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Article

Gang Peng, Zhiming Gao, Wenjing Yan and Xinlong Feng

This paper aims to consider numerical simulation for radionuclide transport calculations in geological radioactive waste repository.

Abstract

Purpose

This paper aims to consider numerical simulation for radionuclide transport calculations in geological radioactive waste repository.

Design/methodology/approach

The nonlinear two-point flux approximation is used to discretize the diffusion flux and has a fixed stencil. The cell-vertex unknowns are applied to define the auxiliary unknowns and can be interpolated by the cell-centered unknowns. The approximation of convection flux is based on the second-order upwind method with a slope limiter.

Findings

Numerical results illustrate that the positivity-preserving is satisfied in solving this convection-diffusion system and has a second-order convergence rate on the distorted meshes.

Originality/value

A new positivity-preserving nonlinear finite volume scheme is proposed to simulate the far-field model used in the geological radioactive waste repository. Numerical results illustrate that the positivity-preserving is satisfied in solving this convection-diffusion system and has a second-order convergence rate on the distorted meshes.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Perumandla Karunakar and Snehashish Chakraverty

The purpose of this paper is to find the solution of classical nonlinear shallow-water wave (SWW) equations in particular to the tsunami wave propagation in crisp and…

Abstract

Purpose

The purpose of this paper is to find the solution of classical nonlinear shallow-water wave (SWW) equations in particular to the tsunami wave propagation in crisp and interval environment.

Design/methodology/approach

Homotopy perturbation method (HPM) has been used for handling crisp and uncertain differential equations governing SWW equations.

Findings

The wave height and depth-averaged velocity of a tsunami wave in crisp and interval cases have been obtained.

Originality/value

Present results by HPM are compared with the existing solution (in crisp case), and they are found to be in good agreement. Also, the residual error of the solutions is found for the convergence conformation and reliability of the present results.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Di Yang and Zhiming Gao

A finite volume scheme for diffusion equations on non-rectangular meshes is proposed in [Deyuan Li, Hongshou Shui, Minjun Tang, J. Numer. Meth. Comput. Appl.…

Abstract

Purpose

A finite volume scheme for diffusion equations on non-rectangular meshes is proposed in [Deyuan Li, Hongshou Shui, Minjun Tang, J. Numer. Meth. Comput. Appl., 1(4)(1980)217–224 (in Chinese)], which is the so-called nine point scheme on structured quadrilateral meshes. The scheme has both cell-centered unknowns and vertex unknowns which are usually expressed as a linear weighted interpolation of the cell-centered unknowns. The critical factor to obtain the optimal accuracy for the scheme is the reconstruction of vertex unknowns. However, when the mesh deformation is severe or the diffusion tensor is discontinuous, the accuracy of the scheme is not satisfactory, and the author hope to improve this scheme.

Design/methodology/approach

The authors propose an explicit weighted vertex interpolation algorithm which allows arbitrary diffusion tensors and does not depend on the location of discontinuity. Both the derivation of the scheme and that of vertex reconstruction algorithm satisfy the linearity preserving criterion which requires that a discretization scheme should be exact on linear solutions. The vertex interpolation algorithm can be easily extended to 3 D case.

Findings

Numerical results show that it maintain optimal convergence rates for the solution and flux on 2 D and 3 D meshes in case that the diffusion tensor is taken to be anisotropic, at times heterogeneous, and/or discontinuous.

Originality/value

This paper proposes a linearity preserving and explicit weighted vertex interpolation algorithm for cell-centered finite volume approximations of diffusion equations on general grids. The proposed finite volume scheme with the new interpolation algorithm allows arbitrary continuous or discontinuous diffusion tensors; the final scheme is applicable to arbitrary polygonal grids, which may have concave cells or degenerate ones with hanging nodes. The final scheme has second-order convergence rate for the approximate solution and higher than first-order accuracy for the flux on 2 D and 3 D meshes. The explicit weighted interpolation algorithm is easy to implement in three dimensions in case that the diffusion tensor is continuous or discontinuous.

