Application of hybrid Cartesian grid and gridless approach to moving boundary flow problems

The paper presents a hybrid Cartesian grid and gridless approach to solve unsteady moving boundary flow problems. Unlike the Chimera clouds of points approach, the hybrid approach uses a Cartesian grid to cover most of the computational domain and a gridless method to calculate a relatively small region adjacent to the body surface, making use of the flexibility of the gridless method in handling surface grid with complicated geometry and the computational efficiency of the Cartesian grid. Four cases were conducted to examine the applicability, accuracy and robustness of the hybrid approach. Steady flows over a single NACA0012 airfoil and dual NACA0012 airfoils at different Mach numbers and angles of attack were simulated. Moreover, by implementing a dynamic hole cutting, node identification and information communication between the Cartesian grid and the gridless regions, unsteady flows over a pitching NACA0012 airfoil (small displacement) and two‐dimensional airfoil/store separation (large displacement) were performed. The computational results were found to agree well with earlier experimental data as well as computational results. Shock waves were accurately captured. The computational results show that the hybrid approach is of potential to solve the moving boundary flow problems. Copyright © 2013 John Wiley & Sons, Ltd.     

A hybrid building‐block and gridless method for compressible flows

A hybrid building‐block Cartesian grid and gridless method is presented to compute unsteady compressible flows for complex geometries. In this method, a Cartesian mesh based on a building‐block grid is used as a baseline mesh to cover the computational domain, while the boundary surfaces are represented using a set of gridless points. This hybrid method combines the efficiency of a Cartesian grid method and the flexibility of a gridless method for the complex geometries. The developed method is used to compute a number of test cases to validate the accuracy and efficiency of the method. The numerical results obtained indicate that the use of this hybrid method leads to a significant improvement in performance over its unstructured grid counterpart for the time‐accurate solution of the compressible Euler equations. An overall speed‐up factor from six to more than one order of magnitude and a saving in storage requirements up to one order of magnitude for all test cases in comparison with the unstructured grid method are demonstrated. Copyright © 2008 John Wiley & Sons, Ltd.     

复杂无粘流场数值模拟的矩形/三角形混合网格技术

建立了一套模拟复杂无粘流场的矩形／三角形混合网格技术，其中三角形仅限于物面附近，发挥非结构网格的几何灵活性，以少量的网格模拟复杂外型；同时在以外的区域采用矩形结构网格，发挥矩形网格计算简单快速的优势，有效地克服全非结构网格计算方法需要较大内存量和较长ＣＰＵ时间的不足．混合网格系统由修正的四分树方法生成．将ＮＮＤ有限差分与ＮＮＤ有限体积格式有机地融合于混合网格计算，消除了全矩形网格模拟曲边界的台阶效应，同时保证了网格间的通量守恒．数值实验表明本方法在模拟复杂无粘流场方面的灵活性和高效性．     

高雷诺数下求解NS方程的无网格算法

提出了一种适合高雷诺数NS方程求解的隐式无网格算法。针对高雷诺数粘性流动的特点,在附面层内的粘性影响区域采用法向层次推进布点的方法形成离散点云,在附面层外的计算区域内实行填充式布点的方法形成离散点云。根据附面层内外点云的不同构造特点,推导出运用格林公式和最小二乘曲面拟合方法求取空间导数的统一形式,在此基础上运用AUSM _up格式求得数值通量,并引入BL湍流模型对雷诺平均NS方程的湍流应力项进行封闭。时间推进格式方面,采用了计算效率较高的隐式高斯-赛德尔迭代算法。为了验证本文方法的计算精度和鲁棒性,对NACA0012翼型低速流动、RAE2822翼型跨音速绕流和二维圆柱的分离流动进行了数值模拟。     

动态混合网格生成及隐式非定常计算方法

建立了一种基于动态混合网格的非定常数值计算方法. 混合网格由贴体的四边形网格、外场 的多层次矩形网格和中间的三角形网格构成. 当物体运动时，贴体四边形网格随物体运动而 运动，而外场的矩形网格保持静止，中间的三角形网格随之变形；当物体运动位移较大，导 致三角形网格的质量降低，甚至导致网格相交时，在局部重新生成网格. 新网格上的物理量 由旧网格上的物理量插值而得. 为了提高计算效率，采用了双时间步和子迭代相结合的隐式 有限体积格式计算非定常Navier-Stokes方程. 子迭代采用高效的块LU-SGS方法. 利用该 方法数值模拟了NACA0012振荡翼型的无黏和黏性绕流，得到了与实验和他人计算相当一致 的结果.     

