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41.
A non-conforming finite element method with anisotropic mesh grading for the Stokes problem in domains with edges 总被引:5,自引:0,他引:5
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 CrouzeixRaviart (nonconformingP1 ) elements and the pressure by piecewise constants. Thismethod is stable for general meshes (without minimal or maximalangle condition). Denoting by Ne the number of elements in themesh, the interpolation and consistency errors are of the optimalorder h Ne1/3 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. 相似文献
42.
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-calledmatching function. A numerical example supports the anisotropic error analysis. 相似文献
43.
Lan-chieh Huang 《计算数学(英文版)》2000,(5)
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(… 相似文献
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45.
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. 相似文献
46.
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. 相似文献
47.
Houde Han Ming Yan 《计算数学(英文版)》2008,(6):816-824
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. 相似文献
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49.
Miguel A. T. Walter Aline A. Q. Abdu Luís Fernando Figueira da Silva Joo Luiz F. Azevedo 《国际流体数值方法杂志》2005,49(9):999-1014
The compressible gas flows of interest to aerospace applications often involve situations where shock and expansion waves are present. Decreasing the characteristic dimension of the computational cells in the vicinity of shock waves improves the quality of the computed flows. This reduction in size may be accomplished by the use of mesh adaption procedures. In this paper an analysis is presented of an adaptive mesh scheme developed for an unstructured mesh finite volume upwind computer code. This scheme is tailored to refine or coarsen the computational mesh where gradients of the flow properties are respectively high or low. The refinement and coarsening procedures are applied to the classical gas dynamic problems of the stabilization of shock waves by solid bodies. In particular, situations where oblique shock waves interact with an expansion fan and where bow shocks arise around solid bodies are considered. The effectiveness of the scheme in reducing the computational time, while increasing the solution accuracy, is assessed. It is shown that the refinement procedure alone leads to a number of computational cells which is 20% larger than when alternate passes of refinement and coarsening are used. Accordingly, a reduction of computational time of the same order of magnitude is obtained. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
50.
The study of rotor–fuselage interactional aerodynamics is central to the design and performance analysis of helicopters. However, regardless of its significance, rotor–fuselage aerodynamics has so far been addressed by very few authors. This is mainly due to the difficulties associated with both experimental and computational techniques when such complex configurations, rich in flow physics, are considered. In view of the above, the objective of this study is to develop computational tools suitable for rotor–fuselage engineering analysis based on computational fluid dynamics (CFD). To account for the relative motion between the fuselage and the rotor blades, the concept of sliding meshes is introduced. A sliding surface forms a boundary between a CFD mesh around the fuselage and a rotor‐fixed CFD mesh which rotates to account for the movement of the rotor. The sliding surface allows communication between meshes. Meshes adjacent to the sliding surface do not necessarily have matching nodes or even the same number of cell faces. This poses a problem of interpolation, which should not introduce numerical artefacts in the solution and should have minimal effects on the overall solution quality. As an additional objective, the employed sliding mesh algorithms should have small CPU overhead. The sliding mesh methods developed for this work are demonstrated for both simple and complex cases with emphasis placed on the presentation of the inner workings of the developed algorithms. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献