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Article
Publication date: 1 December 1999

M.T. Manzari

1377

Abstract

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International Journal of Numerical Methods for Heat & Fluid Flow, vol. 9 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 28 November 2018

Mojtaba Moshiri and Mehrdad T. Manzari

This paper aims to numerically study the compositional flow of two- and three-phase fluids in one-dimensional porous media and to make a comparison between several upwind and…

97

Abstract

Purpose

This paper aims to numerically study the compositional flow of two- and three-phase fluids in one-dimensional porous media and to make a comparison between several upwind and central numerical schemes.

Design/methodology/approach

Implicit pressure explicit composition (IMPEC) procedure is used for discretization of governing equations. The pressure equation is solved implicitly, whereas the mass conservation equations are solved explicitly using different upwind (UPW) and central (CEN) numerical schemes. These include classical upwind (UPW-CLS), flux-based decomposition upwind (UPW-FLX), variable-based decomposition upwind (UPW-VAR), Roe’s upwind (UPW-ROE), local Lax–Friedrichs (CEN-LLF), dominant wave (CEN-DW), Harten–Lax–van Leer (HLL) and newly proposed modified dominant wave (CEN-MDW) schemes. To achieve higher resolution, high-order data generated by either monotone upstream-centered schemes for conservation laws (MUSCL) or weighted essentially non-oscillatory (WENO) reconstructions are used.

Findings

It was found that the new CEN-MDW scheme can accurately solve multiphase compositional flow equations. This scheme uses most of the information in flux function while it has a moderate computational cost as a consequence of using simple algebraic formula for the wave speed approximation. Moreover, numerically calculated wave structure is shown to be used as a tool for a priori estimation of problematic regions, i.e. degenerate, umbilic and elliptic points, which require applying correction procedures to produce physically acceptable (entropy) solutions.

Research limitations/implications

This paper is concerned with one-dimensional study of compositional two- and three-phase flows in porous media. Temperature is assumed constant and the physical model accounts for miscibility and compressibility of fluids, whereas gravity and capillary effects are neglected.

Practical implications

The proposed numerical scheme can be efficiently used for solving two- and three-phase compositional flows in porous media with a low computational cost which is especially useful when the number of chemical species increases.

Originality/value

A new central scheme is proposed that leads to improved accuracy and computational efficiency. Moreover, to the best of authors knowledge, this is the first time that the wave structure of compositional model is investigated numerically to determine the problematic situations during numerical solution and adopt appropriate correction techniques.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 February 1998

Mehrdad T. Manzari and Majid T. Manzari

Using a non‐Fourier heat conduction (NFHC) hypothesis, the governing equations of thermal wave propagation are established. The resulting differential equations are transformed to…

688

Abstract

Using a non‐Fourier heat conduction (NFHC) hypothesis, the governing equations of thermal wave propagation are established. The resulting differential equations are transformed to integral forms using the Galerkin weighted residual method and then are discretized by a finite element technique. The proposed finite element formulation is verified by comparing the results of analytical and numerical solutions to a number of selected 1‐D problems. A couple of 2‐D sample problems are solved and the responses of the system to various input signals are studied. The proposed mixed approach shows superiority to the conventional finite element solution of hyperbolic heat conduction equation, because of the simultaneous determination of heat fluxes and temperature at each nodal point. The mixed approach is also shown to be capable of capturing the sudden temperature jump due to heat pulses.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 8 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 March 2003

M.T. Manzari

A finite element solution procedure is presented for the simulation of transient incompressible fluid flows using triangular meshes. The algorithm is based on the artificial…

1330

Abstract

A finite element solution procedure is presented for the simulation of transient incompressible fluid flows using triangular meshes. The algorithm is based on the artificial compressibility technique in connection with a dual time‐stepping approach. A second‐order discretization is employed to achieve the required accuracy in real‐time while an explicit multistage Runge‐Kutta scheme is used to march in the pseudo‐time domain. A standard Galerkin finite element method, stabilized by using an artificial dissipation technique, is used for the spatial discretization. The performance of the proposed algorithm is demonstrated by solving a set of internal and external problems including flows with purely transient and periodic behavior.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 2
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 May 2001

R.W. Lewis, M.T. Manzari and D.T. Gethin

The general procedure of thermal optimisation in the sand casting process is addressed. Various aspects of design including the size and position of feeders and chills are…

1477

Abstract

The general procedure of thermal optimisation in the sand casting process is addressed. Various aspects of design including the size and position of feeders and chills are discussed and practical approaches are presented to search for optimum design configurations. An algorithm is also presented for finding the optimum size, position and number of chills in a sand casting process. The presence of the chill(s) in the casting configuration is simulated using a one‐dimensional heat conduction model and proper inter‐facial heat transfer coefficients. The method is efficient as all computations are carried out on the same grid and there is no need for re‐meshing due to re‐sizing or re‐positioning of the chills. A finite element thermal analysis module is linked to a commercial optimisation tool to search for the optimum set of design variables and a computationally efficient sensitivity analysis method is introduced. Three sand casting test cases are solved to validate and demonstrate the optimisation procedure and these show its use to determine the optimum size, location and number of feeders and chills on a section through a casting.

