直接控制网格节点分布的曲线网格生成技术研究

指出了Thompson与Thomas曲线网格生成方法中控制网格分布的调节函数的问题所在,克服了Thomas曲线网格生成法中边界处局部线性化近似假定的缺陷,经过严格推导得出一组新的调节函数P、Q的表达式,并给出了曲线网格生成实例.实例检验表明,该调节函数能够对复杂边界的单连通域或多连通域生成理想的曲线网格,即边界处网格正交,内部网格分布能够适应物理量场变化的情形.在实际水利工程流场数值模拟中,该方法能够准确地使用边界条件,提高求解的精确度.     

Generation of Voronoi Grid Based on Vorticity for Coarse-Scale Modeling of Flow in Heterogeneous Formations

We present a novel unstructured coarse grid generation technique based on vorticity for upscaling two-phase flow in permeable media. In the technique, the fineness of the gridblocks throughout the domain is determined by vorticity distribution such that where the larger is the vorticity at a region, the finer are the gridblocks at that region. Vorticity is obtained from single-phase flow on original fine grid, and is utilized to generate a background grid which stores spacing parameter, and is used to steer generation of triangular and finally Voronoi grids. This technique is applied to two channelized and heterogeneous models and two-phase flow simulations are performed on the generated coarse grids and, the results are compared with the ones of fine scale grid and uniformly gridded coarse models. The results show a close match of unstructured coarse grid flow results with those of fine grid, and substantial accuracy compared to uniformly gridded coarse grid model.     

基于Voronoi cells的二维不规则自适应网格的生成及其应用

基于Voronoi cells的数据结构和算法，给出了一种二维不规则自适应网格的生成方法，用VisualC＋＋语言在微机上开发了Windows环境下网格自动生成的可视化软件。既可以得到Voronoi cells网格，也可得到相应的Delaunay triangles网格，网格生成的实例表明，本文方法所得到的网格非常适合于多尺度系统的流动问题的计算，具有较好的应用前景。     

Surface grid generation with a linkage to geometric generation

This paper describes a new method to generate surface grids over complex configurations defined by a geometric generation system. The scheme is designed for direct utilization of the surface definition provided by a geometric modeller based on a boundary representation (the so-called B-rep modeller). Thus, the conversion of the geometric representation for the surface grid generator is not required. Consequently, this technique eliminates not only laborious tedium in the conversion of data, but also errors in the representation of the surface induced in the process of the conversion. The proposed method is accomplished over several stages. First, the triangulation is performed on the surface of the geometry, on which the area to be grided is laid. Then linear partial differential equations are mapped and solved on these triangular elements. Finally, the surface grid is constructed by searching for the contours inside the solution domain. After the co-ordinate values of the grid points are obtained by a linear interpolation within each triangular element, these values are mapped onto the surface of the geometry through surface parametric functions provided by the B-rep modeller. An example of generating surface grid over a car configuration is given to illustrate the capability of the method.     

An unstructured/structured multi‐layer hybrid grid method and its application

A multi‐layer hybrid grid method is constructed to simulate complex flow field around 2‐D and 3‐D configuration. The method combines Cartesian grids with structured grids and triangular meshes to provide great flexibility in discretizing a domain. We generate the body‐fitted structured grids near the wall surface and the Cartesian grids for the far field. In addition, we regard the triangular meshes as an adhesive to link each grid part. Coupled with a tree data structure, the Cartesian grid is generated automatically through a cell‐cutting algorithm. The grid merging methodology is discussed, which can smooth hybrid grids and improve the quality of the grids. A cell‐centred finite volume flow solver has been developed in combination with a dual‐time stepping scheme. The flow solver supports arbitrary control volume cells. Both inviscid and viscous flows are computed by solving the Euler and Navier–Stokes equations. The above methods and algorithms have been validated on some test cases. Computed results are presented and compared with experimental data. Copyright © 2006 John Wiley & Sons, Ltd.     

