Multivariate Refinement Equations and Convergence of Cascade Algorithms in Lp（0〈p〈1）Spaces

We consider the solutions of refinement equations written in the form

A non-conforming finite element method with anisotropic mesh grading for the Stokes problem in domains with edges

The solution of the Stokes problem in three-dimensional domainswith edges has anisotropic singular behaviour which is treatednumerically by using anisotropic finite element meshes. Thevelocity is approximated by Crouzeix–Raviart (nonconformingP₁ ) elements and the pressure by piecewise constants. Thismethod is stable for general meshes (without minimal or maximalangle condition). Denoting by N_e the number of elements in themesh, the interpolation and consistency errors are of the optimalorder h N_e^–1/3 which is proved for tensor product meshes.As a by-product, we analyse also nonconforming prismatic elementswith P₁ [oplus ] span {x₃²} as the local space for the velocitywhere x₃ is the direction of the edge.     

A posteriori L2 error estimation on anisotropic tetrahedral finite element meshes

A new a posteriori L₂ norm error estimator is proposed for thePoisson equation. The error estimator can be applied to anisotropictetrahedral or triangular finite element meshes. The estimatoris rigorously analysed for Dirichlet and Neumann boundary conditions. The lower error bound relies on specifically designed anisotropicbubble functions and the corresponding inverse inequalities.The upper error bound utilizes non-standard anisotropic interpolationestimates. Its proof requires H² regularity of the Poisson problem,and its quality depends on how good the anisotropic mesh resolvesthe anisotropy of the problem. This is measured by a so-called‘matching function’. A numerical example supports the anisotropic error analysis.     

NUMERICAL SOLUTION OF THE UNSTEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON THE CURVILINEAR HALF-STAGGERED MESH NUMERICAL SOLUTION OF THE UNSTEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON THE CURVILINEAR HALF-STAGGERED MESH

1. IntroductionLet us consider the unsteady incompressible Navier--Stokes equatinns (qSE)on a twedimensional reginn n with boundary On. Here w is the velocity vector; interms of its Caxtesian,components w = (u, v)"; p is the Pressure. The initial conditionis given assatisheng (1.2). We are concerned mainly with the solid wall boundary conditiollbut we will also briefly discuss the outflow boundary conditinn. Note the convectionterm can ajBo be written in conservative form (w' glad)w = div(…     

圆柱和直桨叶突然启动瞬态流动的数值研究

采用基于动网格方法的有限体积法对圆柱和直桨叶突然启动引起的二维非定常不可压粘性流进行了数值模拟,给出了计算方法.通过计算得到了Re=5000和9500时圆柱突然启动后的流场随时间演化的非定常过程.将计算结果与实验结果进行了对比,两者吻合较好;采用大涡模拟对高雷诺数下的直桨叶突然旋转启动的流场进行了计算,得到了完成启动后叶片内部瞬态流场的分布结果.     

THE COMPACTION OF TIME-DEPENDENT VISCOUS GRANULAR MATERIALS CONSIDERING INERTIAL FORCES

In the present paper, compactions of time-dependent viscous granular materials are simulated step by step using the automatic adaptive mesh generation schemes. Inertial forces of the viscous incompressible aggregates are taken into account. The corresponding conservation equations, the weighted-integral formulations, and penalty finite element model are investigated. The fully discrete finite element equations for the simulation are derived. Polygonal particles of aggregates are simplified as mixed three-node and four-node elements. The automatic adaptive mesh generation schemes include contact detection algorithms, and mesh upgrade schemes. Solutions of the numerical simulation are in good agreement with some results from literatures. With minor modification, the proposed numerical model can be applied in several industries, including the pharmaceutical, ceramic, food, and household product manufacturing.     

A conservative unstructured scheme for rapidly varied flows

This article introduces a new semi‐implicit, staggered finite volume scheme on unstructured meshes for the modelling of rapidly varied shallow water flows. Rapidly varied flows occur in the inundation of dry land during flooding situations. They typically involve bores and hydraulic jumps after obstacles such as road banks. Near such sudden flow transitions, the grid resolution is often low compared with the gradients of the bathymetry. Locally the hydrostatic pressure assumption may become invalid. In these situations, it is crucial to apply the correct conservation properties to obtain accurate results. An important feature of this scheme is therefore its ability to conserve momentum locally or, by choice, preserve constant energy head along a streamline. This is achieved using a special interpolation method and control volumes for momentum. The efficiency of inundation calculations with locally very high velocities, and in the case of unstructured meshes locally very small grid distances, is severely hampered by the Courant condition. This article provides a solution in the form of a locally implicit time integration for the advective terms that allows for an explicit calculation in most of the domain, while maintaining unconditional stability by implicit calculations only where necessary. The complex geometry of flooded urban areas asks for the flexibility of unstructured meshes. The efficient calculation of the pressure gradient in this, and other semi‐implicit staggered schemes, requires, however, an orthogonality condition to be put on the grid. In this article a simple method is introduced to generate unstructured hybrid meshes that fulfil this requirement. Copyright © 2008 John Wiley & Sons, Ltd.     

A MIXED FINITE ELEMENT METHOD ON A STAGGERED MESH FOR NAVIER-STOKES EQUATIONS

In this paper, we introduce a mixed finite element method on a staggered mesh for the numerical solution of the steady state Navier-Stokes equations in which the two components of the velocity and the pressure are defined on three different meshes. This method is a conforming quadrilateral Q1 × Q1 - P0 element approximation for the Navier-Stokes equations. First-order error estimates are obtained for both the velocity and the pressure. Numerical examples are presented to illustrate the effectiveness of the proposed method.     

拟矩形剖分上的样条空间的维数

矩形剖分~(记为$\Delta_{QR}$)~是指在矩形剖分~(记为$\Delta_{R}$)的基础上进行局部修改后得到的剖分,通常包括T-剖分~(记为$\Delta_{T}$)~和L-剖分~(记为$\Delta_{L}$).本文利用光滑余因子协调方法讨论了该剖分上的二元样条空间$S^\mu_k(\Delta_{QR})$的维数.在满足一定约束条件下, 得到了仅依赖于样条空间的次数,光滑度和剖分拓扑结构的显式维数公式.     

On the use of fuzzy inference techniques in assessment models: part I—theoretical properties

An assessment model is a mathematical model that produces a measuring index, either in the form of a numerical score or a category to a situation/object, with respect to the subject of measure. From the numerical score, decision can be made and action can be taken. To allow valid and useful comparisons among various situations/objects according to their associated numerical scores to be made, the monotone output property and the output resolution property are essential in fuzzy inference-based assessment problems. We investigate the conditions for a fuzzy assessment model to fulfill the monotone output property using a derivative approach. A guideline on how the input membership functions should be tuned is also provided. Besides, the output resolution property is defined as the derivative of the output of the assessment model with respect to its input. This derivative should be greater than the minimum resolution required. From the derivative, we suggest improvements to the output resolution property by refining the fuzzy production rules.