解系统。改进了出口边界的处理策略，能有效地处理“无反射”出口边界问题。对不同的密度比的两流体系统进行了验证分析。
(4)建立了κ-ε紊流模型，壁面采用对数率壁函数处理技术。
(5)从两流体角度对污水排海问题建立了二维和三维数学模型，详细探讨了污水排海工程中海水入侵的机理。
Stratified flows are often induced by single component (e.g. temperature, active scalars) or multi-components in natural water body. Multi-components caused complicated flow characteristics of stratified flows due to the difference of their own diffusion and component's contribution to water density. In the paper, the Level Set Method is applied to track the moving interface between two fluids and every phase is calculated respectively combined the interface effects. Finally, Sewage outfall problem is simulated by 2D and 3D system based the paper, and the process and mechanism of the saline intrusion is explained. The main works of the paper include as follows:
(1) To track the moving interface,the Level Set Method is applied in the paper. Under the unstructured grids system, the method is studed and established based the idea of Fast Marching Method and Source Point Scanning Method, and then the Level Set Method is compared with the VOF Method based a given example.
(2) On the paremeters of the cell near the interface between the two fluids, such as the density and diffusion coefficient, etc. in the paper, two different methods is studied. To the 2D problem, the volume of phase fluids can be calculated from sign distance function,and then the paremeters can be acquired also; To the 3D problem, the paremeters are dealed smothly using sinusoid. Finally ,the method of isobaric fix ghost is applied to extend the variable of the cell near the interface.
(3) In the paper, the density-equation and momentum-equation are unified as a integral style by transforming the momentum-equation, and then the equations are dispersed under unstructured grids with the use of reconstruction of grads and superbee limiter. SIMPLE(SIMPLEC) Method and Artificiale Compressibility Method are improved to solve the pressure-velocity coupling . The problem of outlet boundary is studied in the paper, and some technique are put forward to deal the free boundary. Finally , some example are given to test the technique.
(4) In the paper, the standard k-εturbulence model is established with Wall Functions dealing the flow near walls.
(5) Finally, Sewage outfall problem is simulated by 2D and 3D system based the paper, and the process and mechanism of the saline intrusion is explained.
引文
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