Unstructured Grid Immersed Boundary Method for Numerical Simulation of Fluid Structure Interaction

This paper presents an improved unstructured grid immersed boundary method.The advantages of both immersed boundary method and body fitted grids which are generated by unstructured grid technology are used to enhance the computation efficiency of fluid structure interaction in complex domain.The Navier-Stokes equation was discretized spacially with collocated finite volume method and Euler implicit method in time domain.The rigid body motion was simulated by immersed boundary method in which the fluid and rigid body interface interaction was dealt with VOS(volume of solid) method.A new VOS calculation method based on graph was presented in which both immersed boundary points and cross points were collected in arbitrary order to form a graph.The method is verified with flow past oscillating cylinder.

New Immersed Boundary Method on the Adaptive Cartesian Grid Applied to the Local Discontinuous Galerkin Method

Currently, many studies on the local discontinuous Galerkin method focus on the Cartesian grid with low computational e ciency and poor adaptability to complex shapes. A new immersed boundary method is presented, and this method employs the adaptive Cartesian grid to improve the adaptability to complex shapes and the immersed boundary to increase computational e ciency. The new immersed boundary method employs different boundary cells(the physical cell and ghost cell) to impose the boundary condition and the reconstruction algorithm of the ghost cell is the key for this method. The classical model elliptic equation is used to test the method. This method is tested and analyzed from the viewpoints of boundary cell type, error distribution and accuracy. The numerical result shows that the presented method has low error and a good rate of the convergence and works well in complex geometries. The method has good prospect for practical application research of the numerical calculation research.

Sharp interface direct forcing immersed boundary methods： A summary of some algorithms and applications

Body-fitted mesh generation has long been the bottleneck of simulating fluid flows involving complex geometries. Immersed boundary methods are non-boundary-conforming methods that have gained great popularity in the last two decades for their simplicity and flexibility, as well as their non-compromised accuracy. This paper presents a summary of some numerical algori- thms along the line of sharp interface direct forcing approaches and their applications in some practical problems. The algorithms include basic Navier-Stokes solvers, immersed boundary setup procedures, treatments of stationary and moving immersed bounda- ries, and fluid-structure coupling schemes. Applications of these algorithms in particulate flows, flow-induced vibrations, biofluid dynamics, and free-surface hydrodynamics are demonstrated. Some concluding remarks are made, including several future research directions that can further expand the application regime of immersed boundary methods.

Numerical simulation of two-dimensional viscous flows using combined finite element-immersed boundary method

In this paper, a method that combines the characteristic-based split finite element method（CBS-FEM） and the direct forcing immersed boundary（IB） method is proposed for the simulation of incompressible viscous flows. The structured triangular meshes without regarding the location of the physical boundary of the body is adopted to solve the flow, and the no-slip boundary condition is imposed on the interface. In order to improve the computational efficiency, a grid stretching strategy for the background structured triangular meshes is adopted. The obtained results agree very well with the previous numerical and experimental data. The order of the numerical accuracy is shown to be between 1 and 2. Moreover, the accuracy control by adjusting the number density of the mark points purely at certain stages is explored, and a second power law is obtained. The numerical experiments for the flow around a cylinder behind a backward-facing step show that the location of the cylinder can affect the sizes and the shapes of the corner eddy and the main recirculation region. The proposed method can be applied further to the fluid dynamics with complex geometries, moving boundaries, fluid-structure interactions, etc..

NUMERICAL METHOD FOR MULTI-BODY FLUID INTERACTION BASED ON IMMERSED BOUNDARY METHOD

A Cartesian grid based on Immersed Boundary Method （IBM）, proposed by the present authors, is extended to unstructured grids. The advantages of IBM and Body Fitted Grid （BFG） are taken to enhance the computation efficiency of the fluid structure interaction in a complex domain. There are many methods to generate the BFG, among which the unstructured grid method is the most popular. The concept of Volume Of Solid （VOS） is used to deal with the multi rigid body and fluid interaction. Each body surface is represented by a set of points which can be traced in an anti-clockwise order with the solid area on the left side of surface. An efficient Lagrange point tracking algorithm on the fixed grid is applied to search the moving boundary grid points. This method is verified by low Reynolds number flows in the range from Re = 100 to 1000 in the cavity with a moving lid. The results are in a good agreement with experimental data in literature. Finally, the flow past two moving cylinders is simulated to test the capability of the method.

