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Article
Publication date: 11 February 2021

J.N. Reddy, Matthew Martinez and Praneeth Nampally

The purpose of this study is to extend a novel numerical method proposed by the first author, known as the dual mesh control domain method (DMCDM), for the solution of…

Abstract

Purpose

The purpose of this study is to extend a novel numerical method proposed by the first author, known as the dual mesh control domain method (DMCDM), for the solution of linear differential equations to the solution of nonlinear heat transfer and like problems in one and two dimensions.

Design/methodology/approach

In the DMCDM, a mesh of finite elements is used for the approximation of the variables and another mesh of control domains for the satisfaction of the governing equation. Both meshes fully cover the domain but the nodes of the finite element mesh are inside the mesh of control domains. The salient feature of the DMCDM is that the concept of duality (i.e. cause and effect) is used to impose boundary conditions. The method possesses some desirable attributes of the finite element method (FEM) and the finite volume method (FVM).

Findings

Numerical results show that he DMCDM is more accurate than the FVM for the same meshes used. Also, the DMCDM does not require the use of any ad hoc approaches that are routinely used in the FVM.

Originality/value

To the best of the authors’ knowledge, the idea presented in this work is original and novel that exploits the best features of the best competing methods (FEM and FVM). The concept of duality is used to apply gradient and mixed boundary conditions that FVM and its variant do not.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 June 2003

Jaroslav Mackerle

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view…

1021

Abstract

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

Details

Engineering Computations, vol. 20 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 June 2000

A. Savini

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic…

1041

Abstract

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 19 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 June 1992

J.C. CAVENDISH, C.A. HALL and T.A. PORSCHING

We describe a novel mathematical approach to deriving and solving covolume models of the incompressible 2‐D Navier‐Stokes flow equations. The approach integrates three…

94

Abstract

We describe a novel mathematical approach to deriving and solving covolume models of the incompressible 2‐D Navier‐Stokes flow equations. The approach integrates three technical components into a single modelling algorithm: 1. Automatic Grid Generation. An algorithm is described and used to automatically discretize the flow domain into a Delaunay triangulation and a dual Voronoi polygonal tessellation. 2. Covolume Finite Difference Equation Generation. Three covolume discretizations of the Navier‐Stokes equations are presented. The first scheme conserves mass over triangular control volumes, the second scheme over polygonal control volumes and the third scheme conserves mass over both. Simple consistent finite difference equations are derived in terms of the primitive variables of velocity and pressure. 3. Dual Variable Reduction. A network theoretic technique is used to transform each of the finite difference systems into equivalent systems which are considerably smaller than the original primitive finite difference system.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 2 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 10 May 2019

Kumar Kaushik Ranjan, Sandeep Kumar, Amit Tyagi and Ambuj Sharma

The real challenge in the solution of contact problems is the lack of an optimal adaptive scheme. As the contact zone is a priori unknown, successive refinement and…

Abstract

Purpose

The real challenge in the solution of contact problems is the lack of an optimal adaptive scheme. As the contact zone is a priori unknown, successive refinement and iterative method are necessary to obtain a high-accuracy solution. The purpose of this paper is to provide an optimal adaptive scheme based on second-generation finite element wavelets for the solution of non-linear variational inequality of the contact problem.

Design/methodology/approach

To generate an elementary multi-resolution mesh, the authors used hierarchical bases (HB) composed of Lagrange finite element interpolation functions. These HB functions are customized using second-generation wavelet techniques for a fast convergence rate. At each step of the algorithm, the active set method along with mesh adaptation is used for solving the constrained minimization problem of contact case. Wavelet coefficients-based error indicators are used, and computation is focused on mesh zones with a high error indication. The authors take advantage of the wavelet transform to develop a parameter-free adaptive scheme to generate an appropriate and optimal mesh.

