Numerical solution of two-layer,two-dimensional tidal flow in a boundary-fitted orthogonal curvilinear co-ordinate system

A new two-layer, two-dimensional mathematical model employing a finite difference method based on numerically generated boundary-fitted orthogonal co-ordinates and a grid ‘block’ technique for unsteady boundary problems is developed which can be used to simulate flows with density stratification in a natural water-body with complicated topography. In the model the turbulent exchange across the interface is treated empirically and a time-splitting finite difference method with two fractional steps is employed to solve the governing equations. The model is calibrated and verified by comparing the computational results with data measured in Tolo Harbour, Hong Kong. The simulation results mimie the field measurements very closely. The computation shows that the model reproduces the two-layer, two-dimensional tidal flow with density stratification in Tolo Harbour very well. The computed velocity hodographs show that the tidal circulations at various positions in each layer have different patterns and that the features of the patterns are independent of the tidal type except for their scales. The computed Lagrangian pathlines show that the tidal excursion is dependent on the tidal type, especially in the inner harbour and side-coves.     

Numerical study of turbulent in-cylinder flow during motoring utilizing a general curvilinear coordinate system

A finite-volume numerical calculation method is presented to predict the flow field at unsteady, turbulent levels in a motoring reciprocating engine. An algebraic grid generation technique is used to map the complex fluid domain, on which the cylinder head is a deformed boundary, onto a rectangle for every time step. Hence the metric of the coordinate transformation can be determined by direct analytic differentiation. The model gives a good account of the axial, radial, and swirl velocity components and engine turbulence by means of a two-equation model of turbulence and wall functions. Effects of the shapes of both cylinder head and grid distribution on in-cylinder air motion are investigated.     

基于贴体网格的VOF方法数模流场研究

提出了一种基于VOF方法的模拟具有复杂边界形状结构物附近流场的新算法,BFC—SIMPLE—VOF算法。采用坐标变换方法实现了任意复杂区域的结构化网格划分,在贴体网格下对二维不可压缩粘性流体的控制方程进行了离散。提出了基于交错网格的修正SIMPLE算法来迭代求解压力一速度场,修正了贴体坐标下的界面跟踪方法（VOF方法）...     

A PLIC volume tracking method for the simulation of two‐fluid flows

Numerical methodologies for computer simulations of two‐fluid flows are presented. These methodologies fall into the category of volume tracking methods with piecewise‐linear interface calculation (PLIC). The scope of this work is limited to laminar flows of immiscible, non‐reacting, incompressible Newtonian fluids, without phase change, in planar two‐dimensional geometries. The following novel or enhanced procedures are proposed: a parallelogram scheme for multidimensional advection of the volume‐fraction field; a circle‐fit technique for the orientation of the interface segments and the calculation of curvature; a novel contact angle treatment; and a staggered formulation for volumetric body forces that can accurately balance pressure forces in the vicinity of the interface. In addition, surface‐tension‐derived and hydrostatic‐derived pressure adjustments are introduced as a means of accurately calculating pressure forces in cells that contain the interface, so as to minimize the non‐physical flows that afflict many available volume tracking methods. The proposed method is validated using four test problems that involve simulations of pure advection, a static drop, an oscillating bubble, and a static meniscus. Copyright © 2006 John Wiley & Sons, Ltd.     

A numerical study on a Cartesian-based body-fitted adaptive grid method

ABSTRACT

A hybrid Cartesian-based body-fitted adaptive grid method for compressible Navier–Stokes equations is implemented and investigated. In this method, the body-fitted structured grids are generated around the geometries, and the left regions are filled with Cartesian grids. To transfer the data between the different grids, the donor cell searching technique is adopted. An unstructured data-based finite volume update procedure is used, and least squares method is suggested to retain the second order in the overlap region. The moving shock waves with different speeds and vortex passing through the interfaces of the hybrid Cartesian grid are used to explore the accuracy and conservation. A new technique is presented to deal with the non-physical stagnation of slowly moving shock wave around the interface of grid. Numerical examples are presented to demonstrate the results. The three-dimensional extension has also been shown by a benchmark problem.     

