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Article
Publication date: 1 June 2001

P. Nithiarasu

A comparative study has been carried out to investigate the performance of two different time stepping schemes for convective heat transfer and flow in a fluid saturated…

Abstract

A comparative study has been carried out to investigate the performance of two different time stepping schemes for convective heat transfer and flow in a fluid saturated porous medium. Both the schemes are based on the velocity correction procedure. The first scheme is a semi‐implicit one in which the linear and non‐linear porous medium terms of the momentum equation are treated implicitly but solution of the simultaneous equation system is avoided by lumping the mass. The second procedure (quasi‐implicit) treats the porous medium and viscous terms implicitly and a simultaneous equation system is constructed to solve the equations of momentum conservation. Two numerical examples have been considered and both the schemes are tested for various parameters governing the flow and heat transfer in these problems. Results show that, at smaller Rayleigh numbers and on fine meshes, the quasi‐implicit scheme gives faster convergence to steady state in both Darcy and non‐Darcy regimes than that of the semi‐implicit scheme. At higher Rayleigh numbers, the semi‐implicit scheme is faster in the Darcy regime. Also, the semi‐implicit scheme is faster than that of the quasi‐implicit scheme on a coarse mesh used in this study. In general both the schemes predict transient cyclic developments well.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 11 no. 4
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 June 1993

C.P.T. GROTH and J.J. GOTTLIEB

Partially‐decoupled upwind‐based total‐variation‐diminishing (TVD) finite‐difference schemes for the solution of the conservation laws governing two‐dimensional…

Abstract

Partially‐decoupled upwind‐based total‐variation‐diminishing (TVD) finite‐difference schemes for the solution of the conservation laws governing two‐dimensional non‐equilibrium vibrationally relaxing and chemically reacting flows of thermally‐perfect gaseous mixtures are presented. In these methods, a novel partially‐decoupled flux‐difference splitting approach is adopted. The fluid conservation laws and species concentration and vibrational energy equations are decoupled by means of a frozen flow approximation. The resulting partially‐decoupled gas‐dynamic and thermodynamic subsystems are then solved alternately in a lagged manner within a time marching procedure, thereby providing explicit coupling between the two equation sets. Both time‐split semi‐implicit and factored implicit flux‐limited TVD upwind schemes are described. The semi‐implicit formulation is more appropriate for unsteady applications whereas the factored implicit form is useful for obtaining steady‐state solutions. Extensions of Roe's approximate Riemann solvers, giving the eigenvalues and eigenvectors of the fully coupled systems, are used to evaluate the numerical flux functions. Additional modifications to the Riemann solutions are also described which ensure that the approximate solutions are not aphysical. The proposed partially‐decoupled methods are shown to have several computational advantages over chemistry‐split and fully coupled techniques. Furthermore, numerical results for single, complex, and double Mach reflection flows, as well as corner‐expansion and blunt‐body flows, using a five‐species four‐temperature model for air demonstrate the capabilities of the methods.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 3 no. 6
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 11 February 2021

Mingyang Liu, Huifen Zhu, Guangjun Gao, Chen Jiang and G.R Liu

The purpose of this paper is to investigate a novel stabilization scheme to handle convection and pressure oscillation in the process of solving incompressible laminar…

Abstract

Purpose

The purpose of this paper is to investigate a novel stabilization scheme to handle convection and pressure oscillation in the process of solving incompressible laminar flows by finite element method (FEM).

Design/methodology/approach

The semi-implicit stabilization scheme, characteristic-based polynomial pressure projection (CBP3) consists of the Characteristic-Galerkin method and polynomial pressure projection. Theoretically, the proposed scheme works for any type of element using equal-order approximation for velocity and pressure. In this work, linear 3-node triangular and 4-node tetrahedral elements are the focus, which are the simplest but most difficult elements for pressure stabilizations.

Findings

The present paper proposes a new scheme, which can stabilize FEM solution for flows of both low and relatively high Reynolds numbers. And the influence of stabilization parameters of the CBP3 scheme has also been investigated.

Research limitations/implications

The research in this work is limited to the laminar incompressible flow.

Practical implications

The verification and validation of the CBP3 scheme are conducted by several 2 D and 3 D numerical examples. The scheme could be used to deal with more practical fluid problems.

Social implications

The application of scheme to study complex hemodynamics of patient-specific abdominal aortic aneurysm is also presented, which demonstrates its potential to solve bio-flows.