NEAR-WAKE FLOW CALCULATIONS BY AN IMPLICIT 2D NAVIER-STOKES ROE RIEMANN SOLVER

Abstract

A flux formulation using a projected 2D Roe Riemann solver on unstructured grids (R2D Solver) is introduced for solving the Navier-Stokes equations and is applied to calculations of axisymmetric laminar near-wake flows behind a spherical-conical body. The numerical framework was first developed by P. L. Roe et al, in the late eighties. They looked for unsteady solutions to Euler's equations using a rather simple but exact three state linearization on triangular grids and decomposing the solution using some effective wave models. Our approach differs from their techniques by constructing a second order accurate and conservative flux functions under the well-known classical finite volume formulation. However, our Riemann Solver is obtained by a suitable linearization procedure upon all three prescribed nodal values given on each triangle. Our numerical method is applied to a Mach 4.3 flow problem for refined unstructured triangular grid behind the body. Numerical results indicate that our technique is stable, accurate and converges successfully to a stationary solution as the cell size is reduced from the coarse lo the finest grid.     

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．     

The shallow flow equations solved on adaptive quadtree grids

This paper describes an adaptive quadtree grid‐based solver of the depth‐averaged shallow water equations. The model is designed to approximate flows in complicated large‐scale shallow domains while focusing on important smaller‐scale localized flow features. Quadtree grids are created automatically by recursive subdivision of a rectangle about discretized boundary, bathymetric or flow‐related seeding points. It can be fitted in a fractal‐like sense by local grid refinement to any boundary, however distorted, provided absolute convergence to the boundary is not required and a low level of stepped boundary can be tolerated. Grid information is stored as a tree data structure, with a novel indexing system used to link information on the quadtree to a finite volume discretization of the governing equations. As the flow field develops, the grids may be adapted using a parameter based on vorticity and grid cell size. The numerical model is validated using standard benchmark tests, including seiches, Coriolis‐induced set‐up, jet‐forced flow in a circular reservoir, and wetting and drying. Wind‐induced flow in the Nichupté Lagoon, México, provides an illustrative example of an application to flow in extremely complicated multi‐connected regions. Copyright © 2001 John Wiley & Sons, Ltd.     

边界处正交的曲线网格生成技术合理调节因子选取的研究

指出了 Thompson的曲线网格生成方法中调节因子的问题所在 ;借助于势流理论中的流线与势线正交的物理机理 ,导出了一种新的调节因子的表达式 ,并给出了曲线网格生成实例。实例检验表明 ,该调节因子能够对复杂边界的单连通域或多连通域的水域生成理想的曲线网格 ,即边界处网格正交 ,内部网格分布能够适应物理量场的变化情形。     

Aerodynamic shape optimization on overset grids using the adjoint method

This paper deals with the use of the continuous adjoint equation for aerodynamic shape optimization of complex configurations with overset grids methods. While the use of overset grid eases the grid generation process, the non‐trivial task of ensuring communication between overlapping grids needs careful attention. This need is effectively addressed by using a practically useful technique known as the implicit hole cutting (IHC) method. The method depends on a simple cell selection process based on the criterion of cell size, and all grid points including interior points and fringe points are treated indiscriminately in the computation of the flow field. This paper demonstrates the simplicity of the IHC method for the adjoint equation. Similar to the flow solver, the adjoint equations are solved on conventional point‐matched and overlapped grids within a multi‐block framework. Parallel computing with message passing interface is also used to improve the overall efficiency of the optimization process. The method is successfully demonstrated in several two‐ and a three‐dimensional shape optimization cases for both external and internal flow problems. Copyright © 2009 John Wiley & Sons, Ltd.     

