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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

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 least‐squares (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: 1 July 1996

J. SHI and E.F. TORO

A new approach for solving steady incompressible Navier‐Stokes equations is presented in this paper. This method extends the upwind Riemann‐problem‐based techniques to viscous

Abstract

A new approach for solving steady incompressible Navier‐Stokes equations is presented in this paper. This method extends the upwind Riemann‐problem‐based techniques to viscous flows, which is obtained by applying modified artificial compressibility Navier‐Stokes equations and fully discrete high‐order numerical schemes for systems of advection‐diffusion equations. In this approach, utilizing the local Riemann solutions the steady incompressible viscous flows can be solved in a similar way to that of inviscid hyperbolic conservation laws. Numerical experiments on the driven cavity problem indicate that this approach can give satisfactory solutions.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 6 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 8 March 2023

Jordi Vila-Pérez, Matteo Giacomini and Antonio Huerta

This study aims to assess the robustness and accuracy of the face-centred finite volume (FCFV) method for the simulation of compressible laminar flows in different regimes, using…

Abstract

Purpose

This study aims to assess the robustness and accuracy of the face-centred finite volume (FCFV) method for the simulation of compressible laminar flows in different regimes, using numerical benchmarks.

Design/methodology/approach

The work presents a detailed comparison with reference solutions published in the literature –when available– and numerical results computed using a commercial cell-centred finite volume software.

Findings

The FCFV scheme provides first-order accurate approximations of the viscous stress tensor and the heat flux, insensitively to cell distortion or stretching. The strategy demonstrates its efficiency in inviscid and viscous flows, for a wide range of Mach numbers, also in the incompressible limit. In purely inviscid flows, non-oscillatory approximations are obtained in the presence of shock waves. In the incompressible limit, accurate solutions are computed without pressure correction algorithms. The method shows its superior performance for viscous high Mach number flows, achieving physically admissible solutions without carbuncle effect and predictions of quantities of interest with errors below 5%.

Originality/value

The FCFV method accurately evaluates, for a wide range of compressible laminar flows, quantities of engineering interest, such as drag, lift and heat transfer coefficients, on unstructured meshes featuring distorted and highly stretched cells, with an aspect ratio up to ten thousand. The method is suitable to simulate industrial flows on complex geometries, relaxing the requirements on mesh quality introduced by existing finite volume solvers and alleviating the need for time-consuming manual procedures for mesh generation to be performed by specialised technicians.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 September 2005

M.J. Chern, A.G.L. Borthwick and R. Eatock Taylor

The research is directed at development of an efficient and accurate technique for modelling incompressible free surface flows in which viscous effects may not be neglected. The…

1093

Abstract

Purpose

The research is directed at development of an efficient and accurate technique for modelling incompressible free surface flows in which viscous effects may not be neglected. The paper describes the methodology, and gives illustrative results for simple geometries.

Design/methodology/approach

The pseudospectral matrix element method of discretisation is selected as the basis for the CFD technique adopted, because of its high spectral accuracy. It is implemented as a means of solving the Navier‐Stokes equations coupled with the modified compressibility method.

Findings

The viscous solver has been validated for the benchmark cases of uniform flow past a cylinder at a Reynolds number of 40, and 2D cavity flows. Results for sloshing of a viscous fluid in a tank have been successfully compared with those from a linearised analytical solution. Application of the method is illustrated by the results for the interaction of an impulsive wave with a surface piercing circular cylinder in a cylindrical tank.

Research limitations/implications

The paper demonstrates the viability of the approach adopted. The limitation of small amplitude waves should be tackled in future work.

Practical implications

The results will have particular significance in the context of validating computations from more complex schemes applicable to arbitrary geometries.

Originality/value

The new methodology and results are of interest to the community of those developing numerical models of flow past marine structures.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 15 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 27 May 2014

D.C. Lo, Chih-Min Hsieh and D.L. Young

The main advantage of the proposed method is that the computations can be performed on a Cartesian grid with complex immersed boundaries (IBs). The purpose of this paper is to…

Abstract

Purpose

The main advantage of the proposed method is that the computations can be performed on a Cartesian grid with complex immersed boundaries (IBs). The purpose of this paper is to device a numerical scheme based on an embedding finite element method for the solution of two-dimensional (2D) Navier-Stokes equations.

Design/methodology/approach

Geometries featuring the stationary solid obstacles in the flow are embedded in the Cartesian grid with special discretizations near the embedded boundary to ensure the accuracy of the solution in the cut cells. To comprehend the complexities of the viscous flows with IBs, the paper adopts a compact interpolation scheme near the IBs that allows to satisfy the second-order accuracy and the conservation property of the solver. The interpolation scheme is designed by virtue of the shape function in the finite element scheme.

Findings

Three numerical examples are selected to demonstrate the accuracy and flexibility of the proposed methodology. Simulation of flow past a circular cylinder for a range of Re=20-200 shows excellent agreements with other results using different numerical schemes. Flows around a pair of tandem cylinders and several bodies are particularly investigated. The paper simulates the time-based variation of the flow phenomena for uniform flow past a pair of cylinders with various streamwise gaps between two cylinders. The results in terms of drag coefficient and Strouhal number show excellent agreements with the results available in the literature.

Originality/value

Details of the flow characteristics, such as velocity distribution, pressure and vorticity fields are presented. It is concluded the combined embedding boundary method and FE discretizations are robust and accurate for solving 2D fluid flows with complex IBs.

