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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 December 1998

N. Massarotti, P. Nithiarasu and O.C. Zienkiewicz

In our earlier papers we have presented a general algorithm for the solution of both compressible and incompressible Navier‐Stokes equations. The objective of the present…

Abstract

In our earlier papers we have presented a general algorithm for the solution of both compressible and incompressible Navier‐Stokes equations. The objective of the present work is to show the performance of this algorithm when it is used to solve thermal flow problems. Both natural and forced convection and transient problems are considered in this study. The semi‐implicit form of the algorithm has been used to deal with a variety of these problems.

Details

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

Keywords

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Article
Publication date: 3 May 2016

Nicola Massarotti, Michela Ciccolella, Gino Cortellessa and Alessandro Mauro

The purpose of this paper is to focus on the numerical analysis of transient free convection heat transfer in partially porous cylindrical domains. The authors analyze the…

Abstract

Purpose

The purpose of this paper is to focus on the numerical analysis of transient free convection heat transfer in partially porous cylindrical domains. The authors analyze the dependence of velocity and temperature fields on the geometry, by analyzing transient flow behavior for different values of cavity aspect ratio and radii ratio; both inner and outer radius are assumed variable in order to not change the difference ro-ri. Moreover, several Darcy numbers have been considered.

Design/methodology/approach

A dual time-stepping procedure based on the transient artificial compressibility version of the characteristic-based split algorithm has been adopted in order to solve the transient equations of the generalized model for heat and fluid flow through porous media. The present model has been validated against experimental data available in the scientific literature for two different problems, steady-state free convection in a porous annulus and transient natural convection in a porous cylinder, showing an excellent agreement.

Findings

For vertically divided half porous cavities, with Rayleigh numbers equal to 3.4×106 for the 4:1 cavity and 3.4×105 for the 8:1 cavity, the numerical results show that transient oscillations tend to disappear in presence of cylindrical geometry, differently from what happens for rectangular one. The magnitude of this phenomenon increases with radii ratio; the porous layer also affects the stability of velocity and temperature fields, as oscillations tend to decrease in presence of a porous matrix with lower value of the Darcy number.

Research limitations/implications

A proper analysis of partially porous annular cavities is fundamental for the correct estimation of Nusselt numbers, as the formulas provided for rectangular domains are not able to describe these problems.

Practical implications

The proposed model represents a useful tool for the study of transient natural convection problems in porous and partially porous cylindrical and annular cavities, typical of many engineering applications. Moreover, a fully explicit scheme reduces the computational costs and ensures flexibility.

Originality/value

This is the first time that a fully explicit finite element scheme is employed for the solution of transient natural convection in partially porous tall annular cavities.

Details

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

Keywords

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Article
Publication date: 6 November 2017

Fahimeh Saberi Zafarghandi, Maryam Mohammadi, Esmail Babolian and Shahnam Javadi

The purpose of this paper is to introduce a local Newton basis functions collocation method for solving the 2D nonlinear coupled Burgers’ equations. It needs less computer…

Abstract

Purpose

The purpose of this paper is to introduce a local Newton basis functions collocation method for solving the 2D nonlinear coupled Burgers’ equations. It needs less computer storage and flops than the usual global radial basis functions collocation method and also stabilizes the numerical solutions of the convection-dominated equations by using the Newton basis functions.

Design/methodology/approach

A meshless method based on spatial trial space spanned by the local Newton basis functions in the “native” Hilbert space of the reproducing kernel is presented. With the selected local sub-clusters of domain nodes, an approximation function is introduced as a sum of weighted local Newton basis functions. Then the collocation approach is used to determine weights. The method leads to a system of ordinary differential equations (ODEs) for the time-dependent partial differential equations (PDEs).

Findings

The method is successfully used for solving the 2D nonlinear coupled Burgers’ equations for reasonably high values of Reynolds number (Re). It is a well-known issue in the analysis of the convection-diffusion problems that the solution becomes oscillatory when the problem becomes convection-dominated if the standard methods are followed without special treatments. In the proposed method, the authors do not detect any instability near the front, hence no technique is needed. The numerical results show that the proposed method is efficient, accurate and stable for flow with reasonably high values of Re.

