利用GPU实现基于物理模型的流体运动仿真

纳维-斯托克斯方程是描述流体运动的基础物理模型。首先简要介绍了在计算机上实现该模型的数值解算方法。在流体运动的计算机视觉仿真中,密度渲染才是最终结果,因此,又阐述了流体的密度场与速度场的关系,并且给出了流体仿真的基本流程。由于可编程图形处理器(GPU)具有并行性和速度快等特点,流体模拟的解算和渲染在图形处理器上运行更加高效,但是利用GPU编程实现流体仿真必须要实现3个核心转换,最后以支持3维纹理的Direct3D10为例,给出了利用GPU实现流体运动仿真两个简单实例。     

Computational fluid dynamics modeling of abutment scour under steady current using the level set method

The scour and deposition pattern around an abutment under constant discharge condition is calculated using a three dimensional (3D) Computational Fluid Dynamics (CFD) model. The Reynolds-Averaged Navier Stokes (RANS) equations are solved in three dimensions using a CFD model. The Level Set Method (LSM) is used for calculation of both free surface and bed topography. The two-equation turbulence model (k-ε and k-ω) is used to calculate the eddy viscosity in the RANS equations. The pressure term in the RANS equations on a staggered grid is modeled using the Chorin's projection method. The 5th order Weighted Essentially Non-Oscillatory (WENO) scheme discretizes the convective term of the RANS equations. The Kovacs and Parker and Dey formulations are used for the reduction in bed shear stress on the sloping bed. The model also used the sandslide algorithm which limits bed shear stress reduction during the erosion process. The numerical model solution is validated against experimental results collected at the Politecnico di Milano, Milan, Italy. Further, the numerical model is tested for performance by varying the grid sizes and key parameters like the space and time discretization schemes. The effect of varying bed porosity has been evaluated. Overall, the free surface is well represented in a realistic manner and bed topography is well predicted using the Level Set Method (LSM).     

Numerical modeling of lock-exchange gravity/turbidity currents by a high-order upwinding combined compact difference scheme

This study presents two-dimensional direct numerical simulations for sediment-laden current with higher density propagating forward through a lighter ambient water.The incompressible NavierStokes equations including the buoyancy force for the density difference between the light and heavy fluids are solved by a finite difference scheme based on a structured mesh.The concentration transport equations are used to explore such rich transport phenomena as gravity and turbidity currents.Within the framework of an Upwinding Combined Compact finite Difference(UCCD)scheme,rigorous determination of weighting coefficients underlies the modified equation analysis and the minimization of the numerical modified wavenumber.This sixth-order UCCD scheme is implemented in a four-point grid stencil to approximate advection and diffusion terms in the concentration transport equations and the first-order derivative terms in the Navier-Stokes equations,which can greatly enhance convective stability and increase dispersive accuracy at the same time.The initial discontinuous concentration field is smoothed by solving a newly proposed Heaviside function to prevent numerical instabilities and unreasonable concentration values.A two-step projection method is then applied to obtain the velocity field.The numerical algorithm shows a satisfying ability to capture the generation,development,and dissipation of the Kelvin-Helmholz instabilities and turbulent billows at the interface between the current and the ambient fluid.The simulation results also are compared with the data in published literatures and good agreements are found to prove that the present numerical model can well reproduce the propagation,particle deposition,and mixing processes of lock-exchange gravity and turbidity currents.     

三棱柱形网格下自由表面流的三维数值模拟

为了模拟自由表面流动问题,建立了基于三棱柱形网格的三维Navier-Stokes方程的半隐式动压离散模型。出流边界采用在动量方程右端附加线性衰减项的海绵层处理方式来消减波能。引入k-ε双方程紊流模型求解涡黏性系数,使方程达到封闭。用规则周期波通过淹没障碍物的传播变形和复合明渠流动算例,验证了当遇到短波高频问题时,所述模型模拟结果与测量值吻合良好,体现了模型的精确性和有效性。     

