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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 two-part…

226

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

Keywords

Article
Publication date: 3 November 2022

Shashi Kant Ratnakar, Utpal Kiran and Deepak Sharma

Structural topology optimization is computationally expensive due to the involvement of high-resolution mesh and repetitive use of finite element analysis (FEA) for computing the…

149

Abstract

Purpose

Structural topology optimization is computationally expensive due to the involvement of high-resolution mesh and repetitive use of finite element analysis (FEA) for computing the structural response. Since FEA consumes most of the computational time in each optimization iteration, a novel GPU-based parallel strategy for FEA is presented and applied to the large-scale structural topology optimization of 3D continuum structures.

Design/methodology/approach

A matrix-free solver based on preconditioned conjugate gradient (PCG) method is proposed to minimize the computational time associated with solution of linear system of equations in FEA. The proposed solver uses an innovative strategy to utilize only symmetric half of elemental stiffness matrices for implementation of the element-by-element matrix-free solver on GPU.

Findings

Using solid isotropic material with penalization (SIMP) method, the proposed matrix-free solver is tested over three 3D structural optimization problems that are discretized using all hexahedral structured and unstructured meshes. Results show that the proposed strategy demonstrates 3.1× –3.3× speedup for the FEA solver stage and overall speedup of 2.9× –3.3× over the standard element-by-element strategy on the GPU. Moreover, the proposed strategy requires almost 1.8× less GPU memory than the standard element-by-element strategy.

Originality/value

The proposed GPU-based matrix-free element-by-element solver takes a more general approach to the symmetry concept than previous works. It stores only symmetric half of the elemental matrices in memory and performs matrix-free sparse matrix-vector multiplication (SpMV) without any inter-thread communication. A customized data storage format is also proposed to store and access only symmetric half of elemental stiffness matrices for coalesced read and write operations on GPU over the unstructured mesh.

Details

Engineering Computations, vol. 39 no. 10
Type: Research Article
ISSN: 0264-4401

Keywords

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. Topics…

1165

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

Keywords

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 meshing

1892

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

Keywords

Article
Publication date: 30 June 2021

Zhiwei Liu, Jianjun Chen, Yifan Xia and Yao Zheng

Sizing functions are crucial inputs for unstructured mesh generation since they determine the element distributions of resulting meshes to a large extent. Meanwhile, automating…

Abstract

Purpose

Sizing functions are crucial inputs for unstructured mesh generation since they determine the element distributions of resulting meshes to a large extent. Meanwhile, automating the procedure of creating a sizing function is a prerequisite to set up a fully automatic mesh generation pipeline. In this paper, an automatic algorithm is proposed to create a high-quality sizing function for an unstructured surface and volume mesh generation by using a triangular mesh as the background mesh.

Design/methodology/approach

A practically efficient and effective solution is developed by using local operators carefully to re-mesh the tessellation of the input Computer Aided Design (CAD) models. A nonlinear programming (NLP) problem has been formulated to limit the gradient of the sizing function, while in this study, the object function of this NLP is replaced by an analytical equation that predicts the number of elements. For the query of the sizing value, an improved algorithm is developed by using the axis-aligned bounding box (AABB) tree structure.

Findings

The local operations of re-meshing could effectively and efficiently resolve the banding issue caused by using the default tessellation of the model to define a sizing function. Experiments show that the solution of the revised NLP, in most cases, could provide a better solution at the lower cost of computational time. With the help of the AABB tree, the sizing function defined at a surface background mesh can be also used as the input of volume mesh generation.

Originality/value

Theoretical analysis reveals that the construction of the initial sizing function could be reduced to the solution of an optimization problem. The definitions of the banding elements and surface proximity are also given. Under the guidance of this theoretical analysis, re-meshing and ray-casting technologies are well-designed to initial the sizing function. Smoothing with the revised NLP and querying by the AABB tree, the paper provides an automatic method to get a high-quality sizing function for both surface and volume mesh generation.

Details

Engineering Computations, vol. 38 no. 10
Type: Research Article
ISSN: 0264-4401

Keywords

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 are…

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

Keywords

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 predicted…

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

Keywords

Article
Publication date: 8 March 2023

Jordi Vila-Pérez, Matteo Giacomini and Antonio Huerta

This study aims to assess the robustness and accuracy of the face-centred finite volume (FCFV) method for the simulation of compressible laminar flows in different regimes, using…

Abstract

Purpose

This study aims to assess the robustness and accuracy of the face-centred finite volume (FCFV) method for the simulation of compressible laminar flows in different regimes, using numerical benchmarks.

Design/methodology/approach

The work presents a detailed comparison with reference solutions published in the literature –when available– and numerical results computed using a commercial cell-centred finite volume software.

Findings

The FCFV scheme provides first-order accurate approximations of the viscous stress tensor and the heat flux, insensitively to cell distortion or stretching. The strategy demonstrates its efficiency in inviscid and viscous flows, for a wide range of Mach numbers, also in the incompressible limit. In purely inviscid flows, non-oscillatory approximations are obtained in the presence of shock waves. In the incompressible limit, accurate solutions are computed without pressure correction algorithms. The method shows its superior performance for viscous high Mach number flows, achieving physically admissible solutions without carbuncle effect and predictions of quantities of interest with errors below 5%.

Originality/value

The FCFV method accurately evaluates, for a wide range of compressible laminar flows, quantities of engineering interest, such as drag, lift and heat transfer coefficients, on unstructured meshes featuring distorted and highly stretched cells, with an aspect ratio up to ten thousand. The method is suitable to simulate industrial flows on complex geometries, relaxing the requirements on mesh quality introduced by existing finite volume solvers and alleviating the need for time-consuming manual procedures for mesh generation to be performed by specialised technicians.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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 around…

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

Keywords

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 extended to…

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

Keywords

1 – 10 of 917