Originality/value

The authors used more stable basis functions than the standard basis of translated kernels for representing of kernel-based approximants for the numerical solution of partial differential equations (PDEs). The local character of the method, having a well-structured implementation including enforcing the Dirichlet and Neuman boundary conditions, and producing accurate and stable results for flow with reasonably high values of Re for the numerical solution of the 2D nonlinear coupled Burgers’ equations without any special technique are the main values of the paper.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

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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

Keywords

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Article
Publication date: 1 August 2001

N. Massarotti, P. Nithiarasu and O.C. Zienkiewicz

Natural convection in porous medium‐fluid interface problems are numerically studied by using the characteristic based split (CBS) algorithm. The finite element method is…

Abstract

Natural convection in porous medium‐fluid interface problems are numerically studied by using the characteristic based split (CBS) algorithm. The finite element method is used to solve the governing generalized porous medium equations. The accuracy of the scheme is estimated by comparing the present predictions for a porous cavity with those results available for the same problem. Two different types of interface problems have been considered. In the first case, the domain is vertically divided into two equal parts, while in the second problem the division is along the horizontal direction. Results obtained from the present investigation are compared extensively with existing experimental and numerical data and they are in good agreement with the available literature. Also present results are smooth along the interface and are without any jumps in the solution.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 11 no. 5
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 11 January 2008

A.K. Arnold, P. Nithiarasu and P.G. Tucker

This paper seeks to numerically model electro‐osmotic flow (EOF) through microchannels using a finite element‐based unstructured mesh solution methodology.

Abstract

Purpose

This paper seeks to numerically model electro‐osmotic flow (EOF) through microchannels using a finite element‐based unstructured mesh solution methodology.

Design/methodology/approach

The finite element method (FEM) combined with the characteristic‐based split (CBS) algorithm is used to solve the coupled Navier‐Stokes equations in order to simulate EOFs. The Laplace and Poisson‐Boltzmann equations are solved explicitly a priori to the solution of the fluid dynamic equations. The external electric field and internal potential values are then used to construct the source terms of the fluid dynamics equations.

Findings

Proposed methodology works excellently on unstructured meshes for both two‐ and three‐dimensional flow problems. The results obtained for benchmark channel flow problems show an excellent agreement with analytical and experimental data.

Originality/value

The idea of using the FEM and the CBS algorithm to solve the governing equations of EOFs is proposed. This particular method of solving these equations is unprecedented. In addition to benchmark examples, a problem of practical importance is also solved in this paper.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 18 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 1 January 2005

P. Nithiarasu, N. Massarotti and J.S. Mathur

To numerically model forced convection heat transfer over arrays of solder balls.

Abstract

Purpose

To numerically model forced convection heat transfer over arrays of solder balls.

Design/methodology/approach

The characteristic based split (CBS) scheme has been used to solve the incompressible Navier‐Stokes equations on unstructured meshes.

Findings

The results show an increase in heat transport with increase in Reynolds numbers. A significant change in heat transfer is also noticed with change in angle of attack.

Originality/value

The presented results will be useful in designing cooling systems for electronic components.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 15 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 27 March 2008

P. Nithiarasu

This paper aims to present briefly a unified fractional step method for fluid dynamics, incompressible solid mechanics and heat transfer calculations. The proposed method

Abstract

Purpose

This paper aims to present briefly a unified fractional step method for fluid dynamics, incompressible solid mechanics and heat transfer calculations. The proposed method is demonstrated by solving compressible and incompressible flows, solid mechanics and conjugate heat transfer problems.

Design/methodology/approach

The finite element method is used for the spatial discretization of the equations. The fluid dynamics algorithm used is often referred to as the characteristic‐based split scheme.

Findings

The proposed method can be employed as a unified approach to fluid dynamics, heat transfer and solid mechanics problems.

Originality/value

The idea of using a unified approach to fluid dynamics and incompressible solid mechanics problems is proposed. The proposed approach will be valuable in complicated engineering problems such as fluid‐structure interaction and problems involving conjugate heat transfer and thermal stresses.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 18 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 1 October 2004

M.F. Webster, I.J. Keshtiban and F. Belblidia

We introduce a second‐order accurate time‐marching pressure‐correction algorithm to accommodate weakly‐compressible highly‐viscous liquid flows at low Mach number. As the…

Abstract

We introduce a second‐order accurate time‐marching pressure‐correction algorithm to accommodate weakly‐compressible highly‐viscous liquid flows at low Mach number. As the incompressible limit is approached (Ma ≈ 0), the consistency of the compressible scheme is highlighted in recovering equivalent incompressible solutions. In the viscous‐dominated regime of low Reynolds number (zone of interest), the algorithm treats the viscous part of the equations in a semi‐implicit form. Two discrete representations are proposed to interpolate density: a piecewise‐constant form with gradient recovery and a linear interpolation form, akin to that on pressure. Numerical performance is considered on a number of classical benchmark problems for highly viscous liquid flows to highlight consistency, accuracy and stability properties. Validation bears out the high quality of performance of both compressible flow implementations, at low to vanishing Mach number. Neither linear nor constant density interpolations schemes degrade the second‐order accuracy of the original incompressible fractional‐staged pressure‐correction scheme. The piecewise‐constant interpolation scheme is advocated as a viable method of choice, with its advantages of order retention, yet efficiency in implementation.

Details

Engineering Computations, vol. 21 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

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