Findings

Adaptive wavelet Galerkin scheme (AWGS), a newly developed method for multi-scale mesh adaptivity in this work, is a combination of the second-generation wavelet transform and finite element method and significantly improves the accuracy of the results without approximating an additional problem of error estimation equations. A comparative study is performed taking a solution on a highly refined mesh and results are generated using AWGS.

Practical implications

The proposed adaptive technique can be utilized in the simulation of mechanical and biomechanical structures where multiple bodies come into contact with each other. The algorithm of the method is easy to implement and found to be successful in producing a sufficiently accurate solution with relatively less number of mesh nodes.

Originality/value

Although many error estimation techniques have been developed over the past several years to solve contact problems adaptively, because of boundary non-linearity development, a reliable error estimator needs further investigation. The present study attempts to resolve this problem without having to recompute the entire solution on a new mesh.

Details

Engineering Computations, vol. 36 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 10 August 2010

Kemelli C. Estacio, Graham F. Carey and Norberto Mangiavacchi

The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele‐Shaw model.

Abstract

Purpose

The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele‐Shaw model.

Design/methodology/approach

The scheme involves dual dynamic meshes with active and inactive cells determined from an initial background pointset. The quasi‐static pressure solution in each timestep for this evolving unstructured mesh system is approximated using a control volume finite element method formulation coupled to a corresponding modified volume of fluid method. The flow is considered to be isothermal and non‐Newtonian.

Findings

Supporting numerical tests and performance studies for polystyrene described by Carreau, Cross, Ellis and Power‐law fluid models are conducted. Results for the present method are shown to be comparable to those from other methods for both Newtonian fluid and polystyrene fluid injected in different mold geometries.

Research limitations/implications

With respect to the methodology, the background pointset infers a mesh that is dynamically reconstructed here, and there are a number of efficiency issues and improvements that would be relevant to industrial applications. For instance, one can use the pointset to construct special bases and invoke a so‐called “meshless” scheme using the basis. This would require some interesting strategies to deal with the dynamic point enrichment of the moving front that could benefit from the present front treatment strategy. There are also issues related to mass conservation and fill‐time errors that might be addressed by introducing suitable projections. The general question of “rate of convergence” of these schemes requires analysis. Numerical results here suggest first‐order accuracy and are consistent with the approximations made, but theoretical results are not available yet for these methods.

Originality/value

This novel unstructured simulation approach involves dual meshes with active and inactive cells determined from an initial background pointset: local active dual patches are constructed “on‐the‐fly” for each “active point” to form a dynamic virtual mesh of active elements that evolves with the moving interface.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 20 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 11 May 2010

A. Bouquet, C. Dedeban and S. Piperno

The use of the prominent finite difference time‐domain (FDTD) method for the time‐domain solution of electromagnetic wave propagation past devices with small geometrical…

Abstract

Purpose

The use of the prominent finite difference time‐domain (FDTD) method for the time‐domain solution of electromagnetic wave propagation past devices with small geometrical details can require very fine grids and can lead to unmanageable computational time and storage. The purpose of this paper is to extend the analysis of a discontinuous Galerkin time‐domain (DGTD) method (able to handle possibly non‐conforming locally refined grids, based on portions of Cartesian grids) and investigate the use of perfectly matched layer regions and the coupling with a fictitious domain approach. The use of a DGTD method with a locally refined, non‐conforming mesh can help focusing on these small details. In this paper, the adaptation to the DGTD method of the fictitious domain approach initially developed for the FDTD is considered, in order to avoid the use of a volume mesh fitting the geometry near the details.

Design/methodology/approach

Based on a DGTD method, a fictitious domain approach is developed to deal with complex and small geometrical details.

Findings

The fictitious domain approach is a very interesting complement to the FDTD method, since it makes it possible to handle complex geometries. However, the fictitious domain approach requires small volume elements, thus making the use of the FDTD on wide, regular, fine grids often unmanageable. The DGTD method has the ability to handle easily locally refined grids and the paper shows it can be coupled to a fictitious domain approach.

