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Article
Publication date: 13 June 2019

P. Utkin

This paper aims to clarify some aspects of the application of the Godunov method for the Baer–Nunziato equations solution on the example of the problem of shock wave …

Abstract

Purpose

This paper aims to clarify some aspects of the application of the Godunov method for the Baer–Nunziato equations solution on the example of the problem of shock wave – dense particles cloud interaction.

Design/methodology/approach

The statement of the problem corresponds to the natural experiment. Mathematical model is based on the Baer–Nunziato system of equations with algebraic right-hand side source terms that takes into account the interphase friction force. Two numerical approaches are used: Harten-Lax-van Leer method and Godunov method.

Findings

For the robust simulation using Godunov method, the application of the pressure relaxation procedure is proposed. The comparative analysis of the simulation results using two methods is carried out. The Godunov method provides significantly smaller numerical diffusion of the solid phase volume fraction in the cloud that leads to the much better agreement of the pressure curves on transducers and the dynamics of the cloud motion with the experimental data.

Originality/value

Godunov method for the Baer–Nunziato equations is applied for the simulation of the natural experiment on the shock wave particles cloud interaction. Up to now, the examples of the application of the Godunov method for the Baer–Nunziato equations to the investigation of the practical problems have been limited by the works of the authors of the method and the field of detonation in the heterogeneous explosives. For the robust simulations in the presence of interphase boundaries, it is proposed to use the Godunov method together with the pressure relaxation procedure.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 27 March 2009

A. Karimi, H. Naderan, M.T. Manzarii and S.K. Hannani

This paper aims to perform a comparative study between capabilities of two numerical schemes from two main branches of numerical methods for solving hyperbolic…

Abstract

Purpose

This paper aims to perform a comparative study between capabilities of two numerical schemes from two main branches of numerical methods for solving hyperbolic conservation equations.

Design/methodology/approach

The accuracy and performance of a newly developed high‐resolution central scheme vs a higher‐order Godunov‐based method are evaluated in the context of black‐oil reservoir simulations. Both methods are modified enabling study of applications that are not strictly hyperbolic and exhibit local linear degeneracies in their wave structure.

Findings

The numerical computations show that while both schemes produce results with virtually the same accuracy, the Godunov method reproduces slightly more accurate results at the expense of calculation of eigen‐structures.

Research limitations/implications

The paper investigates only one dimensional problems, but the idea can be easily extended to multi‐dimensional problems.

Practical implications

The paper shows the strengths and weaknesses of two practical numerical methods.

Originality/value

Such comparative study has not been published elsewhere and in particular, the performance of numerical methods on simulating hysteresis effect in hydrocarbon reservoirs has not been investigated in detail before.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 1 February 1995

S. Sivaloganathan and J.M. Stockie

The purpose of this paper is twofold. Firstly, to present a detailedaccount of the generalized Lagrangian formulation of Hui and Zhao, in whichthe stream function ζ and…

Abstract

The purpose of this paper is twofold. Firstly, to present a detailed account of the generalized Lagrangian formulation of Hui and Zhao, in which the stream function ζ and Lagrangian distance λ, are used as independent variables, and secondly to assess and compare the performance of various flux limiters in this formulation with their corresponding performance in the Eulerian formulation. The generalized Lagrangian formulation is obtained by a transformation from the cartesian co‐ordinates (x, y) to the Lagrangian co‐ordinates (λ, ζ). In this manner, the number of independent variables for steady, 3‐D flow is reduced from four to three, placing this formulation on the same footing as the Eulerian formulation even for steady flows (as opposed to the conventional Lagrangian formulation which apparently still requires four independent variables even for steady flows). The generalized Lagrangian formulation with the Godunov scheme (using flux limiters) appears to have distinct advantages over the corresponding Eulerian formulation, particularly with respect to accuracy. Furthermore, the method requires no grid generation.

Details

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

Keywords

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Article
Publication date: 18 September 2007

H. Naderan, M.T. Manzari and S.K. Hannani

The purpose of this paper is to investigate the performance of a specific class of high‐resolution central schemes in conjunction with the black oil models for hydrocarbon…

Abstract

Purpose

The purpose of this paper is to investigate the performance of a specific class of high‐resolution central schemes in conjunction with the black oil models for hydrocarbon reservoir simulation.

Design/methodology/approach

A generalized black oil model is adopted, in which the solubility of gas in both oil and water and evaporation of oil are considered, leading to a system of equations prone to degeneracy. A computer code is generated and three test cases are solved to evaluate the performance of various schemes in terms of accuracy and discontinuity handling.

Findings

It is shown that, although some of the central schemes are highly sensitive to the choice of Courant‐Friedrich‐Levy (CFL) number and produce overly diffusive results, a certain type of this class is insensitive to the CFL number and can conveniently handle degenerate equations appearing in the reservoir simulation. The obtained results are compared with those available in the literature, showing merits of this class of schemes in complex reservoir simulation models.

Research limitations/implications

This paper gives the one‐dimensional implementation of the above‐mentioned schemes. Extension to higher dimensional black oil model is currently under development by the authors.

Practical implications

The specific class of high‐resolution central schemes investigated here presents the same level of accuracy as more complicated numerical methods, yet keeping it much more simple, by avoiding Riemann solvers.

Originality/value

The high‐resolution central scheme used in this work has been newly developed and applied to simple scalar hyperbolic equations. It has been adopted for the black oil for the first time.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 17 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 6 August 2019

Chaobin Hu and Xiaobing Zhang

This paper aims to improve the reliability of numerical methods for predicting the transient heat transfers in combustion chambers heated internally by moving heat sources.