An Indirect-Forcing Immersed Boundary Method for Incompressible Viscous Flows with Interfaces on Irregular Domains

An indirect-forcing immersed boundary method for solving the incompressible Navier-Stokes equations involving the interfaces and irregular domains is developed.The rigid boundaries and interfaces are represented by a number of Lagrangian control points.Stationary rigid boundaries are embedded in the Cartesian grid and singular forces at the rigid boundaries are applied to impose the prescribed velocity conditions.The singular forces at the interfaces and the rigid boundaries are then distributed to the nearby Cartesian grid points using the immersed boundary method.In the present work,the singular forces at the rigid boundaries are computed implicitly by solving a small system of equations at each time step to ensure that the prescribed velocity condition at the rigid boundary is satisfied exactly.For deformable interfaces,the forces that the interface exerts on the fluid are computed from the configuration of the elastic interface and are applied to the fluid.The Navier-Stokes equations are discretized using finite difference method on a staggered uniform Cartesian grid by a second order accurate projection method.The ability of the method to simulate viscous flows with interfaces on irregular domains is demonstrated by applying to the rotational flow problem,the relaxation of an elastic membrane and flow in a constriction with an immersed elastic membrane.

An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods

An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources.The interface is represented by the zero level set of a Lipschitz functionϕ(x,y).Our adaptive mesh refinement is done within a small tube of|ϕ(x,y)|δwith finer Cartesian meshes.The discrete linear system of equations is solved by a multigrid solver.The AMR methods could obtain solutions with accuracy that is similar to those on a uniform fine grid by distributing the mesh more economically,therefore,reduce the size of the linear system of the equations.Numerical examples presented show the efficiency of the grid refinement strategy.

笛卡尔网格下不同湍流模型的壁面函数方法研究

自适应笛卡尔网格湍流模拟时,网格数目呈雷诺数的指数方量级增长,带来网格规模“灾难”问题。壁面函数方法可以将壁面第一层网格尺度放宽1~2个量级,是有效的解决办法之一,然而,由于笛卡尔网格的非贴体特性,壁面函数的实现及其与不同湍流模型的匹配是关键。针对这一问题,从经典的Spalding壁面函数出发,采用显式赋初值的方式,解决了壁面摩擦速度迭代求解初值敏感及分层壁面函数速度不光滑问题;基于切应力恒定的壁面条件,构造了多层虚拟网格的切向速度和湍流粘性系数,实现了笛卡尔网格下的壁面函数方法;采用结构系综理论,通过DNS数据标定,构造了湍动能随湍流粘性比率变化的关系式,实现了壁面函数与KDO湍流模型的匹配,并以平板T3b、湍流凸包和跨音速NACA0012翼型绕流为算例,与常用的SST、SA湍流模型壁面函数方法进行了对比分析。结果表明:该文提出的KDO湍流模型壁面函数法准确、可靠,且因其形式简单、计算量相对较小,有较大的推广应用价值。

艏部构型对内倾船型运动响应和上浪砰击压力的影响研究

内倾船型的艏部构型对船舶在波浪中的运动和上浪载荷特性具有一定的影响。本文基于艏柱倾斜角度选取了倾角为30°、45°和60°的三种艏部构型方案,采用中国数值水池-直角网格有限差分方法(CNTCGFDM),研究了在不同的艏部构型方案下内倾船型在规则波中的运动响应以及甲板上浪载荷特性。其中物体边界及运动的模拟采用浸没边界法来实现,并利用THINC/SW方法来捕捉自由液面。选取艏柱倾角为45°和60°的船型进行模型试验研究,与试验值相比,本文的数值模拟结果吻合良好。结果表明:艏部构型对内倾船型在规则波中的运动响应总体上影响较小,只在某些海况下表现出一定的局部差异,但对内倾船型的上浪砰击载荷则有一定的影响,相较于倾角为30°和60°的构型方案,艏柱倾角为45°的内倾船型在甲板上浪中的载荷性能更加优异。

