A Moving Mesh Method for Kinetic/Hydrodynamic Coupling

This paper deals with the application of a moving mesh method for kinetic/hydrodynamic coupling model in two dimensions. With some criteria, the domain is dynamically decomposed into three parts: kinetic regions where fluids are far from equilibrium, hydrodynamic regions where fluids are near thermodynamical equilibrium and buffer regions which are used as a smooth transition. The Boltzmann-BGK equation is solved in kinetic regions, while Euler equations in hydrodynamic regions and both equations in buffer regions. By a well defined monitor function, our moving mesh method smoothly concentrate the mesh grids to the regions containing rapid variation of the solutions. In each moving mesh step, the solutions are conservatively updated to the new mesh and the cut-off function is rebuilt first to consist with the region decomposition after the mesh motion. In such a framework, the evolution of the hybrid model and the moving mesh procedure can be implemented independently, therefore keep the advantages of both approaches. Numerical examples are presented to demonstrate the efficiency of the method.     

ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method

We present a new reconnection-based arbitrary-Lagrangian–Eulerian (ALE) method. The main elements in a standard ALE simulation are an explicit Lagrangian phase in which the solution and grid are updated, a rezoning phase in which a new grid is defined, and a remapping phase in which the Lagrangian solution is transferred (conservatively interpolated) onto the new grid. In standard ALE methods the new mesh from the rezone phase is obtained by moving grid nodes without changing connectivity of the mesh. Such rezone strategy has its limitation due to the fixed topology of the mesh. In our new method we allow connectivity of the mesh to change in rezone phase, which leads to general polygonal mesh and allows to follow Lagrangian features of the mesh much better than for standard ALE methods. Rezone strategy with reconnection is based on using Voronoi tessellation. We demonstrate performance of our new method on series of numerical examples and show it superiority in comparison with standard ALE methods without reconnection.     

Remapping-free ALE-type kinetic method for flow computations

Based on the integral form of the fluid dynamic equations, a finite volume kinetic scheme with arbitrary control volume and mesh velocity is developed. Different from the earlier unified moving mesh gas-kinetic method [C.Q. Jin, K. Xu, An unified moving grid gas-kinetic method in Eulerian space for viscous flow computation, J. Comput. Phys. 222 (2007) 155–175], the coupling of the fluid equations and geometrical conservation laws has been removed in order to make the scheme applicable for any quadrilateral or unstructured mesh rather than parallelogram in 2D case. Since a purely Lagrangian method is always associated with mesh entangling, in order to avoid computational collapsing in multidimensional flow simulation, the mesh velocity is constructed by considering both fluid velocity (Lagrangian methodology) and diffusive velocity (Regenerating Eulerian mesh function). Therefore, we obtain a generalized Arbitrary-Lagrangian–Eulerian (ALE) method by properly designing a mesh velocity instead of re-generating a new mesh after distortion. As a result, the remapping step to interpolate flow variables from old mesh to new mesh is avoided. The current method provides a general framework, which can be considered as a remapping-free ALE-type method. Since there is great freedom in choosing mesh velocity, in order to improve the accuracy and robustness of the method, the adaptive moving mesh method [H.Z. Tang, T. Tang, Adaptive mesh methods for one-and two-dimensional hyperbolic conservation laws, SIAM J. Numer. Anal. 41 (2003) 487–515] can be also used to construct a mesh velocity to concentrate mesh to regions with high flow gradients.     

Simulating finger phenomena in porous media with a moving finite element method

The non-equilibrium Richards equation is solved using a moving finite element method in this paper. The governing equation is discretized spatially with a standard finite element method, and temporally with second-order Runge–Kutta schemes. A strategy of the mesh movement is based on the work by Li et al. [R.Li, T.Tang, P.W. Zhang, A moving mesh finite element algorithm for singular problems in two and three space dimensions, Journal of Computational Physics, 177 (2002) 365–393]. A Beckett and Mackenzie type monitor function is adopted. To obtain high quality meshes around the wetting front, a smoothing method which is based on the diffusive mechanism is used. With the moving mesh technique, high mesh quality and high numerical accuracy are obtained successfully. The numerical convergence and the advantage of the algorithm are demonstrated by a series of numerical experiments.     

径向基函数插值方法在动网格技术中的应用

分析用于非结构网格的弹簧比拟和用于结构网格的无限插值动态网格方法在实际应用中的优缺点,提出无需网格连接关系的基于径向基函数(radial basis functions,RBF)插值的动网格技术并编制相应的网格运动计算程序.以二维菱形翼的旋转运动及三维菱形翼的柔性变形为例,分析不同基函数和紧支半径的选取对网格质量及计算效率的影响,并通过与弹簧比拟方法的对比验证了RBF方法的有效性.结果表明:RBF方法数据结构简单,计算效率高,适应大变形能力强,可以有效地实现计算流体力学中的网格运动问题.     