Details

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

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Article

J. Vuillon and D. Zeitoun

High‐power chemical lasers operating in high repetitive rate show a decrease of the output energy laser beam. In such lasers, the characteristic time which depends on the…

Abstract

High‐power chemical lasers operating in high repetitive rate show a decrease of the output energy laser beam. In such lasers, the characteristic time which depends on the laser output is short in comparison with those related to the flow. Consequently, shock waves, acoustic waves and thermal perturbations, induced by the strong electric energy deposition and remaining in the laser cavity between two pulses, may explain the decrease of output energy of the laser beam. For a better understanding of the flowfields, a numerical approach is carried out using flux corrected transport algorithms (FCT methods) associated with a Riemann solver on the computational domain boundaries. Under two‐dimensional assumptions, the inviscid flow in the convergent‐divergent laser cavity is computed to describe the creation and propagation of the wave system and the hot gas column in both single and multidischarge operating modes. Distortions of the contact surfaces are put into evidence through the study of flowfield instabilities. Finally, the limitations of the two‐dimensional modelization become apparent. The numerical resolution is extended to a 3D case in order to take into account the optical direction. This allows to study the influence of shock waves travelling between optics and being generated by a side effect developing at the electrodes. These waves have an effect of long duration on the flowfield and lead to a high residual perturbation level.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 7 no. 1
Type: Research Article
ISSN: 0961-5539

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Article

B.P. Leonard, A.P. Lock and M.K. Macvean

The NIRVANA project is concerned with the development of anonoscillatory, integrally reconstructed,volume‐averaged numerical advectionscheme. The conservative, flux‐based…

Abstract

The NIRVANA project is concerned with the development of a nonoscillatory, integrally reconstructed, volume‐averaged numerical advection scheme. The conservative, flux‐based finite‐volume algorithm is built on an explicit, single‐step, forward‐in‐time update of the cell‐average variable, without restrictions on the size of the time‐step. There are similarities with semi‐Lagrangian schemes; a major difference is the introduction of a discrete integral variable, guaranteeing conservation. The crucial step is the interpolation of this variable, which is used in the calculation of the fluxes; the (analytic) derivative of the interpolant then gives sub‐cell behaviour of the advected variable. In this paper, basic principles are described, using the simplest possible conditions: pure one‐dimensional advection at constant velocity on a uniform grid. Piecewise Nth‐degree polynomial interpolation of the discrete integral variable leads to an Nth‐order advection scheme, in both space and time. Nonoscillatory results correspond to convexity preservation in the integrated variable, leading naturally to a large‐Δt generalisation of the universal limited. More restrictive TVD constraints are also extended to large Δt. Automatic compressive enhancement of step‐like profiles can be achieved without exciting “stair‐casing”. One‐dimensional simulations are shown for a number of different interpolations. In particular, convexity‐limited cubic‐spline and higher‐order polynomial schemes give very sharp, nonoscillatory results at any Courant number, without clipping of extrema. Some practical generalisations are briefly discussed.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 5 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Nikhil Kalkote, Ashwani Assam and Vinayak Eswaran

The purpose of this study is to present and demonstrate a numerical method for solving chemically reacting flows. These are important for energy conversion devices, which…

Abstract

Purpose

The purpose of this study is to present and demonstrate a numerical method for solving chemically reacting flows. These are important for energy conversion devices, which rely on chemical reactions as their operational mechanism, with heat generated from the combustion of the fuel, often gases, being converted to work.

Design/methodology/approach

The numerical study of such flows requires the set of Navier-Stokes equations to be extended to include multiple species and the chemical reactions between them. The numerical method implemented in this study also accounts for changes in the material properties because of temperature variations and the process to handle steep spatial fronts and stiff source terms without incurring any numerical instabilities. An all-speed numerical framework is used through simple low-dissipation advection upwind splitting (SLAU) convective scheme, and it has been extended in a multi-component species framework on the in-house density-based flow solver. The capability of solving turbulent combustion is also implemented using the Eddy Dissipation Concept (EDC) framework and the recent k-kl turbulence model.