Details

Engineering Computations, vol. 31 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 January 1992

TEJWANT SINGH

The theoretical derivation of the start‐up laminar flow of incompressible viscous fluid in a long pipe as suggested by Szymanski, could not be verified experimentally. This leads…

Abstract

The theoretical derivation of the start‐up laminar flow of incompressible viscous fluid in a long pipe as suggested by Szymanski, could not be verified experimentally. This leads to the checking of assumption of constant pressure gradient across the ends of the pipe, on the basis of which the theoretical development was made. Recently, the problem was again investigated for viscous fluid by Otis. In the present paper, the laminar start‐up flow of elastico‐viscous fluid in a pipe, without assuming constant pressure gradient across its ends, has been investigated. The non‐linear governing equations are solved numerically and the effects of start‐up flow parameters and elastico‐viscous parameter on the velocity distribution have been studied.

Details

Engineering Computations, vol. 9 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 21 September 2010

M.A. Hossain, S. Asghar and Rama Subba Reddy Gorla

The purpose of this paper is to consider the unsteady natural convection flow of a viscous incompressible fluid, which is induced by differential heating on the solid vertical…

Abstract

Purpose

The purpose of this paper is to consider the unsteady natural convection flow of a viscous incompressible fluid, which is induced by differential heating on the solid vertical boundary of an open‐ended rectangular cavity with the two horizontal surfaces which are permeable and maintained at the temperature of ambient fluid. Attention is focused on how the flow and heat transfer is affected by variations of the buoyancy force, as well as by the permeability of the surfaces.

Design/methodology/approach

An upwind finite‐difference method in conjunction with a successive over‐relaxation iteration technique is used to solve the governing boundary layer equations. To do this, the first and second derivatives were approximated by central differences and were used in the vorticity, energy and Poisson equations. To preserve the conservative property, the finite‐difference forms of the vorticity and energy equations were written in conservative form for the convective terms.

Findings

Local rate of heat transfer from the heated surface increases owing to an increase in the value of Ra. In the region near the bottom surface, the heat transfer from the left vertical surface decreases, but that increases in the region near the upper surface. Due to blowing of fluid through the permeable surfaces, the rate of heat transfer is higher than the situation where fluid is being withdrawn. This difference was found to be higher in the case of larger value of Ra.

Research limitations/implications

The analysis is valid for unsteady, two‐dimensional natural convection flow of a viscous fluid filled in an open‐ended rectangular enclosure. An extension to three‐dimensional flow case is left for future work.

Practical implications

The method is very useful to analyze solar receiver systems, fire research, electronic cooling, brake housing of an aircraft and many environmental geothermal processes.

Originality/value

The results of this study may be of some interest to engineers interested in heat transfer in ventilated rooms or enclosures.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 20 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 2 March 2015

Rosilene A. Kraft and Alvaro L. G. A. Coutinho

The purpose of this paper is to show benefits of deflated preconditioned conjugate gradients (CG) in the solution of transient, incompressible, viscous flows coupled with heat…

Abstract

Purpose

The purpose of this paper is to show benefits of deflated preconditioned conjugate gradients (CG) in the solution of transient, incompressible, viscous flows coupled with heat transfer.

Design/methodology/approach

This paper presents the implementation of deflated preconditioned CG as the iterative driver for the system of linearized equations for viscous, incompressible flows and heat transfer simulations. The De Sampaio-Coutinho particular form of the Petrov-Galerkin Generalized Least Squares finite element formulation is used in the discretization of the governing equations, leading to symmetric positive definite matrices, allowing the use of the CG solver.

Findings

The use of deflation techniques improves the spectral condition number. The authors show in a number of problems of coupled viscous flow and heat transfer that convergence is achieved with a lower number of iterations and smaller time.

Originality/value

This work addressed for the first time the use of deflated CG for the solution of transient analysis of free/forced convection in viscous flows coupled with heat transfer.

Details

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

Keywords

Article
Publication date: 9 January 2009

P.R. Sharma and Gurminder Singh

Physical properties of a viscous fluid, e.g. viscosity and thermal conductivity change with temperature and in most of the studies concerned with natural convection, generally…

Abstract

Purpose

Physical properties of a viscous fluid, e.g. viscosity and thermal conductivity change with temperature and in most of the studies concerned with natural convection, generally, the simultaneous effect of temperature dependent viscosity, thermal conductivity have been neglected. Hence, the purpose of this paper is to investigate the simultaneous effects of varying viscosity and thermal conductivity on free convection flow of a viscous incompressible electrically conducting fluid and heat transfer along an isothermal vertical non‐conducting plate in the presence of exponentially varying internal heat‐generation and uniform transverse magnetic field.

Design/methodology/approach

The governing equations of motion and energy are transformed into ordinary differential equations using similarity transformation. The resulting boundary valued, coupled and non‐linear differential equations are converted into system of linear differential equations and solved using Runge‐Kutta fourth order technique along with shooting method.

Findings

It was found that: fluid velocity decreases with the increase in magnetic parameter or Prandtl number; fluid temperature increases with the increase in magnetic parameter; velocity and temperature profiles increase due to increase in heat generation parameter; varying viscosity and thermal conductivity modifies the flow and heat transfer characteristic; and skin‐friction and heat transfer are affected by simultaneous change in viscosity and thermal conductivity in presence/absence of exponentially varying heat generation.

Research limitations/implications

The present study is applicable to an incompressible viscous fluid flow and heat transfer with linearly varying viscosity and thermal conductivity.

Originality/value

This paper provides useful information on the physical properties of a viscous fluid with regard to viscosity and thermal conductivity change with temperature.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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