A lattice Boltzmann approach for free-surface-flow simulations on non-uniform block-structured grids

In this paper, we present a hybrid volume-of-fluid-based algorithm for the simulation of free-surface-flow problems. For the solution of the flow field, the lattice Boltzmann method is used. The additional advection equation for the volume-of-fluid (VOF) fill level is discretized with a classical finite volume method. For the interface reconstruction, a piecewise linear interface reconstruction in 3D has been implemented. The free-surface-tracking algorithm is embedded into the 3D, non-uniform, lattice-Boltzmann-based solver VirtualFluids; Freudiger et al. (2009) [1], Freudiger (2009) [2]. The advection algorithm is verified and validated with well-known advection test cases. For the validation of the free-surface algorithm, we present simulations of a breaking-dam benchmark.     

Optimal injection operator and high order schemes for multigrid solution of 3D poisson equation

We present a multigrid solution of the three dimensional Poisson equation with a fourth order 19-point compact finite difference scheme. Using a red–black ordering of the grid points and some geometric considerations, we derive an optimal scaled injection operator for the multigrid algorithm. Numerical computations show that this operator yields not only the smallest overall CPU time, but also the best convergence rate compared to other more traditional projection operators. In addition, we present a family of 19-point compact schemes and numerically show that each one has a different optimal scaled injection operator.     

Implicit methods for fluid dynamics

This paper represents the contributions to the development of implicit procedures for solving the equations of fluid dynamics made by Briley and McDonald (1975)[1], Beam and Warming (1976, 1978) [2] and [3] and Lombard et al. (1983) [4]. The contributions of Briley and McDonald and Beam and Warming are well known, but Lombard has not been fully recognized for his innovative contributions to flux vector splitting and use of the DDADI (Diagonally Dominate Alternating Direction Implicit) algorithm. Their contributions are presented herein.Fully implicit algorithms are applied to two complex flow problems of current interest, (1) hypersonic non-equilibrium flow about a blunt nosed body and (2) flow within an MFD (magneto-fluid dynamics) accelerator. These two applications would be exceeding costly without the use of fully implicit methods.     

An implicit matrix-free Discontinuous Galerkin solver for viscous and turbulent aerodynamic simulations

This paper presents some recent advancements of the computational efficiency of a Discontinuous Galerkin (DG) solver for the Navier–Stokes (NS) and Reynolds Averaged Navier Stokes (RANS) equations. The implementation and the performance of a Newton–Krylov matrix-free (MF) method is presented and compared with the matrix based (MB) counterpart. Moreover two solution strategies, developed in order to increase the solver efficiency, are discussed and experimented. Numerical results of some test cases proposed within the EU ADIGMA (Adaptive Higher-Order Variational Methods for Aerodynamic Applications in Industry) project demonstrate the capabilities of the method.     

Reliable performance prediction for multigrid software on distributed memory systems

We propose a model for describing and predicting the parallel performance of a broad class of parallel numerical software on distributed memory architectures. The purpose of this model is to allow reliable predictions to be made for the performance of the software on large numbers of processors of a given parallel system, by only benchmarking the code on small numbers of processors. Having described the methods used, and emphasized the simplicity of their implementation, the approach is tested on a range of engineering software applications that are built upon the use of multigrid algorithms. Despite their simplicity, the models are demonstrated to provide both accurate and robust predictions across a range of different parallel architectures, partitioning strategies and multigrid codes. In particular, the effectiveness of the predictive methodology is shown for a practical engineering software implementation of an elastohydrodynamic lubrication solver.     

Transparent boundary conditions for quantum-waveguide simulations

We consider the two-dimensional, time-dependent Schrödinger equation discretized with the Crank–Nicolson finite difference scheme. For this difference equation we derive discrete transparent boundary conditions (DTBCs) in order to get highly accurate solutions for open boundary problems. We apply inhomogeneous DTBCs to the transient simulation of quantum waveguides with a prescribed electron inflow.     

Numerical techniques for parallel dynamics in electromagnetic gyrokinetic Vlasov simulations

Numerical techniques for parallel dynamics in electromagnetic gyrokinetic simulations are introduced to regulate unphysical grid-size oscillations in the field-aligned coordinate. It is found that a fixed boundary condition and the nonlinear mode coupling in the field-aligned coordinate, as well as numerical errors of non-dissipative finite difference methods, produce fluctuations with high parallel wave numbers. The theoretical and numerical analyses demonstrate that an outflow boundary condition and a low-pass filter efficiently remove the numerical oscillations, providing small but acceptable errors of the entropy variables. The new method is advantageous for quantitative evaluation of the entropy balance that is required for obtaining a steady state in gyrokinetic turbulence.     