基于反馈力浸入边界法模拟复杂动边界流动

浸入边界法是模拟流固耦合的重要数值方法之一。本文采用反馈力浸入边界方法,对旋转圆柱和水轮机活动导叶旋转摆动绕流后的动边界流场进行数值模拟。其中,固体边界采用一系列离散的点近似代替,流体为不可压缩牛顿流体,使用笛卡尔自适应加密网格,利用有限差分法进行求解。固体对流场的作用通过构造适宜的反馈力函数实现。本文首先通过旋转圆柱绕流的计算结果同实验结果进行对比,吻合较好,验证了该计算方法的可靠性。然后针对水电站水力过渡过程中水轮机活动导叶旋转摆动绕流后的动边界流场进行数值模拟,得到导叶动态绕流后的流场分布特性和涡结构的演化特性。

基于四叉树网格下的浸入边界-格子Boltzmann方法

提出了一种基于非均匀四叉树网格下的浸入边界-格子Boltzmann方法。在不同层网格界面上,为了保证物理量的连续性,需要在时空方向上进行插值。由于四叉树同层网格在空间上步长相等、且相邻时间层上时间步长相等,所以在时空方向上采用平均值插值,这样做的优点是时空方向插值既可以达到二阶精度,又可以简化计算过程,节省资源,对任意边界加密下的网格,格子Boltzmann方法的实现比较容易。为了充分利用均匀笛卡尔网格的优势,物面边界的处理采用了速度修正法,与传统浸入边界-格子Boltzmann方法中的直接力法、动量交换法相比,无滑移边界条件得到了较好的保证。同时,把大涡模型加入到浸入边界-格子Boltzmann方法中,实现了在四叉树网格数据结构、边界处理技术、大涡模拟几种模型相结合下,绕障碍物的较大雷诺数流动的模拟。通过不可压缩粘性流中圆柱绕流算例验证,结果与其它方法结果吻合良好。

基于浸没边界法的水库变动水面模拟及验证

水库水面波动具有复杂的流动边界。对复杂边界条件的处理,将直接影响水资源的开发利用效果。为模拟真实水库自由液面的大幅变动,利用浸没边界法来处理水库自由液面的变动问题,比较水库水温分布、水库下泄水温和坝前垂向水温分布,并通过简单算例予以验证。结果表明:该方法具有良好的可行性和准确性,改进了水库变动水面预测方法,可用于研究水库水面的时空变化规律。

直角网格壁函数的二维高雷诺数机翼绕流计算

针对传统直角网格方法无法准确计算高雷诺数下近壁面区域的流场及剪切应力问题,本文基于自主开发的二维直角网格CFD求解器,采用添加壁面函数的方式模拟了高雷诺数下的机翼绕流。数值模型基于直角网格有限差分方法对N-S方程进行离散,整体求解器的精度在空间和时间上分别达到二阶。通过对低雷诺数下圆柱绕流及机翼绕流的模拟计算,验证了此求解器的精度和可靠性。在高雷诺数下利用壁面函数修正近壁面的速度剖面,使近壁面区域的速度分布更符合实际流动。研究结果表明:本文方法能够有效求解二维高雷诺数机翼绕流问题。同时利用商业计算流体力学软件Star-CCM+采用贴体网格对同样问题进行模拟,数值模拟结果表明本文方法的网格需求要大于贴体网格。

高精度HWENO格式与浸入边界法求解可压缩流问题

在物面边界处采用浸入边界法并构造三阶有限体积HWENO(Hermite Weighted Essentially Non-oscillatory)格式,可在较简单的笛卡尔网格上有效处理上述带复杂物面边界的可压缩流动问题。经典的定常和非定常数值算例验证了该方法的有效性。

HWENO-LW格式与浸入边界法在笛卡尔网格中的应用

由于Lax-Wendroff时间离散的经典高精度有限体积格式对网格质量要求较高,不能直接用于数值模拟计算区域内含有复杂几何外形的物体绕流问题,而浸入边界法能在简单的笛卡尔网格中有效处理复杂物面边界条件,因此,在笛卡尔网格中构造高精度Lax-Wendroff时间离散的有限体积HWENO(Hermite weighted essentially nonoscillatory)格式,并结合浸入边界法求解上述问题.文中采用的Lax-Wendroff时间离散相比于经典的Runge-Kutta时间离散方法能更好地提高格式的计算效率,在解的光滑区域达到时空一致高阶精度.最后,通过数值算例验证该方法的有效性.