Modeling merging and breakup in the moving mesh interface tracking method for multiphase flow simulations

The three-dimensional, moving mesh interface tracking (MMIT) method coupled with local mesh adaptations by Quan and Schmidt [S.P. Quan, D.P. Schmidt, A moving mesh interface tracking method for 3D incompressible two-phase flows, J. Comput. Phys. 221 (2007) 761–780] demonstrated the capability to accurately simulate multiphase flows, to handle large deformation, and also to perform interface pinch-off for some specific cases. However, another challenge, i.e. how to handle interface merging (such as droplet coalescence) has not been addressed. In this paper, we present a mesh combination scheme for interface connection and a more general mesh separation algorithm for interface breakup. These two schemes are based on the conversion of liquid cells in one phase to another fluid by changing the fluid properties of the cells in the combination or separation region. After the conversion, the newly created interface is usually ragged, and a local projection method is employed to smooth the interface. Extra mesh adaptation criteria are introduced to handle colliding interfaces with almost zero curvatures as the distance between the interfaces diminishes. Simulations of droplet pair collisions including both head-on and off-center coalescences show that the mesh adaptations are capable of resolving very small length scales, and the mesh combination and mesh separation schemes can handle the topological transitions in multiphase flows. The potential of our method to perform detailed investigations of droplet coalescence and breakup is also displayed.     

中厚板弯曲问题的Kriging插值无网格法

基于Reissner-Mindlin板弯曲理论,将Kriging插值无网格法应用于中厚板弯曲问题,推导相应的离散方程.该方法可以只依赖于一组离散的节点建立试函数,有效地避免了复杂的网格划分和网格畸变的影响.相对于无网格法中常用的移动最小二乘近似而言,滑动Kriging插值法的形函数满足Kronecker delta函数性质,可以直接施加本质边界条件.算例分析表明,用Kriging插值无网格法分析中厚板弯曲问题,具有效率高,精度高和易于实现等优点.     

基于任意拉格朗日—欧拉型移动网格的反应流广义黎曼问题方法

提出一种在自由重映移动网格下的广义黎曼问题方法模拟反应流.该方法基于显式的自由重映移动网格广义黎曼问题的解.为保证在时间和空间上的高精度，应用广义黎曼问题方法构造数值通量.为保证反应区的高分辨率，采用变分法生成自适应移动网格.该方法不仅能够保证网格质量，而且能有效地避免任意拉格朗日—欧拉方法中由于显式重映过程而带来的数值误差.包括CJ爆轰及不稳定爆轰的数值实验说明该格式的精确性和鲁棒性，证明这种移动网格下的二阶广义黎曼问题方法可以较好地捕捉反应流的间断与光滑结构.     

一维非线性对流占优扩散方程的变网格特征差分方法

针对一维非线性对流占优扩散方程,提出了一类变网格特征差分格式,该格式能够根据解的梯度变化及时对计算网格进行调整.与均匀网格格式相比,给出的变网格特征差分格式对于对流占优扩散问题有着更好的计算效果.     

一种含运动固壁超声速流动的Descartes网格算法

提出一种Descartes网格算法,用于数值求解含任意复杂及运动固壁的超声速流动问题.采用位标集函数确定和跟踪流-固界面.引入虚网格技术处理流-固边界条件,并沿法向和切向分别进行计算.该算法简单、稳健,可与高阶有限差分格式并用.选取一组一维/二维静止或运动物体绕流算例,验证其有效性.     

The non-stationary freefield response for a moving load with a random amplitude

This paper presents a stochastic solution procedure for the calculation of the non-stationary freefield response due to a moving load with a random amplitude. In this case, a non-stationary autocorrelation function and a time-dependent spectral density are required to characterize the response at a fixed point in the freefield. The non-stationary solution is derived from the solution in the case of a moving load with a deterministic amplitude. It is shown how the deterministic solution can be calculated in an efficient way by means of integral transformation methods if the problem geometry exhibits a translational invariance in the direction of the moving load. A key ingredient is the transfer function between the source and the receiver that represents the fundamental response in the freefield due to an impulse load at a fixed location. The solution in the case of a moving load with a random amplitude is formulated in terms of the double forward Fourier transform of the non-stationary autocorrelation function. The solution procedure is illustrated with an example where the non-stationary autocorrelation function and the time-dependent standard deviation of the freefield response are computed for a moving harmonic load with a random phase shift. The results are compared with the response in the deterministic case.     

