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Article
Publication date: 4 January 2021

Carlos Enrique Torres-Aguilar, Pedro Moreno-Bernal, Jesús Xamán, Ivett Zavala Guillen and Irving Osiris Hernández-López

This paper aims to present an evolutionary algorithm (EA) to accelerate the convergence for the radiative transfer equation (RTE) numerical solution using high-order and…

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Abstract

Purpose

This paper aims to present an evolutionary algorithm (EA) to accelerate the convergence for the radiative transfer equation (RTE) numerical solution using high-order and high-resolution schemes by the relaxation coefficients optimization.

Design methodology/approach

The objective function minimizes the residual value difference between iterations in each control volume until its difference is lower than the convergence criterion. The EA approach is evaluated in two configurations, a two-dimensional cavity with scattering media and absorbing media.

Findings

Experimental results show the capacity to obtain the numerical solution for both cases on all interpolation schemes tested by the EA approach. The EA approach reduces CPU time for the RTE numerical solution using SUPERBEE, SWEBY and MUSCL schemes until 97% and 135% in scattering and absorbing media cases, respectively. The relaxation coefficients optimized every two numerical solution iterations achieve a significant reduction of the CPU time compared to the deferred correction procedure with fixed relaxation coefficients.

Originality/value

The proposed EA approach for the RTE numerical solution effectively reduces the CPU time compared to the DC procedure with fixed relaxation coefficients.

Details

Engineering Computations, vol. 38 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 27 March 2008

P.J. Coelho and D. Aelenei

This paper sets out to implement bounded high‐order (HO) resolution schemes in a hybrid finite volume/finite element method for the solution of the radiative transfer equation.

Abstract

Purpose

This paper sets out to implement bounded high‐order (HO) resolution schemes in a hybrid finite volume/finite element method for the solution of the radiative transfer equation.

Design/methodology/approach

The hybrid finite volume/finite element method had formerly been developed using the step scheme, which is only first‐order accurate, for the spatial discretization. Here, several bounded HO resolution schemes, namely the MINMOD, CLAM, MUSCL and SMART schemes, formulated using the normalized variable diagram, were implemented using the deferred correction procedure.

Findings

The results obtained reveal an interaction between spatial and angular discretization errors, and show that the HO resolution schemes yield improved accuracy over the step scheme if the angular discretization error is small.

Research limitations/implications

Although the HO resolution schemes reduce the spatial discretization error, they do not influence the angular discretization error. Therefore, the global error is only reduced if the angular discretization error is also small.

Practical implications

The use of HO resolution schemes is only effective if the angular refinement yields low‐angular discretization errors. Moreover, spatial and angular refinement should be carried out simultaneously.

Originality/value

The paper extends a methodology formerly developed in computational fluid dynamics, and aimed at the improvement of the solution accuracy, to the hybrid finite volume/finite element method for the solution of the radiative transfer equation.

Details

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

Keywords

Article
Publication date: 29 January 2020

Carlos Enrique Torres-Aguilar, Jesús Xamán, Pedro Moreno-Bernal, Iván Hernández-Pérez, Ivett Zavala-Guillén and Irving Osiris Hernández-López

The purpose of this study is to propose a novel relaxation modified factor to accelerate the numerical solution of the radiative transfer equation (RTE) with several…

Abstract

Purpose

The purpose of this study is to propose a novel relaxation modified factor to accelerate the numerical solution of the radiative transfer equation (RTE) with several high-resolution total variation diminishing schemes. The methodology proposed is denoted as the X-factor method.

Design/methodology/approach

The X-factor method was compared with the technique deferred-correction (DC) for the calculations of a two-dimensional cavity with absorting-emiting-scatteting gray media using the discrete ordinates method. Four parameters were considered to evaluate: the absorption coefficient, the emissivity of boundary surface, the scattering albedo and under-relaxation factor.

Findings

The results showed the central processing unit (CPU) time of X-factor method was lower than DC. The reductions of CPU time with the X-factor method were observed from 0.6 to 75.4%.

Originality/value

The superiority of the X-factor method over DC was showed with the reduction of CPU time of the numerical solution of RTE for evaluated cases.