Abstract

Purpose

This paper aims to improve the reliability of numerical methods for predicting the transient heat transfers in combustion chambers heated internally by moving heat sources.

Design/methodology/approach

A two-phase fluid dynamic model was used to govern the non-uniformly distributed moving heat sources. A Riemann-problem-based numerical scheme was provided to update the fluid field and provide convective boundary conditions for the heat transfer. The heat conduction in the solids was investigated by using a thermo-mechanical coupled model to obtain a reliable expanding velocity of the heat sources. The coupling between the combustion and the heat transfer is realized based on user subroutines VDFLUX and VUAMP in the commercial software ABAQUS.

Findings

The capability of the numerical scheme in capturing discontinuities in initial conditions and source terms was validated by comparing the predicted results of commonly used verification cases with the corresponding analytical solutions. The coupled model and the numerical methods are capable of investigating heat transfer problems accompanied by extreme conditions such as transient effects, high-temperature and high-pressure working conditions.

Originality/value

The work provides a reliable numerical method to obtain boundary conditions for predicting the heat transfers in solids heated by expanding multiphase reactive flows.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 1 February 1993

A.E. KANARACHOS and I.P. VOURNAS

An optimized multigrid method (NSFLEX‐MG) for the NSFLEX‐code (Navier‐Stokes solver using characteristic flux extrapolation) of MBB (Messerschmitt Bolkow Blohm GmbH) is…

Abstract

An optimized multigrid method (NSFLEX‐MG) for the NSFLEX‐code (Navier‐Stokes solver using characteristic flux extrapolation) of MBB (Messerschmitt Bolkow Blohm GmbH) is described. The method is based on a correction scheme and implicit relaxation procedures and is applied to two‐dimensional test cases. The principal feature of the flow solver is a Godunov‐type averaging procedure based on the eigenvalues analysis of the Euler equations by means of which the inviscid fluxes are evaluated at the finite volume faces. Viscous fluxes are centrally differenced at each cell face. The performance of NSFLEX‐MG is demonstrated for a large range of Mach numbers for compressible inviscid and viscous (laminar and turbulent) flows over a RAE‐2822 airfoil and over a NACA‐0012 airfoil.

Details

Engineering Computations, vol. 10 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

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Abstract

Details

Transportation and Traffic Theory in the 21st Century
Type: Book
ISBN: 978-0-080-43926-6

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Article
Publication date: 4 October 2018

Alice de Jesus Kozakevicius, Dia Zeidan, Alex A. Schmidt and Stefan Jakobsson

The purpose of this work is to present the implementation of weighted essentially non-oscillatory (WENO) wavelet methods for solving multiphase flow problems. The…

Abstract

Purpose

The purpose of this work is to present the implementation of weighted essentially non-oscillatory (WENO) wavelet methods for solving multiphase flow problems. The particular interest is gas–liquid two-phase mixture with velocity non-equilibrium. Numerical simulations are carried out on different scenarios of one-dimensional Riemann problems for gas–liquid flows. Results are validated and qualitatively compared with solutions provided by other standard numerical methods.

Design/methodology/approach

This paper extends the framework of WENO wavelet adaptive method to a fully hyperbolic two-phase flow model in a conservative form. The grid adaptivity in each time step is provided by the application of a thresholded interpolating wavelet transform. This facilitates the construction of a small yet effective sparse point representation of the solution. The method of Lax–Friedrich flux splitting is used to resolve the spatial operator in which the flux derivatives are approximated by the WENO scheme.

Findings

Hyperbolic models of two-phase flow in conservative form are efficiently solved, as shocks and rarefaction waves are precisely captured by the chosen methodology. Substantial computational gains are obtained through the grid reduction feature while maintaining the quality of the solutions. The results indicate that WENO wavelet methods are robust and sufficient to accurately simulate gas–liquid mixtures.

Originality/value

Resolution of two-phase flows is rarely studied using WENO wavelet methods. It is the first time such a study on the relative velocity is reported in two-phase flows using such methods.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 6 June 2016

Ghislain Tchuen, Pascalin Tiam Kapen and Yves Burtschell

– The purpose of this paper is to present a new hybrid Euler flux fonction for use in a finite-volume Euler/Navier-Stokes code and adapted to compressible flow problems.

Abstract

Purpose

The purpose of this paper is to present a new hybrid Euler flux fonction for use in a finite-volume Euler/Navier-Stokes code and adapted to compressible flow problems.

Design/methodology/approach

The proposed scheme, called AUFSRR can be devised by combining the AUFS solver and the Roe solver, based on a rotated Riemann solver approach (Sun and Takayama, 2003; Ren, 2003). The upwind direction is determined by the velocity-difference vector and idea is to apply the AUFS solver in the direction normal to shocks to suppress carbuncle and the Roe solver across shear layers to avoid an excessive amount of dissipation. The resulting flux functions can be implemented in a very simple manner, in the form of the Roe solver with modified wave speeds, so that converting an existing AUFS flux code into the new fluxes is an extremely simple task.

Findings

The proposed flux functions require about 18 per cent more CPU time than the Roe flux. Accuracy, efficiency and other essential features of AUFSRR scheme are evaluated by analyzing shock propagation behaviours for both the steady and unsteady compressible flows. This is demonstrated by several test cases (1D and 2D) with standard finite-volume Euler code, by comparing results with existing methods.

Practical implications

The hybrid Euler flux function is used in a finite-volume Euler/Navier-Stokes code and adapted to compressible flow problems.

Originality/value

The AUFSRR scheme is devised by combining the AUFS solver and the Roe solver, based on a rotated Riemann solver approach.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Abstract

Details

Transportation and Traffic Theory in the 21st Century
Type: Book
ISBN: 978-0-080-43926-6

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