Rarefied gas flow in a triangular duct based on a boundary fitted lattice

The rarefied fully developed flow of a gas through a duct of a triangular cross section is solved in the whole range of the Knudsen number. The flow is modelled by the BGK kinetic equation, subject to Maxwell diffuse boundary conditions. The numerical solution is based on the discrete velocity method, which is applied for first time on a triangular lattice in the physical space. The boundaries of the flow and computational domains are identical deducing accurate results with modest computational effort. Results on the velocity profiles and on the flow rates for ducts of various triangular cross sections are reported and they are valid in the whole range of gas rarefaction. Their accuracy is validated in several ways, including the recovery of the analytical solutions at the free molecular and hydrodynamic limits. The successful implementation of the triangular grid elements is promising for generalizing kinetic type solutions to rarefied flows in domains with complex boundaries using adaptive and unstructured grids.     

Segmented multigrid domain decomposition procedure for incompressible viscous flows

The application of grid stretching or grid adaptation is generally required in order to optimize the distribution of nodal points for fluid-dynamic simulation. This is necessitated by the presence of disjoint high gradient zones, that represent boundary or free shear layers, reversed flow or vortical flow regions, triple deck structures, etc. A domain decomposition method can be used in conjunction with an adaptive multigrid algorithm to provide an effective methodology for the development of optimal grids. In the present study, the Navier-Stokes (NS) equations are approximated with a reduced Navier-Stokes (RNS) system, that represents the lowest-order terms in an asymptotic Re expansion. This system allows for simplified boundary conditions, more generality in the location of the outflow boundary, and ensures mass conservation in all subdomain grid interfaces, as well as at the outflow boundary. The higher-order (NS) diffusion terms are included through a deferred corrector, in selected subdomains, when necessary. Adaptivity in the direction of refinement is achieved by grid splitting or domain decomposition in each level of the multigrid procedure. Normalized truncation error estimates of key derivatives are used to determine the boundaries of these subdomains. The refinement is optimized in two co-ordinate directions independently. Multidirectional adaptivity eliminates the need for grid stretching so that uniform grids are specified in each subdomain. The overall grid consists of multiple domains with different meshes and is, therefore, heavily graded. Results and computational efficiency are discussed for the laminar flow over a finite length plate and for the laminar internal flow in a backward-facing step channel.     

A scheme for automatic generation of boundary-fitted depth- and depth-gradient- dependent grids in arbitrary two-dimensional regions

In this paper we present a scheme for the numerical generation of boundary-fitted grids that adapt to both water depth and depth gradient. The scheme can be used in arbitrary two-dimensional regions and is based on the application of the well-known control function approach to generate adaptive grids. The method includes the evaluation of water depths at the grid points from a known distribution of depth points and their associated depths plus a procedure for the numerical evaluation of depth gradients. It is demonstrated that the smoothness of the grid can be enhanced by introducing a suitable filtering technique.     

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.     

An algorithm of finite element grid generation for three-dimensional complex connected domain

An automated quasi three-dimensional finite element grid generation method is presented for particular three-dimensional complex connected domain, across which some are simply connected two-dimensional.regions and some are multiply connected two-dimensional regions. A subdivision algorithm based on the variational principle has been developed to ascertain the smoothness and orthogonality of the generated grid in any cross sections. Smooth transition between the simply and multiply connected regions is maintained. For illustration, the method is applied to generate a finite element three-dimensional grid for human above knee stump.     

A parallel gas-kinetic Bhatnagar–Gross–Krook method for the solution of viscous flows on two-dimensional hybrid grids

In this study, a parallel implementation of gas-kinetic Bhatnagar–Gross–Krook method on two-dimensional hybrid grids is presented. Boundary layer regions in wall bounded viscous flows are discretised with quadrilateral grid cells stretched in the direction normal to the solid surface while the rest of the flow domain is discretised by triangular cells. The parallel solution algorithm on hybrid grids is based on the domain decomposition using METIS, a graph partitioning software. The flow solutions obtained in parallel significantly improve the computation time, a significant deficiency of gas-kinetic methods. Several validation test cases presented show the accuracy and robustness of the method developed.     