Findings

The numerical implementation has been demonstrated for several stiff problems in laminar and turbulent combustion. The laminar combustion results are compared from the corresponding results from the Cantera library, and the turbulent combustion computations are found to be consistent with the experimental results.

Originality/value

This paper has extended the single gas density-based framework to handle multi-component gaseous mixtures. This paper has demonstrated the capability of the numerical framework for solving non-reacting/reacting laminar and turbulent flow problems. The all-speed SLAU convective scheme has been extended in the multi-component species framework, and the turbulent model k-kl is used for turbulent combustion, which has not been done previously. While the former method provides the capability of solving for low-speed flows using the density-based method, the later is a length-scale-based method that includes scale-adaptive simulation characteristics in the turbulence modeling. The SLAU scheme has proven to work well for unsteady flows while the k-kL model works well in non-stationary turbulent flows. As both these flow features are commonly found in industrially important reacting flows, the convection scheme and the turbulence model together will enhance the numerical predictions of such flows.

Details

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

Keywords

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Article

Mehdi Dehghan, Mostafa Abbaszadeh, Amirreza Khodadadian and Clemens Heitzinger

The current paper aims to develop a reduced order discontinuous Galerkin method for solving the generalized Swift–Hohenberg equation with application in biological science…

Abstract

Purpose

The current paper aims to develop a reduced order discontinuous Galerkin method for solving the generalized Swift–Hohenberg equation with application in biological science and mechanical engineering. The generalized Swift–Hohenberg equation is a fourth-order PDE; thus, this paper uses the local discontinuous Galerkin (LDG) method for it.

Design/methodology/approach

At first, the spatial direction has been discretized by the LDG technique, as this process results in a nonlinear system of equations based on the time variable. Thus, to achieve more accurate outcomes, this paper uses an exponential time differencing scheme for solving the obtained system of ordinary differential equations. Finally, to decrease the used CPU time, this study combines the proper orthogonal decomposition approach with the LDG method and obtains a reduced order LDG method. The circular and rectangular computational domains have been selected to solve the generalized Swift–Hohenberg equation. Furthermore, the energy stability for the semi-discrete LDG scheme has been discussed.

Findings

The results show that the new numerical procedure has not only suitable and acceptable accuracy but also less computational cost compared to the local DG without the proper orthogonal decomposition (POD) approach.

Originality/value

The local DG technique is an efficient numerical procedure for solving models in the fluid flow. The current paper combines the POD approach and the local LDG technique to solve the generalized Swift–Hohenberg equation with application in the fluid mechanics. In the new technique, the computational cost and the used CPU time of the local DG have been reduced.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Mehdi Dehghan and Vahid Mohammadi

This study aims to apply a numerical meshless method, namely, the boundary knot method (BKM) combined with the meshless analog equation method (MAEM) in space and use a…

Abstract

Purpose

This study aims to apply a numerical meshless method, namely, the boundary knot method (BKM) combined with the meshless analog equation method (MAEM) in space and use a semi-implicit scheme in time for finding a new numerical solution of the advection–reaction–diffusion and reaction–diffusion systems in two-dimensional spaces, which arise in biology.

Design/methodology/approach

First, the BKM is applied to approximate the spatial variables of the studied mathematical models. Then, this study derives fully discrete scheme of the studied models using a semi-implicit scheme based on Crank–Nicolson idea, which gives a linear system of algebraic equations with a non-square matrix per time step that is solved by the singular value decomposition. The proposed approach approximates the solution of a given partial differential equation using particular and homogeneous solutions and without considering the fundamental solutions of the proposed equations.

Findings

This study reports some numerical simulations for showing the ability of the presented technique in solving the studied mathematical models arising in biology. The obtained results by the developed numerical scheme are in good agreement with the results reported in the literature. Besides, a simulation of the proposed model is done on buttery shape domain in two-dimensional space.