An arbitrary Lagrangian Eulerian formulation for residual distribution schemes on moving grids

The arbitrary Lagrangian Eulerian formulation is derived for the residual distribution method on moving meshes. The system of Euler equations is discretized on moving meshes and in case of deforming meshes a geometrical source term has to be taken into account. A conservative linearization guarantees the conservation property of the discretized equations.From the geometric conservation law we obtain the appropriate integration points in time for the cell fluctuation and a guideline for how to distribute the geometrical source term.Testcases include the flow around a transonic oscillating airfoil and a convected vortex. In the first case a rigidly moving mesh is employed, while in the other testcase a deforming mesh is used to investigate the influence of the geometrical source term on the solution.     

An implicit gas-kinetic scheme for turbulent flow on unstructured hybrid mesh

In this study, an implicit scheme for the gas-kinetic scheme (GKS) on the unstructured hybrid mesh is proposed. The Spalart–Allmaras (SA) one equation turbulence model is incorporated into the implicit gas-kinetic scheme (IGKS) to predict the effects of turbulence. The implicit macroscopic governing equations are constructed and solved by the matrix-free lower-upper symmetric-Gauss–Seidel (LU-SGS) method. To reduce the number of cells and computational cost, the hybrid mesh is applied. A modified non-manifold hybrid mesh data(NHMD) is used for both unstructured hybrid mesh and uniform grid. Numerical investigations are performed on different 2D laminar and turbulent flows. The convergence property and the computational efficiency of the present IGKS method are investigated. Much better performance is obtained compared with the standard explicit gas-kinetic scheme. Also, our numerical results are found to be in good agreement with experiment data and other numerical solutions, demonstrating the good applicability and high efficiency of the present IGKS for the simulations of laminar and turbulent flows.     

An efficient and robust method for Lagrangian magnetic particle tracking in fluid flow simulations on unstructured grids

In this paper we report on a newly developed particle tracking scheme for fluid flow simulations on 3D unstructured grids, aiming to provide detailed insights in the particle behaviour in complex geometries. A possible field of applications is the magnetic drug targeting (MDT) technique, on which this paper will be focused. MDT is a promising medical technique that uses locally applied magnetic fields to capture magnetic drug carriers at the desired locations in the human body, strongly increasing the efficiency of medical drugs. The new particle tracking scheme combines the advantages of existing methods and is easy for implementation in a generic numerical code. The scheme is tested and validated for simple MDT cases that include effects of a non-homogeneous magnetic field on deposition of magnetic particles in laminar flow. The first test case is a validation study of the magnetic particle trajectories released in a horizontal circular pipe flow with a current-carrying wire parallel to the flow, for which analytical solutions are reported in literature. The second test case involves particle capture efficiencies in a 90° bent tube for different configurations of the imposed magnetic field. This configuration corresponds more closely to the conditions inside blood vessels, because of the presence of secondary motions. These results are compared with numerical studies from literature too. The obtained results demonstrate that the developed particle tracking scheme is a very robust, efficient and accurate method, which can give detailed insights in particle behaviour in complex geometries. As such it is a good candidate for future applications and optimisations of MDT technique for loco-regional cancer treatment or treatment of cardiovascular diseases.     

基于双特征和松弛边界的随机森林进行异常点检测

针对现有基于随机森林的异常检测算法性能不高的问题，提出一种结合双特征和松弛边界的随机森林算法用于异常点检测。首先，在只使用正常类数据构建随机森林的分类决策树过程中，在二叉决策树的每个节点里记录两个特征的取值范围（每个特征对应一个值域），以此双特征值域作为异常点判断的依据。然后，在进行异常检测时，当某样本不满足决策树节点中的双特征值域时，该样本被标记为候选异常类；否则，该样本进入决策树的下层树节点继续作特征值域的比较，若无下层节点则被标记为候选正常类。最后，由随机森林算法中的判别机制决定该样本的类别。在5个UCI数据集上进行的异常点检测实验结果表明，所提方法比现有的异常检测随机森林算法性能更好，其综合性能与孤立森林（iForest）和一类支持向量机（OCSVM）方法相当或更好，且稳定于较高水平。     

基于UG_OPEN的边界面法CAE模型边界条件可视化算法

针对边界面法分析模型前处理过程中边界条件的加载,提出了一种基于UG/OPEN的可视化算法。算法首先利用UG系统中几何模型的边界表征数据,在参数空间生成背景网格以及计算显示点的坐标,然后再映射到三维空间进行图形显示,映射后能够保证几何信息的准确性。该算法不仅实现了与UG系统的无缝连接、载荷和位移约束条件的自动显示,而且有利于实现CAD和CAE模型的一体化。     

A Tracing Algorithm for Surface-Surface Intersections on Surface Boundaries

In this paper we present an algorithm with a new trace-terminating condition for tracing along surface-surface intersection curves on surface boundaries,while several tracing methods and embedding methods that include tracing scheme may cause false termination with a traditional trace-terminating condition:tracing stops when the surface-domain‘s boundary is reached.And we also suggest another iterative method to calculate intersection points on surface boundaries with parallel surface normal.Some numerical examnples with these two ideas and comparisons to ‘DESIGNBASE‘,ACIS,and Parasolid are included to demonstrate the effectiveness of our algorithm.     