简单有效的运动汽车投影阴影分割算法

在实时的车型识别系统中,由于光照的影响,需要一种简单快速有效的方法将汽车车体与其阴影分割开。利用阴影的光谱属性,同时根据阴影的几何特征及阴影区域内的点和汽车的空间位置、形状等相关特点,提出一种基于小波变换多分辨率特性的阴影分割算法,该算法能有效地分割出阴影与目标之间的分界线。先利用阴影的光谱属性对阴影进行粗分割,然后利用小波变换的多尺度性对候选阴影点进行特征提取,从而获取最后的阴影分界线。该方法不需要事先确定光源的方向、车体的彩色信息和背景纹理信息,能有效地分割任何颜色、任何背景纹理下、任何光源方向下的运动汽车投影阴影。实验表明,该方法定位准确,处理速度快,抗噪能力强,为进一步的车型识别提供基础。     

含运动物体流场计算的自适应非结构二维网格生成方法

采用自动插点的Delaunay方法和局部网格重新生成方法,对含运动边界自适应非结构二维网格生成方法进行了系统研究,实现了带有非定常运动物体流场的数值计算,并进行了数值实验.     

Accurate and fast simulation of Kolmogorov phase screen by combining spectral method with Zernike polynomials method

A new method is proposed to simulate the Kolmogorov phase screen. A hybrid phase screen is achieved by linearly combining two phase screens simulated by both spectral and Zernike polynomials methods. Unlike the imperfection of phase structure function existing at some spatial frequencies in each of the two methods, the mean structure function of the hybrid phase screens coincides remarkably well with theory in the whole spatial frequency domain. Apart from advantage on accuracy, the proposed method also saves considerable computational time. For a phase screen with certain accuracy, the new method is ten times and seven times faster compared with the spectral method and Zernike polynomials method, respectively.     

基于WENO重构的高阶移动网格动理学格式

提出一种基于WENO重构的高阶(至少三阶)移动网格动理学格式.利用流体力学方程的积分形式得到移动网格上离散格式,再利用自适应移动网格方法移动网格,进而得到网格速度,利用WENO重构得到高阶插值多项式,最后使用时间方向上精确的动理学数值方法构造数值通量,得到移动网格单元上新的物理量.数值实验表明这种格式同时具有高精度、高分辨率的特点.     

Moving mesh methods for blowup in reaction–diffusion equations with traveling heat source

In this paper moving mesh methods are used to simulate the blowup in a reaction–diffusion equation with traveling heat source. The finite-time blowup occurs if the speed of the movement of the heat source remains sufficiently low, and the blowup procedure is not fixed at one point not like that for stationary heat source. As time goes to the blowup time, the blowup profile converges to a stationary state. In the simulation a new moving mesh algorithm is designed to deal with the difficulty caused by the delta function in the traveling heat source. The convergence rates are verified and new blowup figures are generated from the numerical experiments.     

统一坐标系下多介质流体力学计算的一种方法

采用一种基于网格节点之间的吸引和排斥重新分布节点的移动网格目的确定网格移动的速度,目的简单,易于实现.数值结果表明,本目的不仅可以显著地提高计算效率,而且仍然具有较高的流场分辨率.     

A Pseudo-Stokes Mesh Motion Algorithm

This work presents a moving mesh methodology based on the solution of a pseudo flow problem. The mesh motion is modeled as a pseudo Stokes problem solved by an explicit finite element projection method. The mesh quality requirements are satisfied by employing a null divergent velocity condition. This methodology is applied to triangular unstructured meshes and compared to well known approaches such as the ones based on diffusion and pseudo structural problems. One of the test cases is an airfoil with a fully meshed domain. A specific rotation velocity is imposed as the airfoil boundary condition. The other test is a set of two cylinders that move toward each other. A mesh quality criterion is employed to identify critically distorted elements and to evaluate the performance of each mesh motion approach. The results obtained for each test case show that the pseudo-flow methodology produces satisfactory meshes during the moving process.     

ENO守恒插值(重映)方法及其在流体计算中的应用

在ENO(Essentially Non-oscillatory)守恒插值方法的基础上,分析和研究现今流体力学计算中涉及的几类网格技术:重叠网格技术、自适应加密技术和运动网格技术.基于ENO插值多项式构造的重映方法具有良好的守恒性,可以有效保证数据传递中物理量的总体守恒.提出该类守恒插值方法在以上几种网格技术中的一些应用前景,并给出一些数值算例.     

Location impact of a pair of magnetic sources on melting of a magneto-Ferro phase change substance

The current numerical study aims to observe the location impact of a pair of magnetic sources on the melting rate of a magneto-ferro phase change substance in a cavity. The advanced moving mesh method is employed to model the phase change at an exact fusion temperature. The left and right walls of the enclosure are subject to the higher and lower temperatures, respectively. Two other walls are kept insulated. The pair of the non-uniform magnetic fields are located in the vicinity of the walls of the enclosure. Galerkin finite element method is employed to obtain the numerical results. The Arbitrary Lagrangian–Eulerian (ALE) deformed mesh technique allowing deformation of the interface of the molten and non-molten regions is set up. The outcomes demonstrate the dependency of the progress of the melting front to the location of the sources. When the pair of sources are placed in the vicinity of the cold wall, the melting rate is higher. On the other hand, the final time of the melting process is almost the same for the cases with the sources placed in the adjacent of the cold left and insulated bottom walls.