An accurate gradient and Hessian reconstruction method for cell‐centered finite volume discretizations on general unstructured grids

In this paper, a novel reconstruction of the gradient and Hessian tensors on an arbitrary unstructured grid, developed for implementation in a cell‐centered finite volume framework, is presented. The reconstruction, based on the application of Gauss' theorem, provides a fully second‐order accurate estimate of the gradient, along with a first‐order estimate of the Hessian tensor. The reconstruction is implemented through the construction of coefficient matrices for the gradient components and independent components of the Hessian tensor, resulting in a linear system for the gradient and Hessian fields, which may be solved to an arbitrary precision by employing one of the many methods available for the efficient inversion of large sparse matrices. Numerical experiments are conducted to demonstrate the accuracy, robustness, and computational efficiency of the reconstruction by comparison with other common methods. Copyright © 2009 John Wiley & Sons, Ltd.     

Hybrid mesh adaptation applied to industrial numerical combustion

This paper presents an anisotropic mesh adaptation method applied to industrial combustion problems. The method is based on a measure of the distance between two Riemannian metrics called metric non‐conformity. This measure, which can be used to build a cost function to adapt meshes comprising several types of mesh elements, provides the basis for a generic mesh adaptation approach applicable to various types of physical problems governed by partial differential equations. The approach is shown to be applicable to industrial combustion problems, through the specification of a target metric computed as the intersection of several Hessian matrices reconstructed from the main variables of the governing equations. Numerical results show that the approach is cost effective in that it can drastically improve the prediction of temperature and species distributions in the flame region of a combustor while reducing computational cost. The results can be used as a basis for pollutant prediction models. Copyright © 2011 John Wiley & Sons, Ltd.     

Ce-Pt-Pd/不锈钢丝网催化剂的制备与催化性能

采用阳极氧化技术在不锈钢丝网上自生长了一层结构致密的阳极氧化膜,并以此为载体,制备出一种高活性、高稳定性的负载型Ce-Pt-Pd催化剂.考察了该系列催化剂对甲苯、丙酮和乙酸乙酯的氧化活性,并用扫描电镜、X射线光电子能谱和程序升温氧化技术对催化剂进行了表征.结果表明,不锈钢丝网载体表面自生长的氧化物膜十分有利于活性组分的负载,制得的催化剂具有较高的催化燃烧有机化合物的活性和稳定性.     

Robust stabilization of uncertain linear dynamical systems with time-varying delay

In this paper, the problem of the robust stabilization for a class of uncertain linear dynamical systems with time-varying delay is considered. By making use of an algebraic Riccati equation, we derive some sufficient conditions for robust stability of time-varying delay dynamical systems with unstructured or structured uncertainties. In our approach, the only restriction on the delay functionh(t) is the knowledge of its upper boundh ^–. Some analytical methods are employed to investigate these stability conditions. Since these conditions are independent of the delay, our results are also applicable to systems with perturbed time delay. Finally, a numerical example is given to illustrate the use of the sufficient conditions developed in this paper.     

On the adjacencies of triangular meshes based on skeleton-regular partitions

For any 2D triangulation τ, the 1-skeleton mesh of τ is the wireframe mesh defined by the edges of τ, while that for any 3D triangulation τ, the 1-skeleton and the 2-skeleton meshes, respectively, correspond to the wireframe mesh formed by the edges of τ and the “surface” mesh defined by the triangular faces of τ. A skeleton-regular partition of a triangle or a tetrahedra, is a partition that globally applied over each element of a conforming mesh (where the intersection of adjacent elements is a vertex or a common face, or a common edge) produce both a refined conforming mesh and refined and conforming skeleton meshes. Such a partition divides all the edges (and all the faces) of an individual element in the same number of edges (faces). We prove that sequences of meshes constructed by applying a skeleton-regular partition over each element of the preceding mesh have an associated set of difference equations which relate the number of elements, faces, edges and vertices of the nth and (n−1)th meshes. By using these constitutive difference equations we prove that asymptotically the average number of adjacencies over these meshes (number of triangles by node and number of tetrahedra by vertex) is constant when n goes to infinity. We relate these results with the non-degeneracy properties of longest-edge based partitions in 2D and include empirical results which support the conjecture that analogous results hold in 3D.     

Domain decomposition preconditioners of Neumann-Neumann type for hp-approximations on boundary layer meshes in three dimensions

We develop and analyse Neumann–Neumann methods for hpfinite-element approximations of scalar elliptic problems ongeometrically refined boundary layer meshes in three dimensions.These are meshes that are highly anisotropic where the aspectratio typically grows exponentially with the polynomial degree.The condition number of our preconditioners is shown to be independentof the aspect ratio of the mesh and of potentially large jumpsof the coefficients. In addition, it only grows polylogarithmicallywith the polynomial degree, as in the case of p approximationson shape-regular meshes. This work generalizes our previousone on two-dimensional problems in Toselli & Vasseur (2003a,submitted to Numerische Mathematik, 2003c to appear in Comput.Methods Appl. Mech. Engng.) and the estimates derived here canbe employed to prove condition number bounds for certain typesof FETI methods.     

Locking-free DGFEM for elasticity problems in polygons

The h-version of the discontinuous Galerkin finite element method(h-DGFEM) for nearly incompressible linear elasticity problemsin polygons is analysed. It is proved that the scheme is robust(locking-free) with respect to volume locking, even in the absenceof H²-regularity of the solution. Furthermore, it is shown thatan appropriate choice of the finite element meshes leads torobust and optimal algebraic convergence rates of the DGFEMeven if the exact solutions do not belong to H².     

Superconvergence of a Nonconforming Finite Element Approximation to Viscoelasticity Type Equations on Anisotropic Meshes

The main aim of this paper is to study the approximation to viscoelasticity type equations with a Crouzeix-Raviart type nonconforming finite element on the anisotropic meshes. The superclose property of the exact solution and the optimal error estimate of its derivative with respect to time are derived by using some novel techniques. Moreover, employing a postprocessing technique, the global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is studied.     

Adaptive unstructured finite element method for two-dimensional detonation simulations

A non-equilibrium reacting flow methodology has been added to a conservative, monotonic, compressible flow solver to allow numerical simulations of gas detonations. This flow solver incorporates unstructured dynamically adaptive meshes with the Finite Element Method – Flux Corrected Transport (FEM-FCT) scheme, which has shown excellent predictive capability of various non-reacting compressible flows. A two-step induction parameter model was used to model the combustion of the gas phase coupled with an energy release equation which was simulated with a point implicit finite element scheme. This combustion model was then applied to a two-dimensional detonation test case of a hypothetical fuel:oxygen mixture. The detonation simulation yielded two transverse waves which continued to propagate. This feature and the detonation shock speed mean and fluctuations were found to be grid-independent based on a resolution of about twenty elements within the average induction length. The resolution was efficiently achieved with the unstructured dynamically adaptive finite elements, which were three orders of magnitude less in number then required for uniform discretization. Received 26 August 1996 / Accepted 31 March 1997