Research limitations/implications

Although the stability and dispersion analysis of the DGTD method is complete, the theoretical analysis of the fictitious domain approach in the DGTD context is not. It is a subject of further investigation (which could provide important insights for potential improvements).

Originality/value

This is believed to be the first time a DGTD method is coupled with a fictitious domain approach.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 29 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 May 1999

Bozidar Sarler and Jure Mencinger

The axisymmetric steady‐state convective‐diffusive thermal field problem associated with direct‐chill, semi‐continuously cast billets has been solved using the dual

Abstract

The axisymmetric steady‐state convective‐diffusive thermal field problem associated with direct‐chill, semi‐continuously cast billets has been solved using the dual reciprocity boundary element method. The solution is based on a formulation which incorporates the one‐phase physical model, Laplace equation fundamental solution weighting, and scaled augmented thin plate splines for transforming the domain integrals into a finite series of boundary integrals. Realistic non‐linear boundary conditions and temperature variation of all material properties are included. The solution is verified by comparison with the results of the classical finite volume method. Results for a 0.500[m] diameter Al 4.5 per cent Cu alloy billet at typical casting conditions are given.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 9 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 June 2005

Andrea Toselli and Xavier Vasseur

A family of preconditioned dual‐primal FETI iterative algorithms for the solution of algebraic systems arising from edge element approximations in two dimensions is presented.

Abstract

Purpose

A family of preconditioned dual‐primal FETI iterative algorithms for the solution of algebraic systems arising from edge element approximations in two dimensions is presented.

Design/methodology/approach

The primal constraints, which determine the size of the coarse problem to be solved at each iteration step, are here suitable averages over subdomain edges. The condition number of the corresponding methods is independent of the number of subdomains and possibly large jumps of the coefficients.

Findings

For h finite elements, it grows only polylogarithmically with the number of unknowns associated with individual substructures, while for hp approximations on geometrically refined meshes, it is independent of arbitrarily large aspect ratios.

Originality/value

Proposes an algorithm with a rate of convergence that is independent of possibly large jumps of the coefficients and mesh aspect ratios.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 24 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 27 January 2022

Matthias Kowalski, Martin Hanke and Christian Kreischer

Resolving eddy currents in three dimensions with finite elements, especially in geometrically complex structures, is very time consuming. Notable additional efforts will…

Abstract

Purpose

Resolving eddy currents in three dimensions with finite elements, especially in geometrically complex structures, is very time consuming. Notable additional efforts will be required, if these eddy currents are influenced by magnetic fields arising from larger parts or range over widespread regions. The purpose of this article is to present a new sub-modelling simulation technique, based on the finite-element approach. This method offers remarkable advantages for solving this type of problems.

Design/methodology/approach

A novel sub-modeling technique is developed for the finite-element method addressing this problem by dividing the process into two steps: firstly, a simulation of a “source”-model is carried out providing magnetic field distributions within the entire domain neglecting local eddy current effects and without modeling it in full detailed geometry. A subsequent “sub”-model comprises only the region of interest in higher resolution and is solved while being constrained with boundary conditions derived from the previous source-model. An implementation in ANSYS Mechanical is carried out with the objective to validate finite-element simulation against measurement results.

Findings

The proposed simulation technique performs robustly and time efficiently. Applying this method to an end-region of a turbogenerator allows comparisons with test data of this region for validation purposes. The comparison between measured and simulated radial flux densities shows good correspondence.

Originality/value

This work is novel in many aspects: a new technique for three-dimensional (3D) finite-element method using edge-elements is introduced. To the best of the authors’ knowledge, for the first time, these 3D sub-models are compared against measurement results of an electric machine with net currents. Leveraged from this work, detailed analyses of eddy current phenomena under influences of external magnetic fields can be investigated in higher detail within shorter calculation times.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 41 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

1 – 10 of 498