非结构动网格在三维可动边界问题中的应用

研究用于非结构动网格的弹簧近似方法,采用顶点弹簧描述, 导出并讨论了弹簧倔强系数的取值. 通过引入边界修正和扭转效应修正,对标准弹簧近似方法进行了改进. 转动翼型算例的结果表明,改进后的方法大大提高了网格变形能力和网格质量. 应用该动网格方法耦合求解基于(Arbitrary Lagrangian-Eulerian, ALE)描述的三维Euler方程,模拟了作俯仰振动的矩形机翼绕流,计算结果与实验数据及文献计算结果十分一致. 作为多个自由刚体与流体耦合运动问题的简单例证,耦合刚体动力学方程,模拟了激波与双立方体的相互作用,得到了非定常流场结构. 研究表明,基于弹簧近似的非结构动网格与有限体积格式流场解算器相结合,是模拟包含运动边界的非定常流动问题的有效方法.     

非结构动网格在可动边界问题中的应用研究

本文对用于非结构动网格生成的弹簧近似方法进行了研究.通过采用顶点弹簧方法,分析研究了弹簧倔强系数的取值,同时通过引入挤压倔强系数和边界修正,对标准弹簧近似方法进行了改进.改进后的方法可以大大提高网格变形能力和网格质量.应用本文发展的非结构动网格生成方法并通过耦合求解基于(Arbitrary Lagrangian-Eulerian ALE)描述的Euler方程,模拟了谐和振动NACA0012翼型及M6机翼的跨音速绕流,计算结果与参考文献提供的结果及实验结果吻合良好.     

在动网格上的多介质界面数值处理方法研究

运用动网格上的ALE方法对一维可压缩多介质Riemann问题进行求解,在处理介质界面上的数值通量时提出了3种不同的数值方法：Lagrange方法、GFM和HLLC方法,并且对这3种方法的数值结果进行了比较,认为GFM方法和HLLC方法在介质界面上出现大压力梯度时能够明显消除界面上密度的非物理震荡,提高介质界面上数值解的精度.     

一种追踪多介质流体界面运动的NND数值模拟方法

把界面捕捉等效方程、Level-Set方程和欧拉方程组耦合,在Stiffened状态方程下,采用高分辨率NND格式求解流体力学方程组并用Level-Set函数捕捉界面的位置。对二维情况下激波和气泡相互作用的问题进行数值模拟,并与波传算法的模拟结果进行比较。计算结果表明该方法能有效的抑制间断附近的非物理振荡,有很强的捕捉界面的能力。     

爆轰驱动多介质问题的Lagrange多分区自适应数值模拟研究

凝聚炸药爆轰驱动惰性金属材料形成的多介质流动问题广泛存在于工程应用领域, Lagrange方法由于其物质界面的高保真特性一直在相关问题的数值模拟中发挥着不可替代的作用.加密网格是提高爆轰驱动多介质问题模拟精度的常用途径之一.然而, Lagrange框架下整体密网格计算常会遇到网格畸变、计算效率低等问题.为此,针对爆轰驱动多介质流动问题,提出了一种Lagrange框架下的非结构网格多层自适应方法,在保证所关心区域局部网格分辨率的前提下,大幅缩减了整体计算规模,提升了Lagrange计算的健壮性.设计了非结构网格多层数据结构,提出了多层网格分层存储、有效网格压至一层进行Lagrange计算的AMR策略,同时还发展了自适应接触滑移耦合算法,实现了AMR计算与多分区接触滑移计算的“紧耦合”.相比于已有工作,所提出的AMR方法既保持了非结构网格多层数据结构的灵活性优势,又避免了Lagrange框架下多层网格分别计算带来的层间耦合困难,同时因实现了与接触滑移的自适应耦合,使得它能很好地适应多分区的多介质问题.在一维、二维爆轰算例验证所提出方法正确性的前提下,开展了拐角爆轰、多层炸药隔爆和有限尺寸弯...     