Automatic generation of unstructured grids with Delaunay triangulation and its application

This paper is consisted of two parts. In the first part, a method is described which generates two-dimensional triangle mesh using the Delaunay triangulation criterion. An automatic algorithm was proposed which combines several advantages of the existing methods. Local mesh refinement can also be easily performed with this method. Examples of generated grids were presented for several convex, non-convex and multi-connected domains to demonstrate the effectiveness and feasibility of the proposed method. In the second part, the turbulent heat transfer in an annular space finned by wave-like longitudinal fins was numerical simulated. The proposed technique was adopted to generate the grid in the cross-section. The standard K-ɛ model in conjuction with wall function method was used to simulate the fluid flow and heat transfer in the complex geometry. The discretization of the governing equations was described. The computational results were compared with the authors' test data and the agreement was reasonably good. Received on 9 July 1998     

Discretizing two‐dimensional complex fractured fields for incompressible two‐phase flow

A method is introduced to discretize irregular and complex two‐dimensional fractured media. The geometry of the fractured media is first analysed by searching and treating the complex configurations. Based on that, the method generated a good mesh quality and allows for including finer grids. An incompressible two‐phase flow problem is solved to compare the developed method and a public method based on the approximation of a 1D fracture by the edges of a 2D finite element grid of the porous media. The comparison showed that the developed method (i) represents better the fractured domain by maintaining the geometric integrity of input surfaces and geologic data, (ii) provides, for sample and complex fractured domains, excellent and more accurate results, and (iii) is much less sensitive to the grid sizes. Furthermore, the method has to be more efficient than the other methods for transport problems and has to provide better predictable results; this is mainly based on point (ii) and because the method produces optimal triangular grids. Copyright © 2009 John Wiley & Sons, Ltd.     

Hybrid grid generation for viscous flow analysis

Cartesian grid with cut‐cell method has drawn attention of CFD researchers owing to its simplicity. However, it suffers from the accuracy near the boundary of objects especially when applied to viscous flow analysis. Hybrid grid consisting of Cartesian grid in the background, body‐fitted layer near the object, and transition layer connecting the two is an interesting alternative. In this paper, we propose a robust method to generate hybrid grid in two‐dimensional (2D) and three‐dimensional (3D) space for viscous flow analysis. In the first step, body‐fitted layer made of quadrangles (in 2D) or prisms (in 3D) is created near the object's boundary by extruding front nodes with a speed function depending on the minimum normal curvature obtained by quadric surface fitting. To solve global interferences effectively, a level set method is used to find candidates of colliding cells. Then, axis‐aligned Cartesian grid (quadtree in 2D or octree in 3D) is filled in the rest of the domain. Finally, the gap between body‐fitted layer and Cartesian grid is connected by transition layer composed of triangles (in 2D) or tetrahedrons (in 3D). Mesh in transition layer is initially generated by constrained Delaunay triangulation from sampled points based on size function and is further optimized to provide smooth connection. Our approach to automatic hybrid grid generation has been tested with many models including complex geometry and multi‐body cases, showing robust results in reasonable time. Copyright © 2012 John Wiley & Sons, Ltd.     

Calculation of laminar recirculating flows using a local non-staggered grid refinement system

A grid-embedding technique for the solution of two-dimensional incompressible flows governed by the Navier-Stokes equations is presented. A finite volume method with collocated primitive variables is employed to ensure conservation at the interfaces of embedding grids as well as global conservation. The discretized equations are solved simultaneously for the whole domain, providing a strong coupling between regions of different refinement. The formulation presented herein is applicable to uniform or non-uniform Cartesian meshes. The method was applied to the solution of two scalar transport equations, to cavity flows driven by body and shear forces and to a sudden plane contraction flow. The numerical predictions are compared with the exact solutions when available and with experimental data. The results show that neither the convergence rate nor the stability of the method is affected by the presence of embedded grids. Embedded grids provide a better distribution of grid nodes over the computational domain and consequently the solution accuracy was improved. The grid-embedding technique proved also that significant savings in computing time could be achieved.