Computation of flow-induced motion of floating bodies

A computational procedure for the prediction of motion of rigid bodies floating in viscous fluids and subjected to currents and waves is presented. The procedure is based on a coupled iterative solution of equations of motion of a rigid body with up to six degrees of freedom and the Reynolds-averaged Navier–Stokes equations describing the two- or three-dimensional fluid flow. The fluid flow is predicted using a commercial CFD package which can use moving grids made of arbitrary polyhedral cells and allows sliding interfaces between fixed and moving grid blocks. The computation of body motion is coupled to the CFD code via user-coding interfaces. The method is used to compute the 2D motion of floating bodies subjected to large waves and the results are compared to available experimental data, showing favorable agreement.     

Axial eigenfunctions and inhomogeneous solutions for the three-dimensional Stokes system with an application to natural convection in a cylinder

This paper presents two contributions to the analysis of three-dimensional slow viscous flows in cylinders of circular section. First the vector axial eigenfunctions for this geometry, namely those that satisfy homogeneous boundary conditions on the flat end walls, are derived. Secondly a method is presented to find particular solutions to the inhomogeneous Stokes equations in this geometry. These new results, together with some results obtained earlier, are used to analyse slow natural convection in a vertical cylinder completely filled with a viscous liquid. The fluid motion is generated by the differential heating of the walls of the cylinder. The natural convection flow field is shown to be a superposition of an inhomogeneous field, the fields generated by the vector eigenfunctions and a Stokes flow field. A by-product of this work has been the identification of constraints on the boundary data that have to be satisfied in order for the eigenfunction expansions to work; this knowledge will be useful when attempts are made to prove the completeness of these Stokes flow eigenfunctions.Received: June 30, 2003; revised: February 26, 2004     

Axial eigenfunctions and inhomogeneous solutions for the three-dimensional Stokes system with an application to natural convection in a cylinder

This paper presents two contributions to the analysis of three-dimensional slow viscous flows in cylinders of circular section. First the vector axial eigenfunctions for this geometry, namely those that satisfy homogeneous boundary conditions on the flat end walls, are derived. Secondly a method is presented to find particular solutions to the inhomogeneous Stokes equations in this geometry. These new results, together with some results obtained earlier, are used to analyse slow natural convection in a vertical cylinder completely filled with a viscous liquid. The fluid motion is generated by the differential heating of the walls of the cylinder. The natural convection flow field is shown to be a superposition of an inhomogeneous field, the fields generated by the vector eigenfunctions and a Stokes flow field. A by-product of this work has been the identification of constraints on the boundary data that have to be satisfied in order for the eigenfunction expansions to work; this knowledge will be useful when attempts are made to prove the completeness of these Stokes flow eigenfunctions.     

MHD slow motion past a sphere

The slow motion of an incompressible, viscous electrically conducting fluid, in the presence of a uniform aligned magnetic field, past a sphere is studied. Solutions obtained by Chester, using Stokes’ approximations, and by Blerkom and Ludford, using Ossen’ approximations, are reviewed. Expressions for stream functions are obtained for MHD Stokes’ flow and Oseen’ flow respectively.     

A Hybrid Immersed Interface Method for Driven Stokes Flow in an Elastic Tube

We present a hybrid numerical method for simulating fluid flow through a compliant, closed tube, driven by an internal source and sink. Fluid is assumed to be highly viscous with its motion described by Stokes flow. Model geometry is assumed to be axisymmetric, and the governing equations are implemented in axisymmetric cylindrical coordinates, which capture 3D flow dynamics with only 2D computations. We solve the model equations using a hybrid approach: we decompose the pressure and velocity fields into parts due to the surface forcings and due to the source and sink, with each part handled separately by means of an appropriate method. Because the singularly-supported surface forcings yield an unsmooth solution, that part of the solution is computed using the immersed interface method. Jump conditions are derived for the axisymmetric cylindrical coordinates. The velocity due to the source and sink is calculated along the tubular surface using boundary integrals. Numerical results are presented that indicate second-order accuracy of the method.     

