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Article
Publication date: 29 August 2019

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

This work aims to describe the physical and numerical modeling of a CFD solver for hypersonic flows in thermo-chemical non-equilibrium. This paper is the second of a…

Abstract

Purpose

This work aims to describe the physical and numerical modeling of a CFD solver for hypersonic flows in thermo-chemical non-equilibrium. This paper is the second of a two-part series that concerns the application of the solver introduced in Part I to adaptive unstructured meshes.

Design/methodology/approach

The governing equations are discretized with an edge-based stabilized finite element method (FEM). Chemical non-equilibrium is simulated using a laminar finite-rate kinetics, while a two-temperature model is used to account for thermodynamic non-equilibrium. The equations for total quantities, species and vibrational-electronic energy conservation are loosely coupled to provide flexibility and ease of implementation. To accurately perform simulations on unstructured meshes, the non-equilibrium flow solver is coupled with an edge-based anisotropic mesh optimizer driven by the solution Hessian to carry out mesh refinement, coarsening, edge swapping and node movement.

Findings

The paper shows, through comparisons with experimental and other numerical results, how FEM + anisotropic mesh optimization are the natural choice to accurately simulate hypersonic non-equilibrium flows on unstructured meshes. Three-dimensional test cases demonstrate how, for high-speed flows, shocks resolution, and not necessarily boundary layers resolution, is the main driver of solution accuracy at walls. Equally distributing the error among all elements in a suitably defined Riemannian space yields highly anisotropic grids that feature well-resolved shock waves. The resulting high level of accuracy in the computation of the enthalpy jump translates into accurate wall heat flux predictions. At the opposite end, in all cases examined, high-quality but isotropic unstructured meshes gave very poor solutions with severely inadequate heat flux distributions not even featuring expected symmetries. The paper unequivocally demonstrates that unstructured anisotropically adapted meshes are the best, and may be the only, way for accurate and cost-effective hypersonic flow solutions.

Originality/value

Although many hypersonic flow solvers are developed for unstructured meshes, few numerical simulations on unstructured meshes are presented in the literature. This work demonstrates that the proposed approach can be used successfully for hypersonic flows on unstructured meshes.

Details

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

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Article
Publication date: 1 June 2003

Jaroslav Mackerle

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view…

Abstract

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

Details

Engineering Computations, vol. 20 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 December 2001

Jaroslav Mackerle

Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for…

Abstract

Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for meshing and remeshing, parallel processing in the finite element modelling, etc. are also included. The bibliography at the end of this paper contains 1,727 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1990 and 2001.

Details

Engineering Computations, vol. 18 no. 8
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 30 April 2020

Hongbin Liu, Hu Ren, Hanfeng Gu, Fei Gao and Guangwen Yang

The purpose of this paper is to provide an automatic parallelization toolkit for unstructured mesh-based computation. Among all kinds of mesh types, unstructured meshes

Abstract

Purpose

The purpose of this paper is to provide an automatic parallelization toolkit for unstructured mesh-based computation. Among all kinds of mesh types, unstructured meshes are dominant in engineering simulation scenarios and play an essential role in scientific computations for their geometrical flexibility. However, the high-fidelity applications based on unstructured grids are still time-consuming, no matter for programming or running.

Design/methodology/approach

This study develops an efficient UNstructured Acceleration Toolkit (UNAT), which provides friendly high-level programming interfaces and elaborates lower level implementation on the target hardware to get nearly hand-optimized performance. At the present state, two efficient strategies, a multi-level blocks method and a row-subsections method, are designed and implemented on Sunway architecture. Random memory access and write–write conflict issues of unstructured meshes have been handled by partitioning, coloring and other hardware-specific techniques. Moreover, a data-reuse mechanism is developed to increase the computational intensity and alleviate the memory bandwidth bottleneck.

Findings

The authors select sparse matrix-vector multiplication as a performance benchmark of UNAT across different data layouts and different matrix formats. Experimental results show that the speed-ups reach up to 26× compared to single management processing element, and the utilization ratio tests indicate the capability of achieving nearly hand-optimized performance. Finally, the authors adopt UNAT to accelerate a well-tuned unstructured solver and obtain speed-ups of 19× and 10× on average for main kernels and overall solver, respectively.