Details

Engineering Computations, vol. 37 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 September 2001

H. Lai and Y.Y. Yan

In this paper the effects of choosing dependent variables and cell face velocities on convergence of the SIMPLE algorithm are discussed. Using different velocity components as…

Abstract

In this paper the effects of choosing dependent variables and cell face velocities on convergence of the SIMPLE algorithm are discussed. Using different velocity components as either dependent variables or cell‐face velocities, both convergent rate and calculation accuracy of the algorithm are compared and studied. A novel method, named “cross‐correction”, is developed to improve the convergence of the algorithm of using non‐orthogonal grids. Cases with benchmark and analytical solutions are used for numerical experiments and validation. The results show that, although different velocity components are employed as either dependent variables or cell face velocities, there is no obvious difference in both the convergent rates and numerical solutions. Moreover, the “cross‐correction” method is validated by computations with several first‐order and high‐order convection schemes; and the generality of convergence improvement achieved by the method is shown in the paper.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 11 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 2 May 2017

Junjie Liang, Wan Luo, Zhigao Huang, Huamin Zhou, Yun Zhang, Yi Zhang and Yang Fu

The purpose of this paper is to develop a finite volume approach for the simulation of three-dimensional two-phase (polymer melt and air) flow in plastic injection molding which…

Abstract

Purpose

The purpose of this paper is to develop a finite volume approach for the simulation of three-dimensional two-phase (polymer melt and air) flow in plastic injection molding which is capable of robustly handling the mesh non-orthogonality and the discontinuities in fluid properties.

Design/methodology/approach

The presented numerical method is based on a cell-centered unstructured finite volume discretization with a volume-of-fluid technique for interface capturing. The over-relaxed approach is adopted to handle the non-orthogonality involved in the discretization of the face normal derivatives to enhance the robustness of the solutions on non-orthogonal meshes. A novel interpolation method for the face pressure is derived to address the numerical stability issues resulting from the density and viscosity discontinuities at the melt–air interface. Various test cases are conducted to evaluate the proposed method.

Findings

The presented method was shown to be satisfactorily accurate by comparing simulations with analytical and experimental results. Besides, the effectiveness of the proposed face pressure interpolation method was verified by numerical examples of a two-phase flow problem with various density and viscosity ratios. The proposed method was also successfully applied to the simulation of a practical filling case.

Originality/value

The proposed finite volume approach is more tolerant of non-orthogonal meshes and the discontinuities in fluid properties for two-phase flow simulation; therefore, it is valuable for engineers in engineering computations.

Details

Engineering Computations, vol. 34 no. 3
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 January 2012

Shumei Lou, Guoqun Zhao and Rui Wang

The paper aims to use the finite volume method widely used in computational fluid dynamics to avoid the serious remeshing and mesh distortion during aluminium profile extrusion…

Abstract

Purpose

The paper aims to use the finite volume method widely used in computational fluid dynamics to avoid the serious remeshing and mesh distortion during aluminium profile extrusion processes simulation when using the finite element method. Block-structured grids are used to fit the complex domain of the extrusion. A finite volume method (FVM) model for aluminium extrusion numerical simulation using non-orthogonal structured grids was established.

Design/methodology/approach

The influences of the elements ' nonorthogonality on the governing equations discretization of the metal flow in aluminium extrusion processes were fully considered to ensure the simulation accuracy. Volume-of-fluid (VOF) scheme was used to catch the free surface of the unsteady flow. Rigid slip boundary condition was applied on non-orthogonal grids.

Findings

This paper involved a simulation of a typical aluminium extrusion process by the FVM scheme. By comparing the simulation by the FVM model established in this paper with the ones simulated by the finite element method (FEM) software Deform-3D and the corresponding experiments, the correctness and efficiency of the FVM model for aluminium alloy profile extrusion processes in this paper was proved.

Originality/value

This paper uses the FVM widely used in CFD to calculate the aluminium profile extrusion processes avoiding the remeshing and mesh distortion during aluminium profile extrusion processes simulation when using the finite element method. Block-structured grids with the advantage of simple data structure, small storage and high numerical efficiency are used to fit the complex domain of the extrusion.

Details

Engineering Computations: International Journal for Computer-Aided Engineering and Software, vol. 29 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 19 April 2011

Huanxin Lai, Gailan Xing, Shantong Tu and Ling Zhao

The purpose of this paper is to present a pressure‐correction procedure for incompressible flows using unstructured meshes. A method of implementing high‐order spatial schemes on…

Abstract

Purpose

The purpose of this paper is to present a pressure‐correction procedure for incompressible flows using unstructured meshes. A method of implementing high‐order spatial schemes on unstructured grids was introduced.

Design/methodology/approach

The procedure used a collocated cell‐centered unstructured grid arrangement. In order to improve the accuracy of calculation, the widely used high‐order schemes for convection, developed for structured grids and in the form of either the normalized variable and space formulation (NVSF) or the total variation diminishing (TVD) flux limiters (FL), were introduced and implemented onto the unstructured grids. This implementation was carried out by constructing a local coordinate and introducing a virtual upstream node.