Meshless solution of two-dimensional incompressible flow problems using the radial basis integral equation method

The two-dimensional incompressible fluid flow problems governed by the velocity–vorticity formulation of the Navier–Stokes equations were solved using the radial basis integral (RBIE) equation method. The RBIE is a meshless method based on the multi-domain boundary element method with overlapping subdomains. It solves at each node for the potential and its spatial derivatives. This feature of the RBIE is advantageous in solving the velocity–vorticity formulation of the Navier–Stokes equations since the calculated velocity gradients can be used to compute the vorticity that is prescribed as a boundary condition to the vorticity transport equation. The accuracy of the numerical solution was examined by solving the test problem with known analytical solution. Two benchmark problems, i.e. the lid driven cavity flow and the thermally driven cavity flow were also solved. The numerical results obtained using the RBIE showed very good agreement with the benchmark solutions.     

黏性流体中运动界面上的速度分解

本文研究黏性流体与零厚度弹性材料界面上的耦合运动问题.利用沉浸边界法与时间步长法,半Lagrange离散法,对速度分解后的Stokes部分与正则部分进行求解,获得了关于耦合运动中二阶PDE求解的一般方法,推广了文献[14,15,18]的结果.     

SOIL EROSION AND DEGRADATION BASED ON SAND PARTICLES TRANSPORT CAUSED BY WIND BLOWING

Abstract In this paper, the effect of sand particles transport caused by wind blowing and its role in the land degradation and desertification process is considered. For the modeling of the 3D landscape, a grayscale height map has been used, the vegetation has been modeled using a Lindenmayer system, and the sand particles have been modeled as a 3D mesh‐free particles system. It was assumed that both the sand motion and the wind motion are incompressible continuum systems and their behavior follows the Navier–Stokes equations. To simulate the sand transport, the Navier–Stokes equations are discretized using the moving particle Semi‐implicit (MPS) method. Different types of revegetation patterns (windbreakers) have been used to show some effective measures preventing soils from erosion.     

基于双分数阶变分光流模型的运动目标检测方法

变分光流法是常用的运动目标检测方法,应用场景中的光照变化会极大影响现存变分光流法的稳定性及准确率,提出基于分数阶的变分光流模型来提高光照变化鲁棒性.该模型将分数阶导数同时应用于经典变分光流模型的数据项及平滑项中;根据图像的数据特征,采用图像函数及光流向量函数的有限离散二重分数阶导数近似拟合求导结果计算光流向量,进而将光...     

Stokes Flow Between Parallel Plates due to a Trausversely Moving End Wall

Consider the two-dimensional Stokes flow in a semi-infinitestrip of viscous fluid due to a transverse velocity of its endwall. This is an idealization of the motion in the asthenospheredue to a subducting slab. We give an iterative scheme for calculatingthe flow, prove existence and uniqueness, and obtain numericalapproximations, using developments of Teodorescu's method andan approximate solution of the infinite matrix equation arisingtherein. (Simple truncation to finite order is not good enough.)Our boundary conditions give rise to singularities which preventother known methods (including the original form of Teodorescu's)from working. The solution reveals how surprisingly good anapproximation its asymptotic forms near the corners and at infinityare in most of the flow field.     

Determination of the aeroelastic transfer functions for streamlined bodies by means of a Navier–Stokes solver

This paper proposes a method to determine the flutter derivatives of two-dimensional streamlined cylinders by means of a modified indicial approach adapted to a Navier–Stokes solver using an Arbitrary Lagrangian Eulerian formulation. The method relies on heave or pitch motion imposed onto the section according to smoothed-ramp time-histories and on the computational evaluation of the transient forces arising on the obstacle. Hence, the indicial transfer function relating the plate motion to the induced force in the frequency domain is obtained. Application to a flat plate of finite thickness and length is proposed. The steady viscous flow simulated around the motionless plate is compared with the well-known Blasius solution. The computed flutter derivatives are compared both with those obtained from the Theodorsen function in the frame of the thin airfoil theory and with those resulting from previous methods in the frame of the computational approach.     