多流体界面不稳定性的守恒和非守恒高精度数值模拟方法

对多流体界面问题守恒和非守恒格式(M)WENO重构方法进行探讨,采用虚拟流动方法并用Level-Set函数捕捉界面的运动变化。数值模拟结果表明本文的数值方法具有较高的分辨率,并能有效地抑制界面附近的非物理振荡。     

非线性流体-刚体结构相互作用问题的一种数值模拟方法

给出了一种模拟非线性流体-刚体结构相互作用问题的数值方法.文中假定结构承受大的刚体运动,流体流动受非线性有粘或无粘的场方程支配并满足自由表面和两相耦合界面上的非线性边界条件,利用任意拉氏-欧氏(ALE)网格系统构造了数值模型.采用所探讨的多块数值格式,允许可动重造网格间有独立的相对运动,从而克服了流体网格与固体大运动匹配的困难.通过数值离散化,导出了描述非线性流固耦合动力学的数值方程并应用耦合迭代过程对其作了求解.通过算例,说明了所提出数值模型的应用.     

ALE动网格法在流固耦合数值模拟中的应用

为了解决流固耦合问题中的物体大幅度运动带来的困难,采用ALE(Arbitrary Lagrange-Euler)动网格方法跟踪自由表面上浮体的运动.计算表明:浮体在无粘流体中的垂荡与弹簧-物体的振动模型理论解符合得较好;浮体在粘性流体中的自由横摇为阻尼运动,其横摇角度随时间的增加而减小,且在不同初始角度下运动系统的固有周期相当.在有外力力矩激励时,外力力矩的周期与系统的固有周期相当时浮体横摇运动趋于共振状态,运动幅度最大.计算结果验证了计算程序的可靠性与精度.本文方法为ALE方法应用于流体-多浮体耦合运动分析奠定了基础.     

多介质流体非守恒律欧拉方程组的数值计算方法

对多介质流体在界面处满足的Euler方程进行了探讨 ,方程组中增加了描述材料参数间断性质的对流形式非守恒律方程组。以波传播算法为基础 ,通过Roe方程近似求解Riemann问题 ,同时采用相同的数值差分格式求解流体动力学Euler方程组和界面方程组。该方法可以有效消除多介质流体在界面处压力、速度可能出现的非物理振荡。给出了部分典型一维和二维数值计算结果。     

真实虚拟流方法在多介质可压缩流动模拟中的应用

为了克服原始虚拟流方法(ghost fluid method,GFM)在处理激波与大密度比流体-流体（气-水）界面相互作用时遇到的困难,采用真实虚拟流法(real ghost fluid method,RGFM)处理流体界面附近的虚拟点,结合HLLC(Harten-Lax-Van Leer with contact discontinuities)格式求解Euler方程,采用五阶WENO(weighted essentially nonoscillatory)格式求解level set输运方程。通过一维和二维算例的物质界面捕捉研究,证明RGFM在处理小密度比界面问题时优于GFM,同时RGFM还可用于求解激波与大密度比物质界面相互作用问题。计算表明,将RGFM引入到本文算法中,可精确捕捉到激波与界面（气-气、气-水界面）相互作用的变化细节,包括大密度比界面的剧烈变形和破碎,并具有较高的计算分辨率。     

A robust algorithm for moving interface of multi-material fluids based on Riemann solutions

In the paper, the numerical simulation of interface problems for multiple material fluids is studied. The level set function is designed to capture the location of the material interface. For multi-dimensional and multi-material fluids, the modified ghost fluid method needs a Riemann solution to renew the variable states near the interface. Here we present a new convenient and effective algorithm for solving the Riemann problem in the normal direction. The extrapolated variables are populated by Taylor series expansions in the direction. The anti-diffusive high order WENO difference scheme with the limiter is adopted for the numerical simulation. Finally we implement a series of numerical experiments of multi-material flows. The obtained results are satisfying, compared to those by other methods.The English text was polished by Boyi Wang.     

Finite volume scheme for the solution of fluid flow problems on unstructured non‐staggered grids

A recently developed non‐staggered methodology which uses the principle of applying fourth‐order dissipation to the governing pressure‐correction equation is developed so it can be applied to unstructured grids. A finite volume methodology is used for discretization. The fourth‐order dissipation term is found using second‐order gradient operators. This makes it straightforward to incorporate the dissipation term on unstructured grids. The new methodology is compared with solutions from a standard finite volume second‐order flow solver and is also tested for a standard laminar driven‐lid flow problem with grids systems that do not have a uniform structure. Finally, we demonstrate how the new methodology can be used to predict flow over a wavy boundary. Copyright © 2002 John Wiley & Sons, Ltd.     