A study of the motion in rotating containers using a boundary fitted co-ordinate system

Numerical solutions are often inaccurate because conventional co-ordinate systems do not represent the complex physical boundaries accurately. In the present work, the numerical solution of linear shallow water wave equations has been obtained by transforming the physical domain into a rectangular computational domain using elliptic differential operators. This work is part of a programme to develop three-dimensional body-fit grid systems for environmental flows. Solutions have been obtained for a cylindrical container and also a parabolic container. The initial conditions chosen are the ones for which analytical solutions exist. The numerical solutions compare well with analytical solutions.     

A geometry‐based level set method for curvilinear overset grids with application to ship hydrodynamics

In a previous work (Int. J. Numer. Meth. Fluids 2007; 55 :867–897), we presented a two‐phase level set method to simulate air/water turbulent flows using curvilinear body‐fitted grids for ship hydrodynamics problems. This two‐phase level set method explicitly enforces jump conditions across the interface, thus resulting in a fully coupled representation of the air/water flow. Though the method works well with multiblock curvilinear grids, severe robustness problems were found when attempting to use it with overset grids. The problem was tracked to small unphysical level set discontinuities across the overset grids with large differences in curvature. Though negligible for single‐phase approaches, the problem magnifies with large density differences between the phases, causing computation failures. In this paper, we present a geometry‐based level set method for curvilinear overset grids that overcomes these difficulties. The level set transport and reinitialization equations are not discretized along grid coordinates, but along the upwind streamline and level set gradient directions, respectively. The method is essentially an unstructured approach that is transparent to the differences between overset grids, but still the discretization is under the framework of a finite differences approach. As a result, significant improvements in robustness and to a less extent in accuracy are achieved for the level set function interpolation between overset grids, especially with big differences in grid curvature. Example tests are shown for the case of bow breaking waves around the surface combatant model David Taylor Model Basin (DTMB) 5415 and for the steady‐state ONR Tumblehome DTMB 5613 with superstructure. In the first case, the results are compared against experimental data available and in the second against results of a semi‐coupled method. Copyright © 2011 John Wiley & Sons, Ltd.     

NUMERICAL METHOD BASED ON HAMILTON SYSTEM AND SYMPLECTIC ALGORITHM TO DIFFERENTIAL GAMES

The resolution of differential games often concerns the difficult problem of two points border value (TPBV), then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and keep the measure of phase plane. From the viewpoint of Hamilton system, the symplectic characters of linear quadratic differential game were probed; as a try, Symplectic-Runge-Kutta algorithm was presented for the resolution of infinite horizon linear quadratic differential game. An example of numerical calculation was given, and the result can illuminate the feasibility of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy.     

基于能量法的双钢板混凝土遮弹层设计计算方法研究

为了深入探讨双钢板混凝土结构抗强冲击时后附钢板的耗能方式变化,基于最小耗能原理和无量纲化分析,反推得到了不同材料和结构尺寸下后附钢板耗能状态。结合混凝土强度极限条件,建立了兼顾塑性变形和侵彻贯穿破坏形态的后附钢板综合耗能计算公式以及后附钢板最小临界厚度解析表达式。计算结果表明,薄钢板综合耗能可达仅考虑贯穿效应耗能的4~5倍。基于能量守恒原理,提出了双钢板混凝土遮弹层防贯穿设计六步法,给出了弹体临界贯穿速度和弹体余速计算公式。该计算公式与已有钢板混凝土结构侵彻试验结果吻合较好。

     

Analytical and level-set method based numerical study on oil-water smooth/wavy stratified-flow in an inclined plane-channel