Improvement of mass source/sink for an immersed boundary method

An improved immersed boundary method using a mass source/sink as well as momentum forcing is developed for simulating flows over or inside complex geometries. The present method is based on the Navier–Stokes solver adopting the fractional step method and a staggered Cartesian grid system. A more accurate formulation of the mass source/sink is derived by considering mass conservation of the virtual cells in the fluid crossed by the immersed boundary. Two flow problems (the decaying vortex problem and uniform flow past a circular cylinder) are used to validate the proposed formulation. The results indicate that the accuracy near the immersed boundary is improved by introducing the accurate mass source/sink. Copyright © 2006 John Wiley & Sons, Ltd.     

Adaptive Runge–Kutta discontinuous Galerkin method for complex geometry problems on Cartesian grid

A Cartesian grid method using immersed boundary technique to simulate the impact of body in fluid has become an important research topic in computational fluid dynamics because of its simplification, automation of grid generation, and accuracy of results. In the frame of Cartesian grid, one often uses finite volume method with second order accuracy or finite difference method. In this paper, an h‐adaptive Runge–Kutta discontinuous Galerkin (RKDG) method on Cartesian grid with ghost cell immersed boundary method for arbitrarily complex geometries is developed. A ghost cell immersed boundary treatment with the modification of normal velocity is presented. The method is validated versus well documented test problems involving both steady and unsteady compressible flows through complex bodies over a wide range of Mach numbers. The numerical results show that the present boundary treatment to some extent reduces the error of entropy and demonstrate the efficiency, robustness, and versatility of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

A sharp‐interface immersed boundary framework for simulations of high‐speed inviscid compressible flows

A new finite‐volume flow solver based on the hybrid Cartesian immersed boundary (IB) framework is developed for the solution of high‐speed inviscid compressible flows. The IB method adopts a sharp‐interface approach, wherein the boundary conditions are enforced on the body geometry itself. A key component of the present solver is a novel reconstruction approach, in conjunction with inverse distance weighting, to compute the solutions in the vicinity of the solid‐fluid interface. We show that proposed reconstruction leads to second‐order spatial accuracy while also ensuring that the discrete conservation errors diminish linearly with grid refinement. Investigations of supersonic and hypersonic inviscid flows over different geometries are carried out for an extensive validation of the proposed flow solver. Studies on cylinder lift‐off and shape optimisation in supersonic flows further demonstrate the efficacy of the flow solver for computations with moving and shape‐changing geometries. These studies conclusively highlight the capability of the proposed IB methodology as a promising alternative for robust and accurate computations of compressible fluid flows on nonconformal Cartesian meshes.     

Simulation of forced deformable bodies interacting with two-dimensional incompressible flows: Application to fish-like swimming

We present an efficient algorithm for simulation of deformable bodies interacting with two-dimensional incompressible fluid flows. The temporal and spatial discretizations of the Navier–Stokes equations in vorticity stream-function formulation are based on classical fourth-order Runge–Kutta scheme and compact finite differences, respectively. Using a uniform Cartesian grid we benefit from the advantage of a new fourth-order direct solver for the Poisson equation to ensure the incompressibility constraint down to machine zero over an optimal grid. For introducing a deformable body in fluid flow, the volume penalization method is used. A Lagrangian structured grid with prescribed motion covers the deformable body which is interacting with the surrounding fluid due to the hydrodynamic forces and the torque calculated on the Eulerian reference grid. An efficient law for controlling the curvature of an anguilliform fish, swimming toward a prescribed goal, is proposed which is based on the geometrically exact theory of nonlinear beams and quaternions. Validation of the developed method shows the efficiency and expected accuracy of the algorithm for fish-like swimming and also for a variety of fluid/solid interaction problems.     

含化学反应膛口流场的无网格数值模拟

基于无网格方法,对包含大位移运动边界和非平衡化学反应的膛口流场进行了数值模拟。所发展算法是基于线性基函数最小二乘显式无网格方法,忽略黏性及湍流的影响,对流场采用ALE(arbitrary Lagrangian-Eulerian)形式的Euler方程描述,对流通量和化学反应源项采用多组分HLLC(Harten-Lax-van Leer-Contact)格式和有限速率反应模型计算,对于运动边界造成的点云畸形采用局部点云重构方法处理,重构过程中采用虚拟边阵面推进。对圆柱绕流和激波诱导燃烧流场进行了数值模拟,验证了重构方法和化学反应计算的有效性。最后对12.7 mm口径机枪膛口流场进行了模拟,结果同实验照片、非结构网格方法结果吻合较好,数值结果清晰地再现了膛口初始冲击波、膛口冲击波、欠膨胀射流波系结构的动力学发展过程,以及膛口焰的时间、空间分布特征。

