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Article
Publication date: 1 December 2005

Alessandro Corsini, Franco Rispoli and Andrea Santoriello

An original finite element scheme for advection‐diffusion‐reaction problems is presented. The new method, called spotted Petrov‐Galerkin (SPG), is a quadratic Petrov‐Galerkin (PG…

Abstract

Purpose

An original finite element scheme for advection‐diffusion‐reaction problems is presented. The new method, called spotted Petrov‐Galerkin (SPG), is a quadratic Petrov‐Galerkin (PG) formulation developed for the solution of equations where either reaction (associated to zero‐order derivatives of the unknown) and/or advection (proportional to first‐order derivatives) dominates on diffusion (associated to second‐order derivatives). The addressed issues are turbulence and advective‐reactive features in modelling turbomachinery flows.

Design/methodology/approach

The present work addresses the definition of a new PG stabilization scheme for the reactive flow limit, formulated on a quadratic finite element space of approximation. We advocate the use of a higher order stabilized formulation that guarantees the best compromise between solution stability and accuracy. The formulation is first presented for linear scalar one‐dimensional advective‐diffusive‐reactive problems and then extended to quadrangular Q2 elements.

Findings

The proposed advective‐diffusive‐reactive PG formulation improves the solution accuracy with respect to a standard streamline driven stabilization schemes, e.g. the streamline upwind or Galerkin, in that it properly accounts for the boundary layer region flow phenomena in presence of non‐equilibrium effects.

Research limitations/implications

The numerical method here proposed has been designed for second‐order quadrangular finite‐elements. In particular, the Reynolds‐Averaged Navier‐Stokes equations with a non‐linear turbulence closure have been modelled using the stable mixed element pair Q2‐Q1.

Originality/value

This paper investigated the predicting capabilities of a finite element method stabilized formulation developed for the purpose of solving advection‐reaction‐diffusion problems. The new method, called SPG, demonstrates its suitability in solving the typical equations of turbulence eddy viscosity models.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 15 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 December 1997

Dan Givoli, Joseph E. Flaherty and Mark S. Shephard

Describes a new finite element scheme for the large‐scale analysis of compressible and incompressible viscous flows. The scheme is based on a combined compressible‐ incompressible…

Abstract

Describes a new finite element scheme for the large‐scale analysis of compressible and incompressible viscous flows. The scheme is based on a combined compressible‐ incompressible Galerkin leastsquares (GLS) space‐time variational formulation. Three‐ dimensional unstructured meshes are employed, with piecewise‐constant temporal interpolation, local time‐stepping for steady flows, and linear continuous spatial interpolation in all the variables. The scheme incorporates automatic adaptive mesh refinement, with a choice of various error indicators. It is implemented on a distributed‐memory parallel computer, and includes an automatic load‐balancing procedure. Demonstrates the ability to solve both compressible and incompressible viscous flow problems using the parallel adaptive framework via numerical examples. These include Mach 3 flow over a flat plate, and a divergence‐free buoyancy‐driven flow in a cavity. The latter is a model for the steady melt flow in a Czochralski crystal growth process.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 7 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 2 March 2015

Mas Irfan Purbawanto Hidayat, Bambang Ariwahjoedi and Setyamartana Parman

The purpose of this paper is to present a new approach of meshless local B-spline based finite difference (FD) method for solving two dimensional transient heat conduction…

253

Abstract

Purpose

The purpose of this paper is to present a new approach of meshless local B-spline based finite difference (FD) method for solving two dimensional transient heat conduction problems.

Design/methodology/approach

In the present method, any governing equations are discretized by B-spline approximation which is implemented in the spirit of FD technique using a local B-spline collocation scheme. The key aspect of the method is that any derivative is stated as neighbouring nodal values based on B-spline interpolants. The set of neighbouring nodes are allowed to be randomly distributed thus enhanced flexibility in the numerical simulation can be obtained. The method requires no mesh connectivity at all for either field variable approximation or integration. Time integration is performed by using the Crank-Nicolson implicit time stepping technique.

Findings

Several heat conduction problems in complex domains which represent for extended surfaces in industrial applications are examined to demonstrate the effectiveness of the present approach. Comparison of the obtained results with solutions from other numerical method available in literature is given. Excellent agreement with reference numerical method has been found.

Research limitations/implications

The method is presented for 2D problems. Nevertheless, it would be also applicable for 3D problems.

Practical implications

A transient two dimensional heat conduction in complex domains which represent for extended surfaces in industrial applications is presented.