Findings

The procedure was validated by calculating the lid‐driven cavity flows which had benchmark numerical solutions. For comparison, these flows were also computed by a commercial package, the FLUENT. The results obtained by the present procedure agreed well with the benchmark solution although very coarse grids were used. For the FLUENT, however, worse agreements with the benchmark solutions were obtained although the grids used for computation were the same. These demonstrated the robustness of the presented numerical procedure.

Originality/value

With the present method, high‐order schemes in either NVSF or TVD FL forms for structured grids can be easily implemented onto unstructured grids. This provides more choices of high‐order schemes for calculating complex flows.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 June 1993

A. KANIEL, M. MOND and G. BEN‐DOR

Isotropic artificial dissipation is added to the Navier‐Stokes equations along with a correction term which cancels the artificial dissipation term in the limit when the mesh size…

Abstract

Isotropic artificial dissipation is added to the Navier‐Stokes equations along with a correction term which cancels the artificial dissipation term in the limit when the mesh size is zero. For a finite mesh size, the correction term replaces the artificial viscosity terms with hyperviscosity terms, i.e., with an artificial dissipation which depends on the fourth derivatives of the velocity. Hyperviscosity more effectively suppresses the higher wave number modes and has a smaller effect on the inertial modes of the flow field than does artificial viscosity. This scheme is implemented using the finite element method and therefore the required amount of dissipation is determined by analysing the discretization on a finite element. The scheme is used to simulate the flow in a driven cavity and over a backward facing step and the results are compared to existing results for these cases.

Details

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

Keywords

Article
Publication date: 7 November 2016

Ying Chen, Chuanjing Lu, Xin Chen, Jie Li and Zhaoxin Gong

Ultrahigh-speed projectile running in water with the velocity close to the speed of sound usually causes large supercavity. The computation of such transonic cavitating flows is…

Abstract

Purpose

Ultrahigh-speed projectile running in water with the velocity close to the speed of sound usually causes large supercavity. The computation of such transonic cavitating flows is usually difficult, thus high-speed model reflecting the compressibility of both the liquid and the vapor phases should be introduced to model such flow. The purpose of this paper is to achieve a model within an in-house developed solver to simulate the ultrahigh-speed subsonic supercavitating flows.

Design/methodology/approach

An improved TAIT equation adjusted by local temperature is adopted as the equation of state (EOS) for the liquid phase, and the Peng-Robinson EOS is used for the vapor phase. An all-speed variable coupling algorithm is used to unify the computations and regulate the convergence at arbitrary Mach number. The ultrahigh-speed (Ma=0.7) supercavitating flows around circular disk are investigated in contrast with the case of low subsonic (Ma=0.007) flow.

Findings

The characteristic physical variables are reasonably predicted, and the cavity profiles are compared to be close to the experimental empirical formula. An important conclusion in the compressible cavitating flow theory is verified by the numerical result that, at any specific cavitation number the cavity’s size and the drag coefficient both increase along with the rise of Mach number. On the contrary, it is found as well that the cavity’s slenderness ratio decreases when Mach number goes up. It indicates that the compressibility has different influences on the length and the radius of the supercavity.

Originality/value

A high-speed model reflecting the compressibility of both the liquid and the vapor phases was suggested to model the ultrahigh-speed supercavitating flows around underwater projectiles.

Details

Engineering Computations, vol. 33 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 27 June 2008

Xiaobing Chen, Peng Yu, S.H. Winoto and Hong‐Tong Low

The purpose of this paper is to report on the flow past a porous square cylinder, implementing the stress jump treatments for the porous‐fluid interface.

1105

Abstract

Purpose

The purpose of this paper is to report on the flow past a porous square cylinder, implementing the stress jump treatments for the porous‐fluid interface.

Design/methodology/approach

The numerical method was developed for flows involving an interface between a homogenous fluid and a porous medium. It is based on the finite volume method with body‐fitted and multi‐block grids. The Brinkman‐Forcheimmer extended model was used to govern the flow in the porous medium region. At its interface, a shear stress jump that includes the inertial effect was imposed, together with a continuity of normal stress.

Findings

The present model is validated by comparing with those for the flow around a solid circular cylinder. Results for flow around porous square cylinder are presented with flow configurations for different Darcy number, 10−2 to 10−5, porosity from 0.4 to 0.8, and Reynolds number 20 to 250. The flow develops from steady to unsteady periodic vortex shedding state. It was found that the stress jump interface condition can cause flow instability. The first coefficient β has a more noticeable effect whereas the second coefficient β1 has very small effect, even for Re=200. The effects of the porosity, Darcy number, and Reynolds number on lift and drag coefficients, and the length of circulation zone or shedding period are studied.

Originality/value

The present study implements the numerical method based on finite volume method with a collocated variable arrangement to treat the stress jump condition.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 18 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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