     

A mesh-free radial basis function–based semi-Lagrangian lattice Boltzmann method for incompressible flows

In this paper, a local radial basis function–based semi-Lagrangian lattice Boltzmann method (RBF-SL-LBM) is proposed. This is a mesh-free method that can be used for the simulation of incompressible flows. In this method, the collision step is performed locally, which is the same as in the standard LBM. In the meanwhile, the steaming step is solved in a semi-Lagrangian framework. The distribution functions at the departure points, which may be not the grid points in general, are computed by the local radial basis function interpolation. Several numerical tests are conducted to validate the present method, including the lid-driven cavity flow, the steady and unsteady flow past a circular cylinder, and the flow past an NACA0012 airfoil. The present results are in good agreement with those published in the previous literature, which demonstrates the capability of RBF-SL-LBM for the simulation of incompressible flows.     

An Adaptive Cartesian Mesh Based Method to Simulate Turbulent Flows of Multiple Rotating Surfaces

An efficient Cartesian cut-cell/level-set method based on a multiple grid approach to simulate turbulent turbomachinery flows is presented. The finite-volume approach in an unstructured hierarchical Cartesian setup with a sharp representation of the complex moving boundaries embedded into the computational domain, which are described by multiple level-sets, ensures a strict conservation of mass, momentum, and energy. Furthermore, an efficient kinematic motion level-set interface method for the rotation of embedded boundaries described by multiple level-set fields on a computational domain distributed over several processors is introduced. This method allows the simulation of multiple boundaries rotating relatively to each other in a fixed frame of reference. To demonstrate the efficiency of the numerical method and the quality of the computed findings the generic test problem of a rotating cylinder surrounded by a stationary hull and the flow over a ducted rotating axial fan with a stationary turbulence generating grid at the inflow are simulated. The computational results of the axial fan show a good agreement with the experimental data.     

A particle–gridless hybrid method for incompressible flows

A particle–gridless hybrid method for the analysis of incompressible flows is presented. The numerical scheme consists of Lagrangian and Eulerian phases as in an arbitrary Lagrangian–Eulerian (ALE) method, where a new‐time physical property at an arbitrary position is determined by introducing an artificial velocity. For the Lagrangian calculation, the moving‐particle semi‐implicit (MPS) method is used. Diffusion and pressure gradient terms of the Navier–Stokes equation are calculated using the particle interaction models of the MPS method. As an incompressible condition, divergence of velocity is used while the particle number density is kept constant in the MPS method. For the Eulerian calculation, an accurate and stable convection scheme is developed. This convection scheme is based on a flow directional local grid so that it can be applied to multi‐dimensional convection problems easily. A two‐dimensional pure convection problem is calculated and a more accurate and stable solution is obtained compared with other schemes. The particle–gridless hybrid method is applied to the analysis of sloshing problems. The amplitude and period of sloshing are predicted accurately by the present method. The range of the occurrence of self‐induced sloshing predicted by the present method shows good agreement with the experimental data. Calculations have succeeded even for the higher injection velocity range, where the grid method fails to simulate. Copyright © 1999 John Wiley & Sons, Ltd.     

Finite volume computation of the turbulent flow over a hill employing 2D or 3D non-orthogonal collocated grid systems

A general numerical method for the solution of the complete Reynolds-averaged Navier-Stokes equations for 2D or 3D flows is described. The method uses non-orthogonal co-ordinates, Cartesian velocity components and a pressure-velocity-coupling algorithm adequate for non-staggered grid systems. The capability of the method and the overall performance of the κ–? eddy viscosity model are demonstrated by calculations of 2D and 3D flow over a hill. Solution error estimations based on fine grids, e.g. 320 × 192 control volumes, together with comparisons with standard turbulence model modifications, low-Reynoldsnumber or streamline curvature effects, have allowed the investigation of model drawbacks in predicting turbulent flows over surface-mounted hills.     

Chimera technique for transporting disturbances

The Chimera technique for moving grids is used to take into account nonhomogeneous unsteady inflow conditions in the simulation of aerodynamic flows. The method is applied to simulate the transport of a large‐scale vortex by a mean velocity field over a large distance, where it finally interacts with an airfoil. The Chimera approach allows one to resolve the vortex on a fine grid, whereas the unstructured background grid covering most of the computational domain can be much coarser. This method shows the same low numerical dissipation as a simulation on a globally fine grid. Several precursor tests are performed with a finite modified analytical Lamb–Oseen type vortex to study the influence of spatial and temporal resolution and the employed numerical scheme. Then, the interaction of an analytical vortex with a NACA0012 airfoil and with an ONERA‐A airfoil near stall is studied. Finally, a realistic vortex is generated by a ramping airfoil and is transported on a moving Chimera block and then interacts with a two‐element airfoil, which allows one to simulate a typical setup for a gust generator in aerodynamic facilities. Copyright © 2012 John Wiley & Sons, Ltd.     

