Numerical simulation of fluid flows using an unstructured finite volume method with adaptive tri‐tree grids

A tri‐tree grid generation procedure is developed together with a finite volume method on the unstructured grid for solving the Navier–Stokes equations. A hierarchic numbering system for the data structure is used. The grid is adapted by adding and removing cell elements dependent on the vorticity magnitude. A special treatment is developed to ensure good quality triangular elements around the cylinder boundary. The adopted finite volume method is based on the cell‐centred scheme. The pressure–velocity coupling is treated using the SIMPLE algorithm. A modified QUICK scheme for unstructured grids is derived. The developed method is used to simulate the flow past a single and multiple cylinders at low Reynolds number. The obtained results are in good agreement with the published data. Copyright © 2002 John Wiley & Sons, Ltd.     

The empirical behavior of sampling methods for stochastic programming

We investigate the quality of solutions obtained from sample-average approximations to two-stage stochastic linear programs with recourse. We use a recently developed software tool executing on a computational grid to solve many large instances of these problems, allowing us to obtain high-quality solutions and to verify optimality and near-optimality of the computed solutions in various ways. Research supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under Contract W-31-109-Eng-38, and by the National Science Foundation under Grant 9726385. Research supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under Contract W-31-109-Eng-38, and by the National Science Foundation under Grant DMS-0073770. Research supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under Contract W-31-109-Eng-38, and by the National Science Foundation under Grants 9726385 and 0082065.     

Benchmark solutions for the incompressible Navier–Stokes equations in general co-ordinates on staggered grids

Benchmark problems are solved with the steady incompressible Navier–Stokes equations discretized with a finite volume method in general curvilinear co-ordinates on a staggered grid. The problems solved are skewed driven cavity problems, recently proposed as non-orthogonal grid benchmark problems. The system of discretized equations is solved efficiently with a non-linear multigrid algorithm, in which a robust line smoother is implemented. Furthermore, another benchmark problem is introduced and solved in which a 90° change in grid line direction occurs.     

Application of Chimera grid to modelling cell motion and aggregation in a narrow tube

A computational scheme using the Chimera grid method is presented for simulation of three‐dimensional motion and aggregation of two red blood cells (RBCs) in a narrow tube. The cells are modelled as rigid ellipsoidal particles; the computational scheme is applicable to deformable fluid‐filled particles. Attractive energy between two RBCs is modelled by a depletion interaction theory and used for simulating aggregation of two cells. Through the simulation, we show that the Chimera grid method is applicable to the simulation of three‐dimensional motion and aggregation of multiple RBCs in a microvessel and microvascular network. Copyright © 2006 John Wiley & Sons, Ltd.     

Multiple pressure variables methods for fluid flow at all Mach numbers

In this paper we present a method for the simulation of incompressible as well as compressible unsteady flows. At first we discuss three different forms, i.e. a primitive‐, conservative‐ and a semi‐conservative form of the governing equations. We use a semi‐implicit time integration in such a fashion that the stability is guaranteed independently of the speed of sound and the resulting method is independent of the Mach number range. Moreover, with the application of the so‐called multiple pressure variables (MPV) approach the difficulties with the pressure term can be circumvented as in the incompressible limit the hydrodynamic pressure decouples from the equation of state. Increasing approximation errors in the low Mach number regime are avoided. As a result, the proposed algorithm can also simulate incompressible flows as limit for zero Mach number. Copyright © 2005 John Wiley & Sons, Ltd.     

High‐order compact numerical schemes for non‐hydrostatic free surface flows

The development of a numerical scheme for non‐hydrostatic free surface flows is described with the objective of improving the resolution characteristics of existing solution methods. The model uses a high‐order compact finite difference method for spatial discretization on a collocated grid and the standard, explicit, single step, four‐stage, fourth‐order Runge–Kutta method for temporal discretization. The Cartesian coordinate system was used. The model requires the solution of two Poisson equations at each time‐step and tridiagonal matrices for each derivative at each of the four stages in a time‐step. Third‐ and fourth‐order accurate boundaries for the flow variables have been developed including the top non‐hydrostatic pressure boundary. The results demonstrate that numerical dissipation which has been a problem with many similar models that are second‐order accurate is practically eliminated. A high accuracy is obtained for the flow variables including the non‐hydrostatic pressure. The accuracy of the model has been tested in numerical experiments. In all cases where analytical solutions are available, both phase errors and amplitude errors are very small. Copyright © 2006 John Wiley & Sons, Ltd.     

半导体瞬态问题特征变网格有限元法和分析

1 引 言考虑平面区域Ω　R2上的二维问题,其数学模型为[1]-△ψ=α（p-e+N（x））,（x,t）∈Ω×J,J（0,T],（1.1）     

A PRECONDITIONER FOR COUPLING SYSTEM OF NATURAL BOUNDARY ELEMENT AND COMPOSITE GRID FINITE ELEMENT

1. IntroductionThe coupling of boundary elemellts and finite elements is of great imPortance for the nu-mercal treatment of boundary value problems posed on unbounded domains. It permits us tocombine the advanages of boundary elements for treating domains extended to infinity withthose of finite elemenis in treating the comP1icated bounded domains.The standard procedure of coupling the boundary elemeni and finite elemeni methods isdescribed as follows. First, the (unbounded) domain is divided…     

Synthesis of bandpass grid filter for linear polarized millimeter wave

A method based on equivalent circuit and transmission line model is proposed to design narrow bandpass grid filters in short millimeter wave. Several bandpass filters with 2, 3 or 4 element inductive wire grids in the 70GHz region have been designed with Butterworth or Chebyshev characteristic for linear polarized wave. The agreement between measurement and design theory is good and this proves the rationality and practicality of our design theory.     

Efficient modelling of rotating disks and cylinders using a cartesian grid

Calculations are presented of flow characteristics in the vicinity of disks and cylinders rotating at speeds typical of those found in modern mechatronics machinery. The rotational speeds are slow or intermittent, and the generated boundary layers are laminar and transitional. Comparison is made with existing experimental data and exact, though idealised, analytical solutions. A three-dimensional finite volume procedure with time dependence was employed as the solution method, and two grid geometries were used, namely, axisymmetric and cartesian. Use of a cartesian grid is very important, as it is compatible with the design of the interiors of mechatronics machinery, and present practice is to model these interiors with computationally economical cartesian grids. Expanding grids were generated normal to surfaces for each of the grid geometries so as to capture the thin boundary layers. To alleviate numerical difficulties, when using the cartesian geometry, an expanding and contracting grid was generated normal to the axis of the disks and cylinders with the grid spacing based on a shifted Chebyshev polynomial.