Originality/value

The presented new meshless local method is simple and accurate, while it is also suitable for analysis in domains of arbitrary geometries.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 April 1994

A. Huerta and F. Casadei

The arbitrary Lagrangian—Eulerian (ALE)formulation, which is already well established in the hydrodynamics andfluid‐structure interaction fields, is extended to materials…

Abstract

The arbitrary Lagrangian—Eulerian (ALE) formulation, which is already well established in the hydrodynamics and fluid‐structure interaction fields, is extended to materials with memory, namely, non‐ linear path‐dependent materials. Previous attempts to treat non‐ linear solid mechanics with the ALE description have, in common, the implicit interpolation technique employed. Obviously, this implies a numerical burden which may be uneconomical and may induce to give up this formulation, particularly in fast‐transient dynamics where explicit algorithms are usually employed. Here, several applications are presented to show that if adequate stress updating techniques are implemented, the ALE formulation could be much more competitive than classical Lagrangian computations when large deformations are present. Moreover, if the ALE technique is interpreted as a simple interpolation enrichment, adequate—in opposition to distorted or locally coarse—meshes are employed. Notice also that impossible computations (or at least very involved numerically) with a Lagrangian code are easily implementable in an ALE analysis. Finally, it is important to observe that the numerical examples shown range from a purely academic test to real engineering simulations. They show the effective applicability of this formulation to non‐linear solid mechanics and, in particular, to impact, coining or forming analysis.

Article
Publication date: 30 September 2014

Seyed Mahmoud Hosseini

The purpose of this paper is to propose a hybrid mesh-free method based on generalized finite difference (GFD) and Newmark finite difference methods to study the elastic wave…

108

Abstract

Purpose

The purpose of this paper is to propose a hybrid mesh-free method based on generalized finite difference (GFD) and Newmark finite difference methods to study the elastic wave propagation in functionally graded nanocomposite reinforced by carbon nanotubes (FGNRCN). The presented hybrid mesh-free method is applied for a thick hollow cylinder, which is made of FGNRCN and excited by various mechanical shock loadings.

Design/methodology/approach

The FG nanocomposite cylinder is assumed to be under shock loading. The elastic wave propagation is obtained and studied for various nonlinear grading patterns and distributions of the aligned carbon nanotubes. The distribution of carbon naotubes in FG nanocomposite are considered to vary as nonlinear function of radius, which varies with various nonlinear grading patterns continuously through radial direction. The effective material properties of functionally graded carbon nanotube are estimated using a micro-mechanical model.

Findings

The mechanical shock analysis of FGNRCN thick hollow cylinder is carried out and the dynamic behavior of displacement field and the time history of radial displacement are obtained for various grading patterns. An effective hybrid mesh-free method based on GFD and Newmark finite difference methods is presented to calculate the average velocity of elastic wave propagation in FGNRCN. The average velocity of elastic wave propagation is obtained for various grading patterns and various kinds of volume fraction. The effects of some parameters on average velocity of elastic wave propagation are obtained and studied in detail.

Originality/value

The calculation of elastic radial wave propagation in a FGNRCN thick hollow cylinder is presented using a hybrid mesh-free method. The effects of some parameters on wave propagation such as various grading patterns of distribution of carbon nanotubes are studied in details.

Details

Engineering Computations, vol. 31 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 June 2002

H. Matallah, P. Townsend and M.F. Webster

This study considers both a single and multi‐mode viscoelastic analysis for wire‐coating flows. The numerical simulations utilise a finite element time‐stepping technique, a…

Abstract

This study considers both a single and multi‐mode viscoelastic analysis for wire‐coating flows. The numerical simulations utilise a finite element time‐stepping technique, a Taylor‐Petrov‐Galerkin/pressure‐correction scheme employing both coupled and decoupled procedures between stress and kinematic fields. An exponential Phan‐Thein/Tanner model is used to predict pressure‐drop and residual stress for this process. Rheometrical data fitting is performed for steady shear and pure extensional flows, considering both high and low density polyethylene melts. Simulations are conducted to match experimental pressure‐drop/flowrate data for a contraction flow. Then, for a complex industrial wire‐coating flow, stress and pressure drop are predicted numerically and quantified. The benefits are extolled of the use of a multi‐mode model that can incorporate a wide‐range discrete relaxation spectrum to represent flow response in complex settings. Contrast is made between LDPE and HDPE polymers, and dependency on individual relaxation modes is identified in its contribution to overall flow behaviour.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 12 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 5 June 2007

Ean Tat Ooi, Sellakkutti Rajendran and Joon Hock Yeo

This paper aims to present an extension of two recently published elements (which are based on Petrov‐Galerkin formulation) to geometric nonlinear (GNL) problems.