Originality/value

The authors design an unstructured mesh toolkit, UNAT, to link the hardware and numerical algorithm, and then, engineers can focus on the algorithms and solvers rather than the parallel implementation. For the many-core processor SW26010 of the fastest supercomputer in China, UNAT yields up to 26× speed-ups and achieves nearly hand-optimized performance.

Details

Engineering Computations, vol. 37 no. 9
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 18 September 2009

Q. Du, D.G. Eskin and L. Katgerman

The purpose of this paper is to investigate the ways to diminish or eliminate numerical diffusion and dispersion. Numerical dispersion and diffusion are present in the…

Abstract

Purpose

The purpose of this paper is to investigate the ways to diminish or eliminate numerical diffusion and dispersion. Numerical dispersion and diffusion are present in the predicted macrosegregation profiles reported in the literature and they hinder the interpretation of the simulation results. With the motivation to eliminate these numerical problems by employing appropriate meshes, simulations of macrosegregation in a billet direct‐chill cast from a multi‐component aluminium alloy has been performed.

Design/methodology/approach

First the idea that numerical dispersion could be alleviated by refining the structured mesh size is tested and the extent of this mesh refining to overcome these numerical problems is discussed. Second the link of numerical dispersion and diffusion to the type of mesh used is investigated.

Findings

Unstructured mesh eliminates the numerical dispersion present in the structured mesh while it introduces the numerical diffusion. It is concluded by performing calculations with the same settings but different meshes that, although refining the structured mesh could alleviate the numerical oscillation, it increases the computation time dramatically. Therefore the best solution to overcome these numerical problems is the employment of a hybrid mesh consisting of both structured and unstructured mesh.

Originality/value

This work reveals the reasons behind the numerical dispersion and diffusion in macrosegregation modelling and gives a practical solution.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 6 July 2015

He-yong Xu, Shi-long Xing and Zheng-yin Ye

The purpose of this paper is to investigate and improve a new method of unstructured rotational dynamic overset grids, which can be used to simulate the unsteady flows…

Abstract

Purpose

The purpose of this paper is to investigate and improve a new method of unstructured rotational dynamic overset grids, which can be used to simulate the unsteady flows around rotational parts of aircraft.

Design/methodology/approach

The computational domain is decomposed into two sub-domains, namely, the rotational sub-domain which contains the rotational boundaries, and the stationary sub-domain which contains the remainder flow field including the stationary boundaries. The artificial boundaries and restriction boundaries are used as the restriction condition to generate the entire computational grid, and then the overset grids are established according to the radius parameters of artificial boundaries set previously. The deformation of rotational boundary is treated by using the linear spring analogy method which is suitable for the dynamic unstructured grid. The unsteady Navier-Stokes/Euler equations are solved separately in the rotational sub-domain and stationary sub-domain, and data coupling is accomplished through the overlapping area. The least squares method is used to interpolate the flow variables for the artificial boundary points with a higher calculating precision. Implicit lower-upper symmetric-Gauss-Seidel (LU-SGS) time stepping scheme is implemented to accelerate the inner iteration during the unsteady simulation.

Findings

The airfoil steady flow, airfoil pitching unsteady flow, three-dimensional (3-D) rotor flow field, rotor-fuselage interaction unsteady flow field and the flutter exciting system unsteady flow field are numerically simulated, and the results have good agreements with the experimental data. It is shown that the present method is valid and efficient for the prediction of complicated unsteady problems which contain rotational dynamic boundaries.

Research limitations/implications

The results are entirely based on computational fluid dynamics (CFD), and the 3D simulations are based on the Euler equations in which the viscous effect is ignored. The current work shows further applicable potential to simulate unsteady flow around rotational parts of aircraft.

Practical implications

The current study can be used to simulate the two-dimensional airfoil pitching, 3-D rotor flow field, rotor-fuselage interaction and the flutter exciting system unsteady flow. The work will help the aircraft designer to get the unsteady flow character around rotational parts of aircraft.

