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首页> 外文期刊>International Journal for Numerical Methods in Fluids >SEMI-IMPLICIT FINITE VOLUME SHALLOW-WATER FLOW AND SOLUTE TRANSPORT SOLVER WITH k- TURBULENCE MODEL
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SEMI-IMPLICIT FINITE VOLUME SHALLOW-WATER FLOW AND SOLUTE TRANSPORT SOLVER WITH k- TURBULENCE MODEL

机译：k湍流模型的半隐式有限体积浅水流和溶质运移求解器

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摘要

A 3D semi-implicit finite volume scheme for shallow- water flow with the hydrostatic pressure assumption has been developed using the -co-ordinate system, incorporating a standard k- turbulence transport model and variable density solute transport with the Boussinesq approximation for the resulting horizontal pressure gradients. The mesh spacing in the vertical direction varies parabolically to give fine resolution near the bed and free surface to resolve high gradients of velocity, k and . In this study, wall functions are used at the bed (defined by the bed roughness) and wind stress at the surface is not considered. Surface elevation gradient terms and vertical diffusion terms are handled implicitly and horizontal diffusion and source terms explicitly, including the Boussinesq pressure gradient term due to the horizontal density gradient. The advection terms are handled in explicit (conservative) form using linear upwind interpolation giving second-order accuracy. A fully coupled solution for the flow field is obtained by substi- tuting for velocity in the depth-integrated continuity equation and solving for surface elevation using a conjugate gradient equation solver. Evaluation of horizontal gradients in the -co-ordinate system requires high-order derivatives which can cause spurious flows and this is avoided by obtaining these gradients in real space. In this paper the method is applied to parallel oscillatory (tidal) flow in deep and shallow water and compared with field measurements. It is then applied to current flow about a conical island of small side slope where vortex shedding occurs and velocities are compared with data from the laboratory. Computed concentration distributions are also compared with dye visualization and an example of the influence of temperature on plume dispersion is presented.
机译：使用-坐标系，开发了带有静水压假设的浅水流动的3D半隐式有限体积方案，该方案将标准k-湍流输运模型和可变密度溶质输运与Boussinesq近似相结合，从而得到了水平压力梯度。垂直方向上的网格间距呈抛物线形变化，以在床层和自由表面附近提供高分辨率，从而解决速度k和k的高梯度。在这项研究中，在床处使用墙函数（由床的粗糙度定义），并且不考虑表面的风应力。隐式处理表面高程梯度项和垂直扩散项，并显式处理水平扩散项和源项，包括由于水平密度梯度而产生的Boussinesq压力梯度项。平流项使用线性逆风插值以显式（保守）形式处理，从而提供二阶精度。通过用深度积分的连续性方程式替换速度，并使用共轭梯度方程式求解器求解表面高程，可获得流场的完全耦合解。在-坐标系中评估水平梯度需要高阶导数，这些导数可能会导致杂散流，这可以通过在实际空间中获得这些梯度来避免。本文将该方法应用于深水和浅水中的平行振荡（潮汐流），并与现场测量结果进行了比较。然后将其应用于围绕小边坡的圆锥形岛的电流，在该岛上会发生涡旋脱落，并将速度与实验室数据进行比较。还将计算出的浓度分布与染料可视化进行了比较，并给出了温度对羽流分散性影响的示例。

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