Generation of random non-overlapping dot patterns for light guides using molecular dynamics simulations with variable r-cut and reflective boundary techniques

This paper presents a molecular dynamics (MD) scheme for the automatic generation of dot patterns for the light guides used in LCD backlight modules. Several MD computational techniques are integrated with the conventional MD scheme to enable the adjustment of the dot density in specific regions of the light guide in order to create a dot distribution with a high dot density variation and a high spatial uniformity. These techniques include the cell division technique, the variable r-cut technique, the boundary smoothing technique and the reflective boundary condition. The reflective boundary condition enables a precise control of the dot density within each cell, and is instrumental in achieving a dot distribution with both a high dot density variation and a high spatial uniformity. The performance of the proposed dot generation scheme is verified by considering the practical example of the dot pattern design of a light guide with a single LED light source located in the lower-right corner. The numerical results confirm the ability of the proposed method to achieve an even luminance condition by establishing a dot pattern whose density increases concentrically with an increasing distance from the light source.     

Wave-splitting and absorbing boundary condition for Maxwell's equations on a curved surface

Wave-splitting of Maxwell's equations on a curved surface in three-dimension is derived from the conditions for out-going and in-coming waves. The condition for out-going wave is used to derive an absorbing boundary condition on a non-planar surface. A local approximation of the absorbing boundary condition is given. As a special case, a spherical absorbing boundary which truncates the computational domain is also considered in detail.     

薄壁圆柱壳的高阶模态振动特性研究

采用解析法研究了不同边界条件下薄壁圆柱壳的高阶模态振动特性.首先基于Love壳体理论,在简支-简支、固支-固支和固支-自由三种边界条件下,通过伽辽金法建立了动力学模型,对模态特性进行求解,得到了高阶固有频率和三维模态振型,并通过文献和有限元法进行了比较.算例结果表明,两端简支边界条件下采用解析法得到的固有频率误差值不超过2%,当周向波数较小时固有频率先减小后增加,在高阶时的固有频率逐渐升高,当轴向半波数增加时固有频率明显增大,通过解析法、文献和有限元法得到的三维模态振型相吻合.     

Successive underrelaxation (SUR) and generalised conjugate gradient (GCG) methods for hyperbolic difference equations on a parallel computer

When we consider the numerical solution of the 2-dimensional linear hyperbolic problem by implicit difference equations we need to solve a set of linear systems Ax = b with many rightband sides b, where A is large, sparse and nonsymmetric. The SUR (Successive Underrelaxation) and GCG (Generalised Conjugate Gradient) methods are used for solving the linear systems. We compare the two methods on sequential and parallel computations. Numerical results indicate that the SUR method is nearly twice as fast as the GCG method and the SUR method has an almost linear speedup.     

A Tailored Finite Point Method for a Singular Perturbation Problem on an Unbounded Domain

In this paper, we propose a tailored-finite-point method for a kind of singular perturbation problems in unbounded domains. First, we use the artificial boundary method (Han in Frontiers and Prospects of Contemporary Applied Mathematics, [2005]) to reduce the original problem to a problem on bounded computational domain. Then we propose a new approach to construct a discrete scheme for the reduced problem, where our finite point method has been tailored to some particular properties or solutions of the problem. From the numerical results, we find that our new methods can achieve very high accuracy with very coarse mesh even for very small ε. In the contrast, the traditional finite element method does not get satisfactory numerical results with the same mesh. Han was supported by the NSFC Project No. 10471073. Z. Huang was supported by the NSFC Projects No. 10301017, and 10676017, the National Basic Research Program of China under the grant 2005CB321701. R.B. Kellogg was supported by the Boole Centre for Research in Informatics at National University of Ireland, Cork and by Science Foundation Ireland under the Basic Research Grant Programme 2004 (Grants 04/BR/M0055, 04/BR/M0055s1).     

A grid generator for 3-D explosion simulations using the staircase boundary approach in Cartesian coordinates based on STL models

In this paper, an automatic grid generator based on STL models is proposed. The staircase boundary treatment is implemented to handle irregular geometries and the computation domain is discretized using a regular Cartesian grid. Using the grid generator, staircase grids that are suitable for fast and accurate finite difference analysis could be generated. Employing the slicing algorithm in RP technologies [1], the STL models are sliced with a set of parallel planes to generate 2D slices after the STL files obtained from a CAD system undergo topology reconstruction. To decrease the staircase error (increase accuracy) and enhance working efficiency, the cross-section at the middle of the layer is taken to represent the cross-section of whole layer. The scan line filling technique of computer graphics [2] is used to achieve grid generation after slicing. Finally, we demonstrate an application of the introduced method to generate staircase grids, which allows successful FDM simulation in the field of explosion. The example shows that the automatic grid generator based on STL models is fast and gives simulation results that are in agreement with practical observations.