Originality/value

The paper simulated 2 D and 3 D numerical examples with superior results compared to existing results and experiments. The novel CBP3 scheme is verified to be very effective in handling convection and pressure oscillation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 5
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 February 1992

GRANT HOCKING

This paper is concerned with the determination of the transient stress and deformational state of plate‐like discontinua subject to flexural cracking. Such a phenomenon…

Abstract

This paper is concerned with the determination of the transient stress and deformational state of plate‐like discontinua subject to flexural cracking. Such a phenomenon can be easily visualized as the type of fragmentation to floating sea ice impacted by an ice‐breaker or offshore platform. The discrete element method is used to solve the dynamic equilibrium equations for each distinct deformable body and the interaction between bodies. Each body may deform elastically and fracture into further pieces if a brittle failure criterion for flexure is exceeded. The discrete plate element is a hybrid thin‐plate (Kirchhoff) mode lumped at element boundaries with transverse shear deformation computed at element centroids. Errors in computed stresses near point loads and cracks by the current element warrant the use of an improved mixed mode plate element. A three‐dimensional application of the discrete element method is presented for the case of fragmentation of floating sea ice impacting an arctic offshore platform. A semi‐implicit solution scheme is introduced to overcome the stringent explicit time step stability conditions due to stiff members in the discrete element formulation.

Details

Engineering Computations, vol. 9 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 13 May 2020

Mehdi Dehghan and Vahid Mohammadi

This study aims to apply a numerical meshless method, namely, the boundary knot method (BKM) combined with the meshless analog equation method (MAEM) in space and use a…

Abstract

Purpose

This study aims to apply a numerical meshless method, namely, the boundary knot method (BKM) combined with the meshless analog equation method (MAEM) in space and use a semi-implicit scheme in time for finding a new numerical solution of the advection–reaction–diffusion and reaction–diffusion systems in two-dimensional spaces, which arise in biology.

Design/methodology/approach

First, the BKM is applied to approximate the spatial variables of the studied mathematical models. Then, this study derives fully discrete scheme of the studied models using a semi-implicit scheme based on Crank–Nicolson idea, which gives a linear system of algebraic equations with a non-square matrix per time step that is solved by the singular value decomposition. The proposed approach approximates the solution of a given partial differential equation using particular and homogeneous solutions and without considering the fundamental solutions of the proposed equations.

Findings

This study reports some numerical simulations for showing the ability of the presented technique in solving the studied mathematical models arising in biology. The obtained results by the developed numerical scheme are in good agreement with the results reported in the literature. Besides, a simulation of the proposed model is done on buttery shape domain in two-dimensional space.

Originality/value

This study develops the BKM combined with MAEM for solving the coupled systems of (advection) reaction–diffusion equations in two-dimensional spaces. Besides, it does not need the fundamental solution of the mathematical models studied here, which omits any difficulties.

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Article
Publication date: 7 September 2015

Tirivanhu Chinyoka and Daniel Oluwole Makinde

The purpose of this paper is to examine the unsteady pressure-driven flow of a reactive third-grade non-Newtonian fluid in a channel filled with a porous medium. The flow…

Abstract

Purpose

The purpose of this paper is to examine the unsteady pressure-driven flow of a reactive third-grade non-Newtonian fluid in a channel filled with a porous medium. The flow is subjected to buoyancy, suction/injection asymmetrical and convective boundary conditions.

Design/methodology/approach

The authors assume that exothermic chemical reactions take place within the flow system and that the asymmetric convective heat exchange with the ambient at the surfaces follow Newton’s law of cooling. The authors also assume unidirectional suction injection flow of uniform strength across the channel. The flow system is modeled via coupled non-linear partial differential equations derived from conservation laws of physics. The flow velocity and temperature are obtained by solving the governing equations numerically using semi-implicit finite difference methods.

Findings

The authors present the results graphically and draw qualitative and quantitative observations and conclusions with respect to various parameters embedded in the problem. In particular the authors make observations regarding the effects of bouyancy, convective boundary conditions, suction/injection, non-Newtonian character and reaction strength on the flow velocity, temperature, wall shear stress and wall heat transfer.