带浸入边界法的新型五阶WENO格式求解双曲守恒律方程

采用一种带浸入边界法的新型五阶有限差分WENO(weighted essentially non-oscillatory)格式在笛卡尔网格上求解含有复杂物面的双曲型守恒律方程。这种结构网格上的新型WENO格式因对计算网格质量依赖性较高,故一般不能直接应用于上述问题的数值模拟。而浸入边界法是一种能较好处理复杂物面边界的方法。将两种方法结合起来,可在笛卡尔网格上数值解决跨音速复杂流动问题,并用四个经典算例验证新型五阶WENO方法的有效性。

A parallel methodology of adaptive Cartesian grid for compressible flow simulations

The combination of Cartesian grid and the adaptive mesh refinement(AMR)technology is an effective way to handle complex geometry and solve complex flow problems.Some high-efficiency Cartesian-based AMR libraries have been developed to handle dynamic changes of the grid in parallel but still can not meet the unique requirements of simulating flow around objects.In this paper,we propose an efficient Cartesian grid generation method and an information transmission approach for the wall boundary to parallelize the implementation of ghost-cell method(GCM).Also,the multi-valued ghost-cell method to handle multi-value points is improved to adapt to the parallel framework.Combining the mentioned methodologies with the open-source library p4est,an automatic and efficient simulation of compressible flow is achieved.The overall performance of the methodology is tested through a wide range of inviscid/viscous flow cases.The results indicate that the capability and parallel scalability of the present numerical methodology for solving multiple types of flows,involving shock and vortices,multi-body flow and unsteady flows are agreeable as compared with related reference data.

An Accurate Cartesian Method for Incompressible Flows with Moving Boundaries

An accurate cartesian method is devised to simulate incompressible viscous flows past an arbitrary moving body.The Navier-Stokes equations are spatially discretized onto a fixed Cartesian mesh.The body is taken into account via the ghost-cell method and the so-called penalty method,resulting in second-order accuracy in velocity.The accuracy and the efficiency of the solver are tested through two-dimensional reference simulations.To show the versatility of this scheme we simulate a threedimensional self propelled jellyfish prototype.

基于非结构自适应网格和嵌入边界法的残差格式研究（英文）

嵌入边界法由于在求解NS方程时能够简化网格生成问题而在计算流体领域受到越来越广泛的关注。简言之,嵌入边界法能够简化大变形和运动条件下多物理流动模拟、流固相互作用耦合问题,然而壁面边界条件的精确处理仍旧是该方法需要解决的问题。在本文工作中,为考虑壁面边界条件而在NS方程中增加了补偿项,同时采用非结构网格自适应技术保持了壁面边界条件的精度。

笛卡儿网格高保真虚拟单元浸入边界法研究与应用

笛卡儿网格下,物面与网格相切割使得笛卡儿网格具有非贴体特性,物面边界处理成为笛卡儿网格流体仿真的关键.本文建立了一种笛卡儿网格浸入边界法下的高保真虚拟单元模型:合理选取“直角三角形”形式的插值模板点,对壁面外法向附近处的变量进行局部重构,使用双二次插值提高插值精度;根据不同的物面边界类型,构造考虑边界条件信息的高阶多项式,获得虚拟单元的流场值.Prandtl-Meyer流动、超声速圆柱绕流、前台阶问题、NACA0012翼型流动等典型算例考核验证结果表明,此方法模板点选取紧凑、鲁棒,可扩展到不同的边界条件,在L^(1)和L^(2)范数下达到2阶精度.