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Article
Publication date: 23 January 2023

Roshith Mittakolu, Sarma L. Rani and Dilip Srinivas Sundaram

A higher-order implicit shock-capturing scheme is presented for the Euler equations based on time linearization of the implicit flux vector rather than the residual vector.

71

Abstract

Purpose

A higher-order implicit shock-capturing scheme is presented for the Euler equations based on time linearization of the implicit flux vector rather than the residual vector.

Design/methodology/approach

The flux vector is linearized through a truncated Taylor-series expansion whose leading-order implicit term is an inner product of the flux Jacobian and the vector of differences between the current and previous time step values of conserved variables. The implicit conserved-variable difference vector is evaluated at cell faces by using the reconstructed states at the left and right sides of a cell face and projecting the difference between the left and right states onto the right eigenvectors. Flux linearization also facilitates the construction of implicit schemes with higher-order spatial accuracy (up to third order in the present study). To enhance the diagonal dominance of the coefficient matrix and thereby increase the implicitness of the scheme, wave strengths at cell faces are expressed as the inner product of the inverse of the right eigenvector matrix and the difference in the right and left reconstructed states at a cell face.

Findings

The accuracy of the implicit algorithm at Courant–Friedrichs–Lewy (CFL) numbers greater than unity is demonstrated for a number of test cases comprising one-dimensional (1-D) Sod’s shock tube, quasi 1-D steady flow through a converging-diverging nozzle, and two-dimensional (2-D) supersonic flow over a compression corner and an expansion corner.

Practical implications

The algorithm has the advantage that it does not entail spatial derivatives of flux Jacobian so that the implicit flux can be readily evaluated using Roe’s approximate Jacobian. As a result, this approach readily facilitates the construction of implicit schemes with high-order spatial accuracy such as Roe-MUSCL.

Originality/value

A novel finite-volume-based higher-order implicit shock-capturing scheme was developed that uses time linearization of fluxes at cell interfaces.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Available. Content available
2358

Abstract

Details

Kybernetes, vol. 41 no. 7/8
Type: Research Article
ISSN: 0368-492X

Available. Open Access. Open Access
Article
Publication date: 16 May 2024

Axel Buck and Christian Mundt

Reynolds-averaged Navier–Stokes (RANS) models often perform poorly in shock/turbulence interaction regions, resulting in excessive wall heat load and incorrect representation of…

336

Abstract

Purpose

Reynolds-averaged Navier–Stokes (RANS) models often perform poorly in shock/turbulence interaction regions, resulting in excessive wall heat load and incorrect representation of the separation length in shockwave/turbulent boundary layer interactions. The authors suggest that this can be traced back to inadequate numerical treatment of the inviscid fluxes. The purpose of this study is an extension to the well-known Harten, Lax, van Leer, Einfeldt (HLLE) Riemann solver to overcome this issue.

Design/methodology/approach

It explicitly takes into account the broadening of waves due to the averaging procedure, which adds numerical dissipation and reduces excessive turbulence production across shocks. The scheme is derived based on the HLLE equations, and it is tested against three numerical experiments.

Findings

Sod’s shock tube case shows that the scheme succeeds in reducing turbulence amplification across shocks. A shock-free turbulent flat plate boundary layer indicates that smooth flow at moderate turbulence intensity is largely unaffected by the scheme. A shock/turbulent boundary layer interaction case with higher turbulence intensity shows that the added numerical dissipation can, however, impair the wall heat flux distribution.

Originality/value

The proposed scheme is motivated by implicit large eddy simulations that use numerical dissipation as subgrid-scale model. Introducing physical aspects of turbulence into the numerical treatment for RANS simulations is a novel approach.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 34 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 1 December 1994

G D van Albada, J M Lagerberg and A Visser

Outlines research work to design a robot calibration system which isportable, accurate and low‐cost. Describes prototype measuring systemwhich is based on a camera in the robot…

406

Abstract

Outlines research work to design a robot calibration system which is portable, accurate and low‐cost. Describes prototype measuring system which is based on a camera in the robot hand, plus a known reference object in the robot workspace. Gives details of the measuring procedure, the camera lens, the reference plate and the possible sources of measurement errors. Concludes that this method, based on photogrammetry to obtain measurements for the calibration of robot systems, has been implemented and tested and provides promising results for practical application.

