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Article
Publication date: 13 June 2019

Arthur Piquet, Boubakr Zebiri, Abdellah Hadjadj and Mostafa Safdari Shadloo

This paper aims to present the development of a highly parallel finite-difference computational fluid dynamics code in generalized curvilinear coordinates system. The objectives…

Abstract

Purpose

This paper aims to present the development of a highly parallel finite-difference computational fluid dynamics code in generalized curvilinear coordinates system. The objectives are to handle internal and external flows in fairly complex geometries including shock waves, compressible turbulence and heat transfer.

Design/methodology/approach

The code is equipped with high-order discretization schemes to improve the computational accuracy of the solution algorithm. Besides, a new method to deal with the geometrical singularities, so-called domain decomposition method (DDM), is implemented. The DDM consists of using two different meshes communicating with each other, where the base mesh is Cartesian and the overlapped one a hollow cylinder.

Findings

The robustness of the present implemented code is appraised through several numerical test cases including a vortex advection, supersonic compressible flow over a cylinder, Poiseuille flow, turbulent channel and pipe flows. The results obtained here are in an excellent agreement when compared to the experimental data and the previous direct numerical simulation (DNS). As for the DDM strategy, it was successful as simulation time is clearly decreased and the connection between the two subdomains does not create spurious oscillations.

Originality/value

In sum, the developed solver was capable of solving, accurately and with high-precision, two- and three-dimensional compressible flows including fairly complex geometries. It is noted that the data provided by the DNS of supersonic pipe flows are not abundant in the literature and therefore will be available online for the community.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 June 1999

Haidong Li and Weng Kong Chan

High order schemes, which are widely used in DNS and LES, received increasing attention in recent years with a number of variants being developed. However most of these schemes

Abstract

High order schemes, which are widely used in DNS and LES, received increasing attention in recent years with a number of variants being developed. However most of these schemes have difficulties in achieving high order accuracy near the boundary points. In order to solve this problem, the analytical discrete method (ADM) is proposed and presented in this paper. In addition, this method is convenient to construct the higher order WENO (weighted essentially non‐oscillatory) scheme. Application of the ADM‐WENO scheme to shock‐tube problems and compressible mixing flows has shown it is robust and accurate in both shock‐capturing and complex flow structures detection.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 9 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 3 August 2015

Shooka Karimpour Ghannadi and Vincent H. Chu

The purpose of this paper is to evaluate the performance of a numerical method for the solution to shallow-water equations on a staggered grid, in simulations for shear…

Abstract

Purpose

The purpose of this paper is to evaluate the performance of a numerical method for the solution to shallow-water equations on a staggered grid, in simulations for shear instabilities at two convective Froude numbers.

Design/methodology/approach

The simulations start from a small perturbation to a base flow with a hyperbolic-tangent velocity profile. The subsequent development of the shear instabilities is studied from the simulations using a number of flux-limiting schemes, including the second-order MINMOD, the third-order ULTRA-QUICK and the fifth-order WENO schemes for the spatial interpolation of the nonlinear fluxes. The fourth-order Runge-Kutta method advances the simulation in time.

Findings

The simulations determine two parameters: the fractional growth rate of the linear instabilities; and the vorticity thickness of the first nonlinear peak. Grid refinement using 32, 64, 128, 256 and 512 nodes over one wave length determines the exact values by extrapolation and the computational error for the parameters. It also determines the overall order of convergence for each of the flux-limiting schemes used in the numerical simulations.

Originality/value

The four-digit accuracy of the numerical simulations presented in this paper are comparable to analytical solutions. The development of this reliable numerical simulation method has paved the way for further study of the instabilities in shear flows that radiate waves.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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…

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

Keywords

Article
Publication date: 4 December 2017

Gaohua Li, Xiang Fu and Fuxin Wang

This paper aims to improve the computational efficiency and to achieve high-order accuracy for the computation of helicopter rotor unsteady flows in forward flight during the…

199

Abstract

Purpose

This paper aims to improve the computational efficiency and to achieve high-order accuracy for the computation of helicopter rotor unsteady flows in forward flight during the industrial preliminary design stage.

Design/methodology/approach

The integral arbitrary Lagrangian–Eulerian form of unsteady compressible Navier–Stokes equations with low Mach number preconditioned pseudo time terms based on non-inertial frame of reference undergoing rotating and translating was derived and discretized in the framework of multi-block structured finite volume grid using three types of spatial reconstruction schemes, i.e. the third-order accurate monotonic upwind scheme for conservation laws, the fifth-order accurate weighted essentially non-oscillatory and the fifth-order accurate weighted compact nonlinear schemes.

Findings

The results show that the present non-inertial computational method can obtain comparable results with other methods, such as the dynamic overset method, and make sure that the higher-order spatial schemes can significantly improve the tip vortex resolution.