Abstract

Purpose

This paper aims to present an extension of two recently published elements (which are based on Petrov‐Galerkin formulation) to geometric nonlinear (GNL) problems.

Design/methodology/approach

Two different sets of shape functions, namely isoparametric and metric, suitably chosen to satisfy the necessary compatibility and completeness conditions, are used as test and trial functions, respectively. Total Lagrangian formulation is used for the implementation of the element.

Findings

In implementing the unsymmetric formulation for nonlinear problems, the deformation gradient tensor can be evaluated invariably using either isoparametric or metric shape functions. The developed elements are found to exhibit improved performance in the presence of mesh distortions.

Research limitations/implications

The numerical problems in this paper involve linear elastic materials.

Originality/value

Extension of US‐QUAD8 and US‐HEXA20 for GNL problems is new.

Details

Engineering Computations, vol. 24 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 10 May 2019

Wenan Wu and Hong Zheng

This study aims to introduce the hybrid finite element (FE) – meshfree method and multiscale variational principle into the traditional mixed FE formulation, leading to a stable…

Abstract

Purpose

This study aims to introduce the hybrid finite element (FE) – meshfree method and multiscale variational principle into the traditional mixed FE formulation, leading to a stable mixed formulation for incompressible linear elasticity which circumvents the need to satisfy inf-sup condition.

Design/methodology/approach

Using the hybrid FE–meshfree method, the displacement and pressure are interpolated conveniently with the same order so that a continuous pressure field can be obtained with low-order elements. The multiscale variational principle is then introduced into the Galerkin form to obtain stable and convergent results.

Findings

The present method is capable of overcoming volume locking and does not exhibit unphysical oscillations near the incompressible limit. Moreover, there are no extra unknowns introduced in the present method because the fine-scale unknowns are eliminated using the static condensation technique, and there is no need to evaluate any user-defined stability parameter as the classical stabilization methods do. The shape functions constructed in the present model possess continuous derivatives at nodes, which gives a continuous and more precise stress field with no need of an additional smooth process. The shape functions in the present model also possess the Kronecker delta property, so that it is convenient to impose essential boundary conditions.

Originality/value

The proposed model can be implemented easily. Its convergence rates and accuracy in displacement, energy and pressure are even comparable to those of second-order mixed elements.

Article
Publication date: 1 September 2004

Elizabeth A. Burroughs, Louis A. Romero, Richard B. Lehoucq and Andrew G. Salinger

Locates the onset of oscillatory instability in the fluid flow inside a differentially heated cavity with aspect ratio 2 by computing a steady‐state and analyzing the stability of…

Abstract

Locates the onset of oscillatory instability in the fluid flow inside a differentially heated cavity with aspect ratio 2 by computing a steady‐state and analyzing the stability of the system via eigenvalue approximation. Discusses the choice of parameters for the Cayley transformation so that the calculation of selected eigenvalues of the transformed system will reliably answer the question of stability. Also presents an argument that due to the symmetry of the problem, the first two unstable modes will have eigenvalues that are nearly identical, and the numerical experiments confirm this. Finally, locates a co‐dimension 2 bifurcation signifying where there is a switch in the mode of initial instability. The results were obtained using a parallel finite element CFD code (MPSalsa) along with an Arnoldi‐based eigensolver (ARPACK), a preconditioned Krylov method code for the necessary linear solves (Aztec), and a stability analysis library (LOCA).

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 14 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 March 1997

N. Nigro, M. Storti and S. Idelsohn

Addresses two difficulties which arise when using a compressible code with equal order interpolation (non‐staggered grids in the finite‐difference nomenclature) to capture a…

Abstract

Addresses two difficulties which arise when using a compressible code with equal order interpolation (non‐staggered grids in the finite‐difference nomenclature) to capture a steady‐state solution in the incompressible limit, i.e. at low Mach numbers. Explains that, first, numerical instabilities in the form of spurious oscillations in pressure pollute the solution and, second, the convergence to the steady state becomes extremely slow owing to bad conditioning of the different speeds of propagation. By using a stabilized method, allows the use of equal‐order interpolations in a consistent (weighted‐residual) formulation which stabilizes both the convection and the continuity terms at the same time. On the other hand, by using specially devised preconditioning, assures a rate of convergence independent of Mach number.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 7 no. 2/3
Type: Research Article
ISSN: 0961-5539

Keywords

21 – 30 of 90