Originality/value

This study develops the BKM combined with MAEM for solving the coupled systems of (advection) reaction–diffusion equations in two-dimensional spaces. Besides, it does not need the fundamental solution of the mathematical models studied here, which omits any difficulties.

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Article

Prasad G. and Bruce Ralphin Rose J.

The purpose of this paper is to analyse an actual representation of ice accretions, which are important during the certification process.

Abstract

Purpose

The purpose of this paper is to analyse an actual representation of ice accretions, which are important during the certification process.

Design/methodology/approach

Ice accretion experiments are conducted in a low-speed subsonic wind tunnel testing facility to evaluate the influence of various ice shapes around the airfoil sections. Ice accumulation changes the shapes of local airfoil sections and thereby affects the aerodynamic performance characteristics of the considered NACA 23012 profile. The ice profiles are impregnated using balsa wood with glace, horn and mixed ice accretion cases for the detailed experimental investigation.

Findings

Computational fluid dynamics analysis is done to compute the influence of different ice shapes on the aerodynamic coefficients (Cl and Cd) while ice accretion occurs at the leading edge of the airfoil sections. It is observed that the Cl and Cd modified immediately more than 40% as compared to the clean wing configuration. In the same fashion, the skin friction coefficient also abruptly changes for different ice shapes that have the potential to induce flutter at the critical speed of the airplane. The computational solutions are further validated through wind tunnel experiments and recent literature concerning certification for flight in icing conditions.

Social implications

The ice accretion study on the aerodynamic surfaces can also be extended for wind turbine blades installed at different cold regions around the globe. Further, the propeller icing influences the entire rotorcraft aerodynamics at low temperature conditions and the findings of this study are strongly connected with such problems.

Originality/value

The aerodynamic characteristics of the baseline airfoil are greatly affected by the ice accretion problem. Although flight through icing condition endures for a short duration, the takeoff path and decision speed are determined based on airplane drag as per federal aviation regulations. Hence, the proposed study is focussed on a cost-effective approach to predict the effect of ice accretion to achieve optimum performance.

Details

Aircraft Engineering and Aerospace Technology, vol. 92 no. 6
Type: Research Article
ISSN: 1748-8842

Keywords

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Article

Nikhil Kalkote, Ashwani Assam and Vinayak Eswaran

The purpose of this paper is to solve unsteady compressible Navier–Stokes equations without the commonly used dual-time loop. The authors would like to use an adaptive…

Abstract

Purpose

The purpose of this paper is to solve unsteady compressible Navier–Stokes equations without the commonly used dual-time loop. The authors would like to use an adaptive time-stepping (ATS)-based local error control instead of CFL-based time-stepping technique. Also, an all-speed flow algorithm is implemented with simple low dissipation AUSM convective scheme, which can be computed without preconditioning which in general destroys the time accuracy.

Design/methodology/approach

In transient flow computations, the time-step is generally determined from the CFL condition. In this paper, the authors demonstrate the usefulness of ATS based on local time-stepping previously used extensively in ordinary differential equations (ODE) integration. This method is implemented in an implicit framework to ensure the numerical domain of dependence always contains the physical domain of dependence.

Findings

In this paper, the authors limit their focus to capture the unsteady physics for three cases: Sod’s shock-tube problem, Stokes’ second problem and a circular cylinder. The use of ATS with local truncation error control enables the solver to use the maximum allowable time-step, for the prescribed tolerance of error. The algorithm is also capable of converging very rapidly to the steady state (if there is any) after the initial transient phase. The authors present here only the first-order time-stepping scheme. An algorithmic comparison is made between the proposed adaptive time-stepping method and the commonly used dual time-stepping approach that indicates the former will be more efficient.

Originality/value

The original method of ATS based on local error control is used extensively in ODE integration, whereas, this method is not so popular in the computational fluid dynamics (CFD) community. In this paper, the authors investigate its use in the unsteady CFD computations. The authors hope that it would provide CFD researchers with an algorithm based on an adaptive time-stepping approach for unsteady calculations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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