Originality/value

The computational grid used by the present method remained static during the whole unsteady computation process, with only local deformations induced by blade cyclic pitch and other operating motions, which greatly reduced the complexity of grid motion and enhanced the efficiency and robustness.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 May 1992

B.P. LEONARD and SIMIN MOKHTARI

In 1982, Smith and Hutton published comparative results of several different convection‐diffusion schemes applied to a specially devised test problem involving…

Abstract

In 1982, Smith and Hutton published comparative results of several different convection‐diffusion schemes applied to a specially devised test problem involving near‐discontinuities and strong streamline curvature. First‐order methods showed significant artificial diffusion, whereas higher‐order methods gave less smearing but had a tendency to overshoot and oscillate. Perhaps because unphysical oscillations are more obvious than unphysical smearing, the intervening period has seen a rise in popularity of low‐order artificially diffusive schemes, especially in the numerical heat‐transfer industry. This paper presents an alternative strategy of using non‐artificially diffusive higher‐order methods, while maintaining strictly monotonic transitions through the use of simple flux‐limiter constraints. Limited third‐order upwinding is usually found to be the most cost‐effective basic convection scheme. Tighter resolution of discontinuities can be obtained at little additional cost by using automatic adaptive stencil expansion to higher order in local regions, as needed.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 2 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 June 2000

A. Savini

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community…

1128

Abstract

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 19 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 29 September 2022

Fei Wang and Tat Leung Chan

The purpose of this study is to present a newly proposed and developed sorting algorithm-based merging weighted fraction Monte Carlo (SAMWFMC) method for solving the population…

Abstract

Purpose

The purpose of this study is to present a newly proposed and developed sorting algorithm-based merging weighted fraction Monte Carlo (SAMWFMC) method for solving the population balance equation for the weighted fraction coagulation process in aerosol dynamics with high computational accuracy and efficiency.

Design/methodology/approach

In the new SAMWFMC method, the jump Markov process is constructed as the weighted fraction Monte Carlo (WFMC) method (Jiang and Chan, 2021) with a fraction function. Both adjustable and constant fraction functions are used to validate the computational accuracy and efficiency. A new merging scheme is also proposed to ensure a constant-number and constant-volume scheme.

Findings

The new SAMWFMC method is fully validated by comparing with existing analytical solutions for six benchmark test cases. The numerical results obtained from the SAMWFMC method with both adjustable and constant fraction functions show excellent agreement with the analytical solutions and low stochastic errors. Compared with the WFMC method (Jiang and Chan, 2021), the SAMWFMC method can significantly reduce the stochastic error in the total particle number concentration without increasing the stochastic errors in high-order moments of the particle size distribution at only slightly higher computational cost.

Originality/value

The WFMC method (Jiang and Chan, 2021) has a stringent restriction on the fraction functions, making few fraction functions applicable to the WFMC method except for several specifically selected adjustable fraction functions, while the stochastic error in the total particle number concentration is considerably large. The newly developed SAMWFMC method shows significant improvement and advantage in dealing with weighted fraction coagulation process in aerosol dynamics and provides an excellent potential to deal with various fraction functions with higher computational accuracy and efficiency.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 14 October 2019

Nagesh Babu Balam and Akhilesh Gupta

Modelling accurately the transient behaviour of natural convection flow in enclosures been a challenging task because of a variety of numerical errors which have limited achieving…

Abstract

Purpose

Modelling accurately the transient behaviour of natural convection flow in enclosures been a challenging task because of a variety of numerical errors which have limited achieving the higher order temporal accuracy. A fourth-order accurate finite difference method in both space and time is proposed to overcome these numerical errors and accurately model the transient behaviour of natural convection flow in enclosures using vorticity–streamfunction formulation.

Design/methodology/approach

Fourth-order wide stencil formula with appropriate one-sided difference extrapolation technique near the boundary is used for spatial discretisation, and classical fourth-order Runge–Kutta scheme is applied for transient term discretisation. The proposed method is applied on two transient case studies, i.e. convection–diffusion of a Gaussian Pulse and Taylor Vortex flow having analytical solution.

Findings

Error magnitude comparison and rate of convergence analysis of the proposed method with these analytical solutions establish fourth-order accuracy and prove the ability of the proposed method to truly capture the transient behaviour of incompressible flow. Also, to test the transient natural convection flow behaviour, the algorithm is tested on differentially heated square cavity at high Rayleigh number in the range of 103-108, followed by studying the transient periodic behaviour in a differentially heated vertical cavity of aspect ratio 8:1. An excellent comparison is obtained with standard benchmark results.

Research limitations/implications

The developed method is applied on 2D enclosures; however, the present methodology can be extended to 3D enclosures using velocity–vorticity formulations which shall be explored in future.

Originality/value

The proposed methodology to achieve fourth-order accurate transient simulation of natural convection flows is novel, to the best of the authors’ knowledge. Stable fourth-order vorticity boundary conditions are derived for boundary and external boundary regions. The selected case studies for comparison demonstrate not only the fourth-order accuracy but also the considerable reduction in error magnitude by increasing the temporal accuracy. Also, this study provides novel benchmark results at five different locations within the differentially heated vertical cavity of aspect ratio 8:1 for future comparison studies.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 March 1997

H. Daiguji, X. Yuan and S. Yamamoto

Proposes a measure to stabilize the fourth(fifth)‐order high resolution schemes for the compressible Navier‐Stokes equations. Solves the N‐S equations of the volume fluxes and the…

Abstract

Proposes a measure to stabilize the fourth(fifth)‐order high resolution schemes for the compressible Navier‐Stokes equations. Solves the N‐S equations of the volume fluxes and the low‐Reynolds number k‐ε turbulence model in general curvilinear co‐ordinates by the delta‐form implicit finite difference methods. Notes that, in order to simulate the flow containing weak discontinuities accurately, it is very effective to use some higher‐order TVD upstream‐difference schemes in the right‐hand side of the equations of these methods; however, the higher‐order correction terms of such schemes in general amplify the numerical disturbances. Therefore, restricts these terms here by operating the minmod functions to the curvatures so as to suppress the occurrence of new inflection points. Computes an unsteady transonic turbine cascade flow where vortex streets occur from the trailing edge of blades and interact with shock waves. Finds that the stabilization measure improves not only the computational results but also the convergency for such a complicated flow problem.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 7 no. 2/3
Type: Research Article
ISSN: 0961-5539

Keywords

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