Details

Industrial Robot: An International Journal, vol. 21 no. 6
Type: Research Article
ISSN: 0143-991X

Keywords

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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…

85

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

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Article
Publication date: 21 June 2019

Jory Seguin, Song Gao, Wagdi George Habashi, Dario Isola and Guido Baruzzi

This paper aims to describe the physical and numerical modeling of a new computational fluid dynamics solver for hypersonic flows in thermo-chemical non-equilibrium. The code uses…

288

Abstract

Purpose

This paper aims to describe the physical and numerical modeling of a new computational fluid dynamics solver for hypersonic flows in thermo-chemical non-equilibrium. The code uses a blend of numerical techniques to ensure accuracy and robustness and to provide scalability for advanced hypersonic physics and complex three-dimensional (3D) flows.

Design/methodology/approach

The solver is based on an edge-based stabilized finite element method (FEM). The chemical and thermal non-equilibrium systems are loosely-coupled to provide flexibility and ease of implementation. Chemical non-equilibrium is modeled using a laminar finite-rate chemical kinetics model while a two-temperature model is used to account for thermodynamic non-equilibrium. The systems are solved implicitly in time to relax numerical stiffness. Investigations are performed on various canonical hypersonic geometries in two-dimensional and 3D.

Findings

The comparisons with numerical and experimental results demonstrate the suitability of the code for hypersonic non-equilibrium flows. Although convergence is shown to suffer to some extent from the loosely-coupled implementation, trading a fully-coupled system for a number of smaller ones improves computational time. Furthermore, the specialized numerical discretization offers a great deal of flexibility in the implementation of numerical flux functions and boundary conditions.

Originality/value

The FEM is often disregarded in hypersonics. This paper demonstrates that this method can be used successfully for these types of flows. The present findings will be built upon in a later paper to demonstrate the powerful numerical ability of this type of solver, particularly with respect to robustness on highly stretched unstructured anisotropic grids.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

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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…

135

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

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Article
Publication date: 1 December 1994

Thomas R Kugler

Describes an automated laser cutting cell used in the automotiveindustry. The cell has the benefits of fast throughput because of highcutting speeds, adaptability of height…

148

Abstract

Describes an automated laser cutting cell used in the automotive industry. The cell has the benefits of fast throughput because of high cutting speeds, adaptability of height sensing, safety of crash protection and flexibility of part modifications via robot path and program modifications. Outlines the feature of the cell which consists of two Nd:YAG lasers with fibre‐optic delivery and two five‐axis robots with trepanning heads, and describes their performance characteristics. Concludes with a summary of the advantages of using a laser cutting cell.

Details

Industrial Robot: An International Journal, vol. 21 no. 6
Type: Research Article
ISSN: 0143-991X

Keywords

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Article
Publication date: 1 December 1994

Klaus Schroer

Describes a robot calibration package which produces a set of identifiedrobot model parameters. Uses a measurement target mounted on therobot’s end effector and a pair of…

220

Abstract

Describes a robot calibration package which produces a set of identified robot model parameters. Uses a measurement target mounted on the robot’s end effector and a pair of theodolites under automatic control. Typically permits the global positioning error of a robot to be reduced from 10 mm to 1mm. Concludes that calibration procedures such as these are essential for successful off‐line programming of robot systems.

Details

Industrial Robot: An International Journal, vol. 21 no. 6
Type: Research Article
ISSN: 0143-991X

Keywords

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Article
Publication date: 1 February 1993

N. Gouvianakis, M. Loupis and B. Dimitriadis

Vision‐based intelligent automation systems have been slow in finding a way to the food industry, mainly due to the conservative nature of the food processing industrial sector…

43

Abstract

Vision‐based intelligent automation systems have been slow in finding a way to the food industry, mainly due to the conservative nature of the food processing industrial sector, and the unproven maturity of the required vision and automation technologies. Vision‐based systems should be convincingly robust, and fulfil the set performance requirements at a reasonable economic investment.

Details

Sensor Review, vol. 13 no. 2
Type: Research Article
ISSN: 0260-2288

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