Level-set method based transient 2D simulation of developing oil-water smooth-stratified (SS) and wavy-stratified (WS) flow in a horizontal and inclined plane-channel is done; for various inlet-velocity (u_in), inlet-interface-height (H_in), inclination-angle (θ), reduced surface-tension (σ ? σ_ow) and reduced gravity (g ? g_e). At the certain critical value of the governing parameters, SS to WS flow transition is captured, analyzed and reasoned. Increase in u_in, H_in and θ and a decrease in σ_ow and g_e are found to destabilize the SS flow. For fully-developed SS flow, a detailed analytical solution of interface-height, maximum axial-velocity, its transverse location, pressure-gradient and wall-shear stress is proposed for an inclined channel; an excellent agreement between the present analytical and numerical results is also reported. The SS flow analytical-results are also compared with the time-averaged WS flow numerical-results (near the channel-outlet), to understand the reasons for flow-transition. Flow development is studied with the help of axial variation of interface-height and maximum (over the cross-section of the channel) axial velocity; time-averaged for WS flow. Furthermore, the variation of development-length for SS flow and WS flow is studied. Finally, stretching of interface-area due to onset of WS flow is presented with the help of interfacial-area-concentration. Its calculation directly from the Dirac-delta function of the level set method is a novel-contribution.     

Application of the VOF method to the sloshing of a fluid in a partially filled cylindrical container

In a previous work we solved numerically the steady-state motion of an ideal fluid that fills a moving cylindrical container with partitions, and were able to compute the equivalent moments of inertia. Here we extend this work in two steps. First we introduce time dependence and then free surfaces, and are able to compute the transient motion of the fluid not filling the container. The main body of the work has to do with the treatment of free surfaces. Our approach is an extention to three dimensions of the volume of fluid method of Hirt and Nichols. The solution algorithm is outlined, and two examples that demonstrate its capability are presented.     

谱体积方法单元分割与问题单元标记方法的改进研究

谱体积方法是一种本质上解决网格依赖性的高精度CFD计算方法,本文研究了二维Euler方程的谱体积方法,提出一种基于切比雪夫多项式的单元分割方法,建立了基于WENO的变量限制器方法,并发展了结合谱体积和控制体的问题单元标记方法.采用15°超声速压缩拐角和NACA0012跨声速流动两个典型算例进行验证,结果表明,该分区方法具有更好的计算精度,标记方法可有效识别不连续区域,在较少的网格下即可获得与密网格传统有限体积法相当的计算精度.     

基于DIC技术的爆炸应力波过异质界面应变场演化规律实验研究

采用氯仿粘结聚碳酸酯（polycarbonate, PC）板和聚甲基丙烯酸甲酯（polymethylmethacrylate, PMMA）板模拟含异质界面模型;在PC介质中布置柱状炮孔并与界面呈一定角度,根据炮孔端部与界面相对位置,分别于柱状炮孔两个端部设置起爆点,起爆点远离界面端部时定义为孔口起爆,靠近界面端部时定义为孔底起爆;借助数字图像相关实验系统,研究爆炸应力波通过异质界面后PMMA介质应变场演化过程及炮孔底部区域拉、压应变变化规律。实验结果表明,异质界面改变了爆炸应力波过界面后的传播形态。孔口起爆时,异质界面受爆破荷载作用后易形成应力集中区,界面处产生开裂,横向拉伸波作用是造成异质界面开裂的主要原因。起爆方式对过界面后介质PMMA的横/纵向拉、压应变场作用贡献不同,主要体现在应变场强度、拉/压应变场位置分布2个方面。在炮孔底部区域,起爆方式对应变场时程特性的影响主要体现在作用时效长短和应变强度2个方面。孔口起爆时,横/纵向应变体现出短时效、高强度的变化特征。就应变强度而言,起爆方式对横向压应变的影响显著强于其对纵向拉应变的影响。对空间分布特性影响主要体现在衰减程度,起爆方式对纵向应变衰减程度影响较大。无论采用何种起爆方式,爆炸应变场在PC介质中衰减速度较快,进入PMMA介质后衰减速度显著降低。

     

AGE method simulations of a turbulent far‐wake compared to spectral DNS

Turbulent flow simulation methods based on finite differences are attractive for their simplicity, flexibility and efficiency, but not always for accuracy or stability. This paper demonstrates that a good compromise is possible with the advected grid explicit (AGE) method. Starting from the same initial field as a previous spectral DNS, AGE method simulations of a planar turbulent wake were carried out as DNS, and then at three levels of reduced resolution. The latter cases were in a sense large‐eddy simulations (LES), although no specific sub‐grid‐scale model was used. Results for the two DNS methods, including variances and power spectra, were very similar, but the AGE simulation required much less computational effort. Small‐scale information was lost in the reduced resolution runs, but large‐scale mean and instantaneous properties were reproduced quite well, with further large reductions in computational effort. Quality of results becomes more sensitive to the value chosen for one of the AGE method parameters as resolution is reduced, from which it is inferred that the numerical stability procedure controlled by the parameter is acting in part as a sub‐grid‐scale model. Copyright © 2002 John Wiley & Sons, Ltd.     

