Element Method For Flow Problems Research Articles

Online basis construction for goal-oriented adaptivity in the generalized multiscale finite element method

In this research, we develop an online enrichment framework for goal-oriented adaptivity within the generalized multiscale finite element method for flow problems in heterogeneous media. The method for approximating the quantity of interest involves construction of residual-based primal and dual basis functions used to enrich the multiscale space at each stage of the adaptive algorithm. Three different online enrichment strategies based on the primal-dual online basis construction are proposed: standard, primal-dual combined and primal-dual product based. Numerical experiments are performed to illustrate the efficiency of the proposed methods for high-contrast heterogeneous problems.

Flux-preserving enforcement of inhomogeneous Dirichlet boundary conditions for strongly divergence-free mixed finite element methods for flow problems

We investigate a flux-preserving enforcement of inhomogeneous Dirichlet boundary conditions for velocity, u|∂Ω=g, for use with finite element methods for incompressible flow problems that strongly enforce mass conservation. Typical enforcement via nodal interpolation is not flux-preserving in general, and it can create divergence error even when divergence-free elements are used. We show with analysis and numerical tests that by slightly (and locally) changing nodal interpolation, the enforcement recovers flux-preservation, is optimally accurate, and delivers divergence-free solutions when used with divergence-free finite elements.

Accuracy of semiGLS stabilization of FEM for solving Navier–Stokes equations and a posteriori error estimates

AbstractStabilization of the finite element method for flow problems at high Reynolds numbers is the main subject of presented research. The semiGLS method is recalled as a modification of the Galerkin least‐squares method. The presented work extends our previous paper on this method by its other important aspects. The main aim of this paper is to analyse and comment on the accuracy of the method. A posteriori error estimates for incompressible Navier–Stokes equations are used as the main tool for error analysis and some conclusions concerning accuracy are derived. Several numerical experiments are presented for both benchmark and practical problems. Copyright © 2008 John Wiley & Sons, Ltd.

Approximation of the Velocity by Coupling Discontinuous Galerkin and Mixed Finite Element Methods for Flow Problems

In this paper, we show how to couple the local discontinuous Galerkin method and the Raviart–Thomas mixed finite element method for elliptic equations modeling flow problems. We then show that the approximation of the velocity converges with the optimal order of k when we take the local discontinuous Galerkin that uses polynomials of degree k and the Raviart–Thomas space of polynomials of degree k−1.

Finite element methods for flow problems with moving boundaries and interfaces

This paper is an overview of the finite element methods developed by the Team for Advanced Flow Simulation and Modeling (T*AFSM) [http://www.mems.rice.edu/TAFSM/] for computation of flow problems with moving boundaries and interfaces. This class of problems include those with free surfaces, two-fluid interfaces, fluid-object and fluid-structure interactions, and moving mechanical components. The methods developed can be classified into two main categories. The interface-tracking methods are based on the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation, where the mesh moves to track the interface, with special attention paid to reducing the frequency of remeshing. The interface-capturing methods, typically used for free-surface and two-fluid flows, are based on the stabilized formulation, over non-moving meshes, of both the flow equations and the advection equation governing the time-evolution of an interface function marking the location of the interface. In this category, when it becomes neccessary to increase the accuracy in representing the interface beyond the accuracy provided by the existing mesh resolution around the interface, the Enhanced-Discretization Interface-Capturing Technique (EDICT) can be used to to accomplish that goal. In development of these two classes of methods, we had to keep in mind the requirement that the methods need to be applicable to 3D problems with complex geometries and that the associated large-scale computations need to be carried out on parallel computing platforms. Therefore our parallel implementations of these methods are based on unstructured grids and on both the distributed and shared memory parallel computing approaches. In addition to these two main classes of methods, a number of other ideas and methods have been developed to increase the scope and accuracy of these two classes of methods. The review of all these methods in our presentation here is supplemented by a number numerical examples from parallel computation of complex, 3D flow problems.

Boundary Element Methods for Flow Problems in Heterogeneous Media.

The boundary element method (BEM) owes its elegance, with regard to the computational accuracy and efficiency, to the existence of the fundamental solution for the governing equation. For heterogeneity problems, there arises difficulty in finding the corresponding fundamental solution; and consequently, the conventional BEM can not be applied to such problems. Among some attempts found in the literature to overcome this shortcoming and to broaden applicability, two kinds of unconventional BEM, the accelerated perturbation BEM and the complex variable BEM, are reviewed.The accelerated perturbation BEM is developed for solving continuous heterogeneity problems. The governing equation is decomposed into various order perturbation equations, for which the fundamental solution can be found. These equations are solved by the BEM, and the complete solution to the original problem is recovered by summing the perturbation solutions. The Padé approximant is applied to improve the convergence of a perturbation series.The complex variable BEM is developed for solving discrete heterogeneity (such as fractures) problems. The difficulty, in modeling singular flow behavior near the tips of thin objects, is dealt by virtue of a conformal mapping technique. The use of complex variables enables us to bridge the gap between the singular solution in a mapped plane and the non-singular solution in a physical plane.To exemplify the practical usefulness of these models, application problems are considered, including heterogeneity detection through type curves, well-to-well displacement predictions, and horizontal-sink productivity estimations. Sound mathematical foundations ensure the high degree of computational accuracy even for heterogeneity problems.