Details

Engineering Computations, vol. 18 no. 3/4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 14 May 2020

Jinting Yang and Tong Zhang

The purpose of this paper is to propose three iterative finite element methods for equations of thermally coupled incompressible magneto-hydrodynamics (MHD) on 2D/3D bounded…

159

Abstract

Purpose

The purpose of this paper is to propose three iterative finite element methods for equations of thermally coupled incompressible magneto-hydrodynamics (MHD) on 2D/3D bounded domain. The detailed theoretical analysis and some numerical results are presented. The main results show that the Stokes iterative method has the strictest restrictions on the physical parameters, and the Newton’s iterative method has the higher accuracy and the Oseen iterative method is stable unconditionally.

Design/methodology/approach

Three iterative finite element methods have been designed for the thermally coupled incompressible MHD flow on 2D/3D bounded domain. The Oseen iterative scheme includes solving a linearized steady MHD and Oseen equations; unconditional stability and optimal error estimates of numerical approximations at each iterative step are established under the uniqueness condition. Stability and convergence of numerical solutions in Newton and Stokes’ iterative schemes are also analyzed under some strong uniqueness conditions.

Findings

This work was supported by the NSF of China (No. 11971152).

Originality/value

This paper presents the best choice for solving the steady thermally coupled MHD equations with different physical parameters.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 12
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 June 2002

Whye‐Teong Ang

The numerical solution of a two‐dimensional thermal problem governed by a third‐order partial differential equation derived from a non‐Fourier heat flux model which may account…

414

Abstract

The numerical solution of a two‐dimensional thermal problem governed by a third‐order partial differential equation derived from a non‐Fourier heat flux model which may account for thermal waves and/or microscopic effects is considered. A dual‐reciprocity boundary element method is proposed for solving the problem in the Laplace transformation domain. The solution in the physical domain is recovered by a numerical inverse Laplace transformation technique.

Details

Engineering Computations, vol. 19 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 21 October 2022

Zahra Moinfar, Shahed Vahabi and Mohammad Vahabi

The purpose of this study is to investigate the effects of the shear-thinning viscoelastic behavior of the surrounding matrix on droplet deformation by weakly compressible…

145

Abstract

Purpose

The purpose of this study is to investigate the effects of the shear-thinning viscoelastic behavior of the surrounding matrix on droplet deformation by weakly compressible smoothed particle hydrodynamics (WC-SPH). Also, the effect of the presence of another droplet is examined.

Design/methodology/approach

A modified consistent weakly compressible SPH method is proposed. After code verification, a complete parameter study is performed for a drop under the simple shear flow of a Giesekus liquid. The investigated parameters are 0.048≤Ca ≤ 14.4, 0.1≤c ≤ 10, 0.04≤De ≤ 10, 0≤α ≤ 1 and 0.12≤Re ≤ 12.

Findings

It is demonstrated that the rheological behavior of the surrounding fluid could dramatically affect the droplet deformation. It is shown that the droplet deformation is increased by increasing Re and Ca. In contrast, the droplet deformation is decreased by increasing a, De and polymer content. Also, it is indicated the presence of another droplet could drastically affect the flow field, and the primary stress difference (N1) is resonated between two droplets.

Originality/value

The main originality of this paper is to introduce a new consistent WC-SPH algorithm. The proposed method is very versatile for tackling the shear-thinning viscoelastic multiphase problems. Furthermore, a complete parameter study is performed for a drop under the simple shear flow of Giesekus liquid. Another novelty of the current paper is studying the effect of the presence of a second droplet. To the best of the authors’ knowledge, this is performed for the first time.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 21 February 2020

Tanmay Basak

This paper aims to investigate the thermal performance involving larger heating rate, targeted heating, heating with least non-uniformity of the spatial distribution of…

189

Abstract

Purpose

This paper aims to investigate the thermal performance involving larger heating rate, targeted heating, heating with least non-uniformity of the spatial distribution of temperature and larger penetration of heating within samples vs shapes of samples (circle, square and triangular).