水下爆炸气泡射流载荷计算的新方法研究

由于存在强冲击、多相界面复杂运动等强非线性效应,目前对于水下爆炸气泡运动的计算方法无法给出较为可信的水射流运动特征及其载荷形式.本文基于多相可压缩流体的five-equation计算模型,引入界面函数和界面密度压缩技术,采用5阶WENO重构与HLLC近似Riemann求解器进行空间离散,时间离散采用3阶TVD Rung...     

A discontinuous Galerkin‐based sharp‐interface method to simulate three‐dimensional compressible two‐phase flow

A numerical method for the simulation of compressible two‐phase flows is presented in this paper. The sharp‐interface approach consists of several components: a discontinuous Galerkin solver for compressible fluid flow, a level‐set tracking algorithm to follow the movement of the interface and a coupling of both by a ghost‐fluid approach with use of a local Riemann solver at the interface. There are several novel techniques used: the discontinuous Galerkin scheme allows locally a subcell resolution to enhance the interface resolution and an interior finite volume Total Variation Diminishing (TVD) approximation at the interface. The level‐set equation is solved by the same discontinuous Galerkin scheme. To obtain a very good approximation of the interface curvature, the accuracy of the level‐set field is improved and smoothed by an additional P_NP_M‐reconstruction. The capabilities of the method for the simulation of compressible two‐phase flow are demonstrated for a droplet at equilibrium, an oscillating ellipsoidal droplet, and a shock‐droplet interaction problem at Mach 3. Copyright © 2015 John Wiley & Sons, Ltd.     

An extension of the SIMPLE based discontinuous Galerkin solver to unsteady incompressible flows

In this paper, we present a SIMPLE based algorithm in the context of the discontinuous Galerkin method for unsteady incompressible flows. Time discretization is done fully implicit using backward differentiation formulae (BDF) of varying order from 1 to 4. We show that the original equation for the pressure correction can be modified by using an equivalent operator stemming from the symmetric interior penalty (SIP) method leading to a reduced stencil size. To assess the accuracy as well as the stability and the performance of the scheme, three different test cases are carried out: the Taylor vortex flow, the Orr‐Sommerfeld stability problem for plane Poiseuille flow and the flow past a square cylinder. (1) Simulating the Taylor vortex flow, we verify the temporal accuracy for the different BDF schemes. Using the mixed‐order formulation, a spatial convergence study yields convergence rates of k + 1 and k in the L²‐norm for velocity and pressure, respectively. For the equal‐order formulation, we obtain approximately the same convergence rates, while the absolute error is smaller. (2) The stability of our method is examined by simulating the Orr–Sommerfeld stability problem. Using the mixed‐order formulation and adjusting the penalty parameter of the symmetric interior penalty method for the discretization of the viscous part, we can demonstrate the long‐term stability of the algorithm. Using pressure stabilization the equal‐order formulation is stable without changing the penalty parameter. (3) Finally, the results for the flow past a square cylinder show excellent agreement with numerical reference solutions as well as experiments. Copyright © 2015 John Wiley & Sons, Ltd.     

结构杆件撤除后简化分析一般方法

本文提出结构杆件撤除后简化分析的一般方法,视杆件撤除后新结构的解为原结构的解与原结构上加以关联荷载解的叠加,利用原结构的解及总体刚度矩阵的逆矩陈求解新结构,无需进行结构重分析,使计算量大大减小,文中基于有限元法导出求关联荷载的一般算式。该法适用于空间网格结构和刚架结构一根杆件撤除问题,也适用于多根杆件同时撤除问题。