A computationally efficient modification of mixed finite element methods for flow problems with full transmissivity tensors

AbstractThe mixed finite element method for approximately solving flow equations in porous media has received a good deal of attention in the literature. The main idea is to solve for the head/pressure and fluid velocity (Darcy velocity) simultaneously to obtain a higher order approximation of the fluid velocity. In the case of a diagonal transmissivity tensor the algebraic equations resulting from the discretization can be reduced to a system of algebraic equations for the head/pressure variable alone. This reduction results in a smaller number of unknows to be solved for in an iterative method such as preconditioned conjugate gradient method. The fluid velocity is then obtained from an algebraic relationship. In the case of full transmissivity tensor, the algebraic reduction is more difficult. This paper investigates some algorithms resulting from the modification of the mixed finite element that take advantage of the mixed finite element method for the diagonal tensor case. The resulting schemes are more efficient implementations that maintain the same order of accuracy as the original schemes. © 1993 John Wiley & Sons, Inc.

7th International conference finite element methods in flow problems

7th International conference finite element methods in flow problems

The computation of turbulent flows of industrial complexity by the finite element method—progress and prospects

AbstractThis paper is an expanded version of that delivered at the recent Sixth International Symposium on Finite Element Methods in Flow Problems, Antibes, France. It begins by reviewing the role of the finite element method (FEM) in turbulent flow simulation during recent years. The difficulties in incorporating sufficiently general descriptions of turbulence (i.e. two‐equation models) into successful finite‐element‐based Navier‐Stokes codes are examined and analysed in some depth. Current progress by various workers in overcoming these difficulties is reviewed and, by concentrating on one particular approach, it is demonstrated that the FEM has now matured into a powerful and flexible tool for solving two‐dimensional turbulent flows of industrial complexity. The applications presented highlight those features which render the FEM attractive in this field (viz., minimal false diffusion, arbitrary local refinement, boundary fitting capabilities and non‐structured grids). Finally, the prospects and challenges for the future are briefly discussed. In particular, the urgency and difficulty of constructing a competitive three‐dimensional capability which preserves these features is examined.

7th international conference on finite element methods in flow problems

7th international conference on finite element methods in flow problems

Proceedings of the Fourth International Symposium on Finite Element Methods in Flow Problems, held in Tokyo, July 1982. Edited by T. Kawai, University of Tokyo Press. Y5500. Also available through Elsevier North‐Holland, Inc. $95.00. ISBN 0‐444‐86477‐6 xvi + 1096 pages

Proceedings of the Fourth International Symposium on Finite Element Methods in Flow Problems, held in Tokyo, July 1982. Edited by T. Kawai, University of Tokyo Press. Y5500. Also available through Elsevier North‐Holland, Inc. $95.00. ISBN 0‐444‐86477‐6 xvi + 1096 pages

Fifth international symposium on finite element methods in flow problems

Fifth international symposium on finite element methods in flow problems

The fifth international symposium on finite element methods in flow problems

International Journal for Numerical Methods in EngineeringVolume 19, Issue 1 p. i-i SymposiumFree Access The fifth international symposium on finite element methods in flow problems First published: January 1983 https://doi.org/10.1002/nme.1620190102AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume19, Issue1January 1983Pages i-i RelatedInformation

Fifth international symposium on finite element methods in flow problems Sponsored by ticom The university of texas at austin 23–26 january 1984

Fifth international symposium on finite element methods in flow problems Sponsored by ticom The university of texas at austin 23–26 january 1984

On an alternating direction implicit finite element method for flow problems

An alternating direction implicit finite element method (ADIFEM) has been developed for flow problems in which the convective terms dominate. Application of the method to the thermal entry problem produces an unconditionally stable algorithm that is computationally more efficient than a corresponding ADI finite difference method. Application of the method to viscous compressible flow produces an algorithm that is only conditionally stable. The off-axis contributions to the convective terms are shown to limit the stability. Illustrative results are presented for the flow past a rectangular obstacle and over a step.

Finite element methods in flow problems, Second International Symposium, Proceedings Conference held at Santa Margharita Ligure, Italy, June 1976. Published by ICCAD, c/o 1st Scienze delle Costruzioni, Via Montallegro 1, 16145 Genova, Italy. $25

Finite element methods in flow problems, Second International Symposium, Proceedings Conference held at Santa Margharita Ligure, Italy, June 1976. Published by ICCAD, c/o 1st Scienze delle Costruzioni, Via Montallegro 1, 16145 Genova, Italy. $25

International symposium on finite element methods in flow problems, 1974

International symposium on finite element methods in flow problems, 1974