Design/methodology/approach

Galerkin finite element method (GFEM) with adaptive meshing in a composite domain (free space and sample) is used in an in-house computer code. The finite element meshing is done in a composite domain involving triangle embedded within a semicircular hypothetical domain. The comparison of heating pattern is done for various shapes of samples involving identical cross-sectional area. Test cases reveal that triangular samples can induce larger penetration of heat and multiple heating fronts. A representative material (beef) with high dielectric loss corresponding to larger microwave power or heat absorption in contrast to low lossy samples is considered for the current study. The average power absorption within lossy samples has been computed using the spatial distribution and finite element basis sets. Four regimes have been selected based on various local maxima of the average power for detailed investigation. These regimes are selected based on thin, thick and intermediate limits of the sample size corresponding to the constant area of cross section, Ac involving circle or square or triangle.

Findings

The thin sample limit (Regime 1) corresponds to samples with spatially invariant power absorption, whereas power absorption attenuates from exposed to unexposed faces for thick samples (Regime 4). In Regimes 2 and 3, the average power absorption non-monotonically varies with sample size or area of cross section (Ac) and a few maxima of average power occur for fixed values of Ac involving various shapes. The spatial characteristics of power and temperature have been critically analyzed for all cross sections at each regime for lossy samples. Triangular samples are found to exhibit occurrence of multiple heating fronts for large samples (Regimes 3 and 4).

Practical implications

Length scales of samples of various shapes (circle, square and triangle) can be represented via Regimes 1-4. Regime 1 exhibits the identical heating rate for lateral and radial irradiations for any shapes of lossy samples. Regime 2 depicts that a larger heating rate with larger temperature non-uniformity can occur for square and triangular-Type 1 lossy sample during lateral irradiation. Regime 3 depicts that the penetration of heat at the core is larger for triangular samples compared to circle or square samples for lateral or radial irradiation. Regime 4 depicts that the penetration of heat is still larger for triangular samples compared to circular or square samples. Regimes 3 and 4 depict the occurrence of multiple heating fronts in triangular samples. In general, current analysis recommends the triangular samples which is also associated with larger values of temperature variation within samples.

Originality/value

GFEM with generalized mesh generation for all geometries has been implemented. The dielectric samples of any shape are surrounded by the circular shaped air medium. The unified mesh generation within the sample connected with circular air medium has been demonstrated. The algorithm also demonstrates the implementation of various complex boundary conditions in residuals. The numerical results compare the heating patterns for all geometries involving identical areas. The thermal characteristics are shown with a few generalized trends on enhanced heating or targeted heating. The circle or square or triangle (Type 1 or Type 2) can be selected based on specific heating objectives for length scales within various regimes.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 10
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 16 September 2013

M. Moshiri, M.T. Manzari, S.K. Hannani and A. Rasouli

In this paper, the flow of multiphase fluids in a one-dimensional homogeneous porous media involving the gravity effects is numerically studied using the dominant wave method. The…

150

Abstract

Purpose

In this paper, the flow of multiphase fluids in a one-dimensional homogeneous porous media involving the gravity effects is numerically studied using the dominant wave method. The paper aims to discuss these issues.

Design/methodology/approach

The numerical scheme used for solving the pressure equations, obtained for the black-oil model, is a backward Euler scheme while the hyperbolic mass conservation equations, derived for both black-oil and Buckley-Leverett models, are solved using the dominant wave method. Higher-order schemes are achieved using either variable derivatives along with the minmod limiter or a MUSCL type interface construction scheme using the Fromm's limiter. The mass conservation equations are solved using the first-order forward Euler method in time. Harten's entropy correction procedure is employed to avoid non-physical expansion shocks.

Findings

It was found that the dominant wave method can accurately solve multiphase flow equations involving gravity effects. Numerical experiments also show that both minmod and Fromm's limiters can be successfully used to construct higher-order schemes while the minmod limiter gives slightly more diffuse solutions.

Research limitations/implications

The flow models considered here include two- and three-phase Buckley-Leverett and the black-oil models and the capillary effects are neglected.

Practical implications

The proposed scheme can be efficiently used for solving problems involving non-convex flux functions especially those experienced during gravity drainage process in hydrocarbon reservoirs.

Originality/value

To the best of authors knowledge, this is the first time that the dominant wave method has been used to tackle multiphase flow problems involving gravity effect.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

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