Flows around moving bodies using a dynamic unstructured overset-grid method

In this article, a computational fluid dynamics algorithm is presented for simulations of complex unsteady flows around rigid moving bodies using an unstructured overset-grid method. For this purpose, a highly automated, three-dimensional, tetrahedral, unstructured overset-grid method is developed with one-cell-width overlapping zone in order to model the arbitrary geometries for steady and unsteady flow simulations. A method has been described to obtain the inter-grid boundaries of the one-cell-wide overlapping zone shared by a background grid and a minor grid. In the overset-grid methodology, vector intersection algorithm and bounding box techniques have been utilised. The mesh refinement and overset-scheme conservation studies proved the accuracy and efficiency of the method developed here. The applications of the developed algorithms were also performed through simulations that included complex internal flows around a flow-control butterfly valve as well as flows in an internal combustion engine with a moving piston. Lastly, validations with experimental data were conducted for both steady and unsteady flows around rigid bodies with relative motions.     

基于非结构化同位网格的SIMPLE算法

通过基于非结构化网格的有限体积法对二维稳态Navier—Stokes方程进行了数值求解。其中对流项采用延迟修正的二阶格式进行离散;扩散项的离散采用二阶中心差分格式;对于压力-速度耦合利用SIMPLE算法进行处理;计算节点的布置采用同位网格技术,界面流速通过动量插值确定。本文对方腔驱动流、倾斜腔驱动流和圆柱外部绕流问题进行了计算,讨论了非结构化同位网格有限体积法在实现SIMPLE算法时,迭代次数与欠松弛系数的关系、不同网格情况的收敛性、同结构化网格的对比以及流场尾迹结构。通过和以往结果比较可知,本文的方法是准确和可信的。     

A sharp interface method for high-speed multi-material flows: strong shocks and arbitrary materialpairs

A general framework is developed for solving high-speed and high-intensity multi-material interaction problems on adaptively refined Cartesian meshes. The framework is applicable for interfaces separating materials with very different properties and in the presence of strong shocks. A sharp interface treatment is maintained through a modified Ghost Fluid Method. The embedded boundaries are tracked and represented with level sets. A tree-based Local Mesh Refinement scheme is employed to efficiently resolve the desired physics. Results are shown for situations that cover varied combination of materials (fluids, rigid solids and deformable solids) with careful benchmarking to establish the validity and the versatility of the approach.     

The simulation of inviscid,compressible flows using an upwind kinetic method on unstructured grids

A kinetic flux-vector-splitting method has been used to solve the Euler equations for inviscid, compressible flow on unstructured grids. This method is derived from the Boltzmann equation and is an upwind, cell-centered, finite volume scheme with an explicit time-stepping procedure. The Delaunay triangulation has been used to generate the grids. The approach is demonstrated for three flow field simulations, namely the subsonic flow over a two-component high-lift aerofoil, the transonic flow over an aerofoil and the supersonic flow in a channel.     

Further contributions on the flow past a stationary and confined cylinder: Creeping and slowly moving flow of Power law fluids

The steady flow of generalized Newtonian fluid around a stationary cylinder placed between two parallel plates was studied numerically. Finite volume method was applied to solve the momentum equations along with the continuity equation and the Power law rheological model within the laminar flow regime for a range of the Reynolds number Re and the Power law index n values. The values of the Reynolds number, based on physical and rheological properties, cylinder radius and bulk velocity, were varied between 0.0001≤Re≤10, while the Power law index values mapped the 0.50≤n≤1.50 range, allowing for the investigation of both shear-thinning and shear-thickening effects at the creeping as well as slowly moving fluid flow conditions. We report accurate results of a systematic study with a focus on the most important characteristics of fluid flow past circular cylinder. It is shown that for the creeping flow regime there exist finite sized redevelopment length, drag and loss coefficient. Last but not least, the present numerical results indicate that the shear-thinning viscous behaviour decreases the onset of flow separation.     

基于ALE方法的3D充填流动模拟

基于任意拉格朗日-欧拉方法发展了三维充填流动的数值模拟方案.该方案采用ALE方法准确地追踪移动自由面的位置并避免了网格扭曲;基于移动最小二乘曲面拟合方法提出了移动自由面上网格节点重定位方法,将充填流动的网格更新过程简化为自由面附近的局部网格重划分过程,并通过分级多面体三角剖分实现,减小了网格划分的计算量,实现了实时网格生成.给出的数值算例结果表明了该数值模型对三维充填流动模拟的有效性.