A study on the extension of a VOF/PLIC based method to a curvilinear co-ordinate system

The conventional volume-of-fluid method has the potential to deal with large free surface deformation on a fixed Cartesian grid. However, when free-surface flows are within or over complex geometries of industrial relevance, such as free-surface flows over offshore oil platforms, it is advantageous to extend the method originally written in Cartesian forms into non-Cartesian forms. In the present study, an algorithm similar to the algorithm described by Rudman in 1997 is proposed for use with curvilinear co-ordinates. This extension results in the ability to model complex geometries which could not be modelled using the original algorithm. Excellent agreement between the solutions obtained on both orthogonal and non-orthogonal meshes is achieved, although in general the L ₁ error, based on the exact solution, on the non-orthogonal mesh is slightly higher than that on the orthogonal mesh. The extended fluid flow solving capacity of the present method is demonstrated through its application to a non-orthogonal Rayleigh–Taylor instability problem.     

CFD结合降阶模型预测阵风响应

传统的阵风响应主要在频域内进行分析,气动载荷基于线性方法计算,不能考虑黏性和跨声速流动影响. 飞机设计需考虑不同频率和不同形状阵风的响应,基于CFD的阵风响应预测由于计算工况太多,工作量巨大. 本文发展了一种CFD结合非定常气动力ARMA(autoregressive-moving-averagemodel)降阶模型的阵风响应分析方法,CFD只要针对给定频率和形状的一种阵风响应进行计算,对获得的气动力时间历程运用线性最小二乘法参数辨识ARMA降阶模型的系数,则对任意频率和形状的阵风,代入降阶模型即可确定该阵风的响应,大大提高了计算效率. 为效验发展的方法,先计算NACA0012翼型在低马赫数0.11的阵风响应,通过对比CFD、ARMA降阶模型及早期发展的不可压阵风响应预测方法的结果,验证了方法的有效性. 再对比CFD、ARMA在跨声速马赫数0.8的阵风响应预测结果,证实所发展的方法对跨声速阵风响应预测亦是有效的.      

High-order overset grid method for detecting particle impaction on a cylinder in a cross flow

An overset grid method was developed to investigate the interaction between a particle-laden flow and a circular cylinder. The method is implemented in the Pencil Code, a high-order finite-difference code for compressible flow simulation. High-order summation-by-parts operators were used at the cylinder boundary, and both bi-linear Lagrangian and bi-quadratic spline interpolation were used to communicate between the Cartesian background grid and the body-conformal cylindrical grid. The performance of the overset grid method was assessed to benchmark cases of steady and unsteady flows past a cylinder. Results show high-order accuracy and good agreement to the literature. Particle-laden flow simulations were performed, with inertial point particles impacting on a cylinder. The simulations reproduced results from the literature at a significantly reduced cost. Further, an investigation into blockage effects on particle impaction revealing that the previously published DNS data is less accurate than assumed for particles with very small Stokes numbers.     

A local domain‐free discretization method for simulation of incompressible flows over moving bodies

This paper presents a local domain‐free discretization (DFD) method for the simulation of unsteady flows over moving bodies governed by the incompressible Navier–Stokes equations. The discretization strategy of DFD is that the discrete form of partial differential equations at an interior point may involve some points outside the solution domain. All the mesh points are classified as interior points, exterior dependent points and exterior independent points. The functional values at the exterior dependent points are updated at each time step by the approximate form of solution near the boundary. When the body is moving, only the status of points is changed and the mesh can stay fixed. The issue of ‘freshly cleared nodes/cells’ encountered in usual sharp interface methods does not pose any particular difficulty in the presented method. The Galerkin finite‐element approximation is used for spatial discretization, and the discrete equations are integrated in time via a dual‐time‐stepping scheme based on artificial compressibility. In order to validate the present method for moving‐boundary flow problems, two groups of flow phenomena have been simulated: (1) flows over a fixed circular cylinder, a harmonic in‐line oscillating cylinder in fluid at rest and a transversely oscillating cylinder in uniform flow; (2) flows over a pure pitching airfoil, a heaving–pitching airfoil and a deforming airfoil. The predictions show good agreement with the published numerical results or experimental data. Copyright © 2010 John Wiley & Sons, Ltd.