固壁近旁Stokes流中粘性液滴的运动和变形

发展了一种模拟固壁近旁轴对称Stokes流中粘性液滴的运动和变形及直接计算固壁上应力的边界积分方法．用此方法对不同的液滴-固壁初始相对间距、粘度比、表面张力和浮力联合参数以及环境流动参数情况进行了数值实验．数值结果显示,由于环境流动和浮力的作用,随着时间的推进,液滴在轴向压缩,在径向拉伸．当环境流动的作用弱于浮力作用时,随着时间的推移,液滴上升并向上弯,固壁上由液滴运动所引起的应力不断减小．当环境流动的作用强于浮力作用时,随着时间的推移,液滴变得越来越扁．在这种情形,当大初始间距时,壁面上的应力随液滴的演变而增大;当小初始间距时,由环境流动、浮力及壁面对流动的较强作用的联合影响,此应力随液滴的演变而减小．由于液滴运动所引起的壁面应力的有效作用仅限于对称轴附近的一个小范围内,且此范围随液滴与固壁的初始间距增大而增大．应力的大小随初始间距增大而大为减小．表面张力对液滴变形有阻止作用．液滴粘性会减小液滴的变形和位置迁移．     

Semi‐invariant solutions of the Navier‐Stokes equations

We present new exact solutions and reduced differential systems of the Navier‐Stokes equations of incompressible viscous fluid flow. We apply the method of semi‐invariant manifolds, introduced earlier as a modification of the Lie invariance method. We show that many known solutions of the Navier‐Stokes equations are, in fact, semi‐invariant and that the reduced differential systems we derive using semi‐invariant manifolds generalize previously obtained results that used ad hoc methods. Many of our semi‐invariant solutions solve decoupled systems in triangular form that are effectively linear. We also obtain several new reductions of Navier‐Stokes to a single nonlinear partial differential equation. In some cases, we can solve reduced systems and generate new analytic solutions of the Navier‐Stokes equations or find their approximations, and physical interpretation.     

On some unsteady flows of a non-Newtonian fluid

Some properties of unsteady unidirectional flows of a fluid of second grade are considered for flows impulsively started from rest by the motion of a boundary or two boundaries or by sudden application of a pressure gradient. Flows considered are: unsteady flow over a plane wall, unsteady Couette flow, flow between two parallel plates suddenly set in motion with the same speed, flow due to one rigid boundary moved suddenly and one being free, unsteady Poiseuille flow and unsteady generalized Couette flow. The results obtained are compared with those of the exact solutions of the Navier–Stokes equations. It is found that the stress at time zero on the stationary boundary for the flows generated by impulsive motion of a boundary or two boundaries is finite for a fluid of second grade and infinite for a Newtonian fluid. Furthermore, it is shown that for unsteady Poiseuille flow the stress at time zero on the boundary is zero for a Newtonian fluid, but it is not zero for a fluid of second grade.     

Schwarz alternating domain decomposition approach for the solution of two‐dimensional Navier–Stokes flow problems by the method of approximate particular solutions

The method of approximate particular solutions (MAPS) is used to solve the two‐dimensional Navier–Stokes equations. This method uses particular solutions of a nonhomogeneous Stokes problem, with the multiquadric radial basis function as a nonhomogeneous term, to approximate the velocity and pressure fields. The continuity equation is not explicitly imposed since the used particular solutions are mass conservative. To improve the computational efficiency of the global MAPS, the domain is split into overlapped subdomains where the Schwarz Alternating Algorithm is employed using velocity or traction values from neighboring subdomains as boundary conditions. When imposing only velocity boundary conditions, an extra step is required to find a reference value for the pressure at each subdomain to guarantee continuity of pressure across subdomains. The Stokes lid‐driven cavity flow problem is solved to assess the performance of the Schwarz algorithm in comparison to a finite‐difference‐type localized MAPS. The Kovasznay flow problem is used to validate the proposed numerical scheme. Despite the use of relative coarse nodal distributions, numerical results show excellent agreement with respect to results reported in literature when solving the lid‐driven cavity (up to Re = 10,000) and the backward facing step (at Re = 800) problems. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 777–797, 2015     