Originality/value

The combined fluid dynamical, porous media and heat transfer effects investigated in this paper have to the authors’ knowledge not been studied. Such fluid dynamical problems find important application in petroleum recovery.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 7
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 November 2003

N. Massarotti, P. Nithiarasu and A. Carotenuto

In this paper, microscopic and macroscopic approaches to the solution of natural convection in enclosures filled with fluid saturated porous media are investigated. At the…

Abstract

In this paper, microscopic and macroscopic approaches to the solution of natural convection in enclosures filled with fluid saturated porous media are investigated. At the microscopic level, the porous medium is represented by different assemblies of cylinders and the Navier‐Stokes equations are assumed to govern the flow. To represent the flow in a macroscopic porous medium approach, the generalised flow model is employed. The characteristic based split scheme is used to solve the conservation equations of both approaches. In addition to the comparison between microscopic and macroscopic approaches of fluid saturated porous enclosures, cavities with interface between fluid saturated porous medium and single phase fluid are also investigated.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 7
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 30 September 2014

Asghar Zajkani, Abolfazl Darvizeh and Mansour Darvizeh

The purpose of this paper is to introduce a computational time dependent modeling to investigate propagation of elastic-viscoplastic zones in the shock wave loaded…

Abstract

Purpose

The purpose of this paper is to introduce a computational time dependent modeling to investigate propagation of elastic-viscoplastic zones in the shock wave loaded circular plates.

Design/methodology/approach

Constitutive equations are implemented incrementally by the Von-Kármán finite deflection system which is coupled with a mixed strain hardening rule and physical-base viscoplastic models. Time integrations of the equations are done by the return mapping technique through the cutting-plane algorithm. An integrated solution is established by pseudo-spectral collocation methodology. The Chebyshev basis functions are utilized to evaluate the coefficients of displacement fields. Temporal terms are discretized by the Houbolt marching method. Spatial linearizations are accomplished by the quadratic extrapolation technique.

Findings

Results of the center point deflections, effective plastic strain and stress (dynamic flow stress) and temperature rise are compared for three features of the Von-Kármán system. Identifying time history of resultant stresses, propagations of the viscoplastic plastic zones are illustrated for two circumstances; with considering strain rate and hardening effects, and without them. Some of modeling and computation aspects are discussed, carefully. When the results are compared with experimental data of shock wave loadings and finite element simulations, good agreements between them are observed.

Originality/value

This computational approach makes coupling the structural equations with the physical descriptions of the high rate deformation through step-by-step spectral solution of the constitutive equations.

Details

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

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Article
Publication date: 3 May 2016

Rhodri LT Bevan, Etienne Boileau, Raoul van Loon, R.W. Lewis and P Nithiarasu

The purpose of this paper is to describe and analyse a class of finite element fractional step methods for solving the incompressible Navier-Stokes equations. The…

Abstract

Purpose

The purpose of this paper is to describe and analyse a class of finite element fractional step methods for solving the incompressible Navier-Stokes equations. The objective is not to reproduce the extensive contributions on the subject, but to report on long-term experience with and provide a unified overview of a particular approach: the characteristic-based split method. Three procedures, the semi-implicit, quasi-implicit and fully explicit, are studied and compared.

Design/methodology/approach

This work provides a thorough assessment of the accuracy and efficiency of these schemes, both for a first and second order pressure split.

Findings

In transient problems, the quasi-implicit form significantly outperforms the fully explicit approach. The second order (pressure) fractional step method displays significant convergence and accuracy benefits when the quasi-implicit projection method is employed. The fully explicit method, utilising artificial compressibility and a pseudo time stepping procedure, requires no second order fractional split to achieve second order or higher accuracy. While the fully explicit form is efficient for steady state problems, due to its ability to handle local time stepping, the quasi-implicit is the best choice for transient flow calculations with time independent boundary conditions. The semi-implicit form, with its stability restrictions, is the least favoured of all the three forms for incompressible flow calculations.

Originality/value

A comprehensive comparison between three versions of the CBS method is provided for the first time.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 3/4
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 2 November 2015

Guo-Dong Zhang and Yinnian He

The purpose of this paper is to consider the numerical implementation of the Euler semi-implicit scheme for three-dimensional non-stationary magnetohydrodynamics (MHD…

Abstract

Purpose

The purpose of this paper is to consider the numerical implementation of the Euler semi-implicit scheme for three-dimensional non-stationary magnetohydrodynamics (MHD) equations. The Euler semi-implicit scheme is used for time discretization and (P 1b , P 1, P 1) finite element for velocity, pressure and magnet is used for the spatial discretization.

Design/methodology/approach

Several numerical experiments are provided to show this scheme is unconditional stability and unconditional L2−H2 convergence with the L2−H2 optimal error rates for solving the non-stationary MHD flows.

Findings

In this paper, the authors mainly focus on the numerical investigation of the Euler semi-implicit scheme for MHD flows. First, the unconditional stability and the L2−H2 unconditional convergence with optimal L2−H2 error rates of this scheme are validated through our numerical tests. Some interesting phenomenons are presented.

Originality/value

The Euler semi-implicit scheme is used to simulate a practical physics model problem to investigate the interaction of fluid and induced magnetic field. Some interesting phenomenons are presented.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

1 – 10 of 297