等效水力隙宽和水力梯度对岩体裂隙网络非线性渗流特性的影响

等效水力隙宽和水力梯度是影响岩体裂隙网络渗流特性的重要因素。制作裂隙网络试验模型,建立高精度渗流试验系统;求解纳维-斯托克斯方程,模拟流体在裂隙网络内的流动状态,研究等效水力隙宽和水力梯度对非线性渗流特性的影响。结果表明,当水力梯度较小时,等效渗透系数保持恒定的常数,流体流动属于达西流动区域,流量与压力具有线性关系,可采用立方定律计算流体流动;当水力梯度较大时,等效渗透系数随着水力梯度的增加而急剧减少,流体流动进入强惯性效应流动区域,流量与压力具有强烈的非线性关系,可采用Forchheimer方程计算流体流动。随着等效水力隙宽的增加,区别线性和非线性流动区域的临界水力梯度呈幂函数关系递减。当水力梯度小于临界水力梯度时,控制方程可选立方定律;当水力梯度大于临界水力梯度时,控制方程可选Forchheimer方程,其参数A和B可根据经验公式计算得到。其研究结果可为临界水力梯度的确定及流体流动控制方程的选取提供借鉴意义。     

Propagation of water waves over permeable rippled beds

Unsteady two-dimensional Navier-Stokes equations and Navier-Stokes type model equations for porous flow were solved numerically to simulate the propagation of water waves over a permeable rippled bed. A boundary-fitted coordinate system was adopted to make the computational meshes consistent with the rippled bed. The accuracy of the numerical scheme was confirmed by comparing the numerical results concerning the spatial distribution of wave amplitudes over impermeable and permeable rippled beds with the analytical solutions. For periodic incident waves, the flow field over the wavy wall is discussed in terms of the steady Eulerian streaming velocity. The trajectories of the fluid particles that are initially located close to the ripples were also determined. One of the main results herein is that under the action of periodic water waves, fluid particles on an impermeable rippled bed initially moved back and forth around the ripple crest, with increasing vertical distance from the rippled wall. After one or two wave periods, they are then lifted towards the next ripple crest. All of the marked particles on a permeable rippled bed were shifted onshore with a much larger displacement than those on an impermeable bed. Finally, the flow fields and the particle motions close to impermeable and permeable beds induced by a solitary wave are elucidated.     

三维交叉裂隙渗流传质特性数值模拟

对交叉裂隙渗流传质特性的定量描述是研究整个裂隙网络渗透传质特性的基础。为真实模拟水流及溶质在三维交叉裂隙中的运移过程,首先通过三维轮廓仪获取天然岩石裂隙表面的形貌数据,再应用三维重构技术生成相应的三维交叉裂隙模型,随后求解Navier-Stokes方程,假定溶质运移满足Fick定律,模拟水流和溶质在三维交叉裂隙中的运移过程。通过对比粗糙裂隙模型与平行平板模型的模拟结果发现：粗糙度对流体的分布及流动状态存在显著的影响;不同进、出口工况下的流体流动及溶质运移状态亦表明：裂隙交叉的几何形貌会显著地影响溶质混合行为。这些结果表明,目前被广泛采用的平行平板模型在评估岩体内特别是交叉口的物质运移特性时将导致较大的偏差,在将来的研究中有必要针对裂隙交叉口的几何特征建立修正的模型以提高评估的准确性。     

A Finite Element Solution of Wave Forces on Submerged Horizontal Circular Cylinders

In this paper, a numerical model is established for estimating the wave forces on a submerged horizontal circular cylinder. For predicting the wave motion, a set of two-dimensional Navier-Stokes equations is solved numerically with a finite element method. In order to track the moving non-linear wave surface boundary, the Navier-Stokes equations are discretized in a moving mesh system. After each computational time step, the mesh is modified according to the changed wave surface boundary. In order to stabilize the numerical procedure, a three-step finite element method is applied in the time integration. The water sloshing in a tank and wave propagation over a submerged bar are simulated for the first time to validate the present model. The computational results agree well with the analytical solution and the experimental data.Finally, the model is applied to the simulation of interaction between waves and a submerged horizontal circular cylinder.The effects of the KC number and the cylinder depth on the wave forces are studied.     

Steady streaming around a circular cylinder in an oscillatory flow

Steady streaming induced by an oscillatory flow around a circular cylinder is investigated using a numerical method. Two-dimensional Reynolds-averaged Navier-Stokes equations are solved using a finite element method with a k-ω turbulent model closure. The range of the Keulegan-Carpenter (KC) number investigated is between 2 and 40, which is substantially higher than those reported in literature related to steady streaming to date. A constant value of Stokes number (β) of 196 is chosen in this study. The steady streaming structures and velocity distribution are analysed in detail. It is found that the characteristics of steady streaming are strongly related to the vortex shedding flow regimes.