用CT-VOF法在数值波试验槽中生成线性和非线性波

为渡水槽中波的模拟和传播提出了二维的数值模型．假设流动的流体为粘性、不可压缩的,并将Navier-Stokes方程和连续性方程作为控制方程．用标准的k-ε模型来模拟紊流流动;用交错网格的有限差分法,离散化Navier-Stokes方程;并用简化的标识和单元(SMAC)方法进行求解．使用活塞型波发生器生成并传播波;数值渡水槽的端部采用敞开式的边界条件．为了证明模型的有效性,进行了一些标准的试验,如顶盖驱动的方腔测试试验、单向的常速度场试验以及干燥河床上的溃坝试验．为了论证方法的性能及其精度,将所生成波的结果与已有波理论的结果进行比较．最后,采用群集技术(CT)生成网格,并提出最佳的网格生成条件．     

Homotopy analysis method for the heat transfer in a asymmetric porous channel with an expanding or contracting wall

The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the porous upper plate is investigated and an analysis is made to determine the heat and mass transfer. The unsteady Navier–Stokes equations are reduced to a generalization of the Proudman–Johnson equation retaining the effect of wall motion using a suitable similarity transformation. The analytical solution for stream function and heat transfer characteristics are obtained by employing homotopy analysis method. The effects of various physical parameters like expansion ratio, Prandtl number, Reynolds number on various momentum and heat transfer characteristics are discussed in detail.     

A Meshless Boundary Method for Computation of Stokes Flow with Particles in the Semicircular Canals of the Inner Ear

Benign paroxismal positional vertigo (BPPV) is modeled by introducing free-floating particles (canaliths) which settle inside the semicircular canals (SCC). The Stokes flow induced by a canalith is evaluated by coupling the force coupling method (FCM) to the method of fundamental solutions (MFS). The proposed methodology results in a straightforward meshless boundary method for the simulation of bounded Stokes flow with finite-size particles. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Internal Flow Analysis for Slow Moving Small Droplets in Contact with Hydrophobic Surfaces

Internal fluid flow behavior for slow moving small droplets in contact with hydrophobic surfaces is analyzed. The shape of the droplet is first computed using the Young-Laplace equation. For this purpose a Finite Element (FE) model [1], in which contact constraints are enforced through Penalty and Augmented Lagrange Multiplier methods, is used. The flow field within the droplet is then analyzed using the Stokes flow model, considering a de-coupled approach. Similar to the membrane deformation model, the formulation for the flow analysis is also expressed in the framework of FE analysis. Both, stabilized (Pressure Stabilizing/Petrov-Galerkin PSPG) and Galerkin FE formulations are considered. The motion of the fluid inside the droplet is governed by the slip condition enforced on the membrane of the droplet. Numerical examples for droplets rolling steadily are presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Singular forces in the immersed interface method for rigid objects in 3D

In the immersed interface method, a boundary immersed in a fluid is represented as a singular force in the Navier–Stokes equations. An explicit approach was proposed recently for determining the singular force for the boundary of a rigid object with prescribed motion in 2D [Sheng Xu, The immersed interface method for simulating prescribed motion of rigid objects in an incompressible viscous flow, J. Comput. Phys. 227 (2008) 5045–5071]. Necessary formulas for extending the approach to 3D are derived in this work. With the implementation of these formulas, the immersed interface method can accurately, stably, and efficiently simulate the prescribed motion of rigid objects in 3D.