Originality/value

A new type of rotational dynamic overset grids is presented and validated, and the current work has a significant contribution to the development of unstructured rotational dynamic overset grids.

Details

Aircraft Engineering and Aerospace Technology: An International Journal, vol. 87 no. 4
Type: Research Article
ISSN: 0002-2667

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Article
Publication date: 1 January 1993

R.D. LONSDALE

A simple algebraic multigrid (AMG) solver for linear equations is presented, and its performance compared with a conjugate gradient scheme. This multigrid method is…

Abstract

A simple algebraic multigrid (AMG) solver for linear equations is presented, and its performance compared with a conjugate gradient scheme. This multigrid method is extended to solve the discrete Navier—Stokes equations, obtained by applying a finite volume approach to three‐dimensional incompressible flow on a finite element mesh. The resulting multigrid solver is incorporated into a general purpose flow code (ASTEC), where it proves faster than the original solution algorithm, based upon SIMPLE. The linear AMG solver is both efficient and robust, but the extension to include coupling in the Navier—Stokes equations does not converge on all problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 3 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 November 1997

J.L. Graysmith and C.T. Shaw

Develops a method which performs Boolean operations on two unstructured arbitrary meshes. Deletes the overlapping or interfering elements of two individual meshes and…

Abstract

Develops a method which performs Boolean operations on two unstructured arbitrary meshes. Deletes the overlapping or interfering elements of two individual meshes and creates a mesh of tetrahedral elements in their place to provide an interface between the remnants of the original meshes. Gives various examples where two volume meshes are joined or where a surface mesh is imposed on a volume mesh. Shows, through these examples, the effects of various input parameters on the quality of the final mesh.

Details

Engineering Computations, vol. 14 no. 7
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 December 1997

Dan Givoli, Joseph E. Flaherty and Mark S. Shephard

Describes a new finite element scheme for the large‐scale analysis of compressible and incompressible viscous flows. The scheme is based on a combined compressible…

Abstract

Describes a new finite element scheme for the large‐scale analysis of compressible and incompressible viscous flows. The scheme is based on a combined compressible‐ incompressible Galerkin least‐squares (GLS) space‐time variational formulation. Three‐ dimensional unstructured meshes are employed, with piecewise‐constant temporal interpolation, local time‐stepping for steady flows, and linear continuous spatial interpolation in all the variables. The scheme incorporates automatic adaptive mesh refinement, with a choice of various error indicators. It is implemented on a distributed‐memory parallel computer, and includes an automatic load‐balancing procedure. Demonstrates the ability to solve both compressible and incompressible viscous flow problems using the parallel adaptive framework via numerical examples. These include Mach 3 flow over a flat plate, and a divergence‐free buoyancy‐driven flow in a cavity. The latter is a model for the steady melt flow in a Czochralski crystal growth process.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 7 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 5 March 2018

Xue Yang, Li Yu and Xiao-Shun Zhao

The purpose of this study is to model the dynamic characteristics of an opened supersonic disk-gap-band parachute.

Abstract

Purpose

The purpose of this study is to model the dynamic characteristics of an opened supersonic disk-gap-band parachute.

Design/methodology/approach

A fluid-structure interaction (FSI) method with body-fitted mesh is used to simulate the supersonic parachute. The compressible flow is modeled using large-eddy simulation (LES). A contact algorithm based on the penalty function with a virtual contact domain is proposed to solve the negative volume problem of the body-fitted mesh. Automatic unstructured mesh generation and automatic mesh moving schemes are used to handle complex deformations of the canopy.

Findings

The opened disk-gap-band parachute is simulated using Mach 2.0, and the simulation results fit well with the wind tunnel test data. It is found that the LES model can successfully predict large-scale turbulent vortex in the flow. This study also demonstrates the capability of the present FSI method as a tool to predict shock oscillation and breathing phenomenon of the canopy.

Originality/value

The contact algorithm based on the penalty function with a virtual contact domain is proposed for the first time. This methodology can be used to solve the negative volume problem of the dynamic mesh in the flow field.

Details

Engineering Computations, vol. 35 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

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