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Article
Publication date: 11 February 2021

Mingyang Liu, Huifen Zhu, Guangjun Gao, Chen Jiang and G.R Liu

The purpose of this paper is to investigate a novel stabilization scheme to handle convection and pressure oscillation in the process of solving incompressible laminar…

Abstract

Purpose

The purpose of this paper is to investigate a novel stabilization scheme to handle convection and pressure oscillation in the process of solving incompressible laminar flows by finite element method (FEM).

Design/methodology/approach

The semi-implicit stabilization scheme, characteristic-based polynomial pressure projection (CBP3) consists of the Characteristic-Galerkin method and polynomial pressure projection. Theoretically, the proposed scheme works for any type of element using equal-order approximation for velocity and pressure. In this work, linear 3-node triangular and 4-node tetrahedral elements are the focus, which are the simplest but most difficult elements for pressure stabilizations.

Findings

The present paper proposes a new scheme, which can stabilize FEM solution for flows of both low and relatively high Reynolds numbers. And the influence of stabilization parameters of the CBP3 scheme has also been investigated.

Research limitations/implications

The research in this work is limited to the laminar incompressible flow.

Practical implications

The verification and validation of the CBP3 scheme are conducted by several 2 D and 3 D numerical examples. The scheme could be used to deal with more practical fluid problems.

Social implications

The application of scheme to study complex hemodynamics of patient-specific abdominal aortic aneurysm is also presented, which demonstrates its potential to solve bio-flows.

Originality/value

The paper simulated 2 D and 3 D numerical examples with superior results compared to existing results and experiments. The novel CBP3 scheme is verified to be very effective in handling convection and pressure oscillation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 29 August 2019

Yongshuai Wang, Md. Abdullah Al Mahbub and Haibiao Zheng

This paper aims to propose a characteristic stabilized finite element method for non-stationary conduction-convection problems.

Abstract

Purpose

This paper aims to propose a characteristic stabilized finite element method for non-stationary conduction-convection problems.

Design/methodology/approach

To avoid difficulty caused by the trilinear term, the authors use the characteristic method to deal with the time derivative term and the advection term. The space discretization adopts the low-order triples (i.e. P1-P1-P1 and P1-P0-P1 triples). As low-order triples do not satisfy inf-sup condition, the authors use the stability technique to overcome this flaw.

Findings

The stability and the convergence analysis shows that the method is stable and has optimal-order error estimates.

Originality/value

Numerical experiments confirm the theoretical analysis and illustrate that the authors’ method is highly effective and reliable, and consumes less CPU time.

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: 7 November 2016

Juan Wen, Yinnian He and Xin Zhao

The purpose of this paper is to propose a new stabilized finite volume element method for the Navier-Stokes problem.

Abstract

Purpose

The purpose of this paper is to propose a new stabilized finite volume element method for the Navier-Stokes problem.

Design/methodology/approach

This new method is based on the multiscale enrichment and uses the lowest equal order finite element pairs P1/P1.

Findings

The stability and convergence of the optimal order in H1-norm for velocity and L2-norm for pressure are obtained.

Originality/value

Using a dual problem for the Navier-Stokes problem, the convergence of the optimal order in L2-norm for the velocity is obtained. Finally, numerical example confirms the theory analysis and validates the effectiveness of this new method.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 6 November 2017

Mahmoud M. El-Gendi and Abdelraheem M. Aly

Boussinesq approximation is widely used in solving natural convection problems, but it has severe practical limitations. Using Boussinesq approximation, the temperature…

Abstract

Purpose

Boussinesq approximation is widely used in solving natural convection problems, but it has severe practical limitations. Using Boussinesq approximation, the temperature difference should be less than 28.6 K. The purpose of this study is to get rid of Boussinesq approximation and simulates the natural convection problems using an unsteady compressible Navier-Stokes solver. The gravity force is included in the source term. Three temperature differences are used namely 20 K, 700 K and 2000 K.

Design/methodology/approach

The calculations are carried out on the square and sinusoidal cavities. The results of low temperature difference have good agreement with the experimental and previous calculated data. It is found that, the high temperature difference has a significant effect on the density.

Findings

Due to mass conservation, the density variation affects the velocity distribution and its symmetry. On the other hand, the density variation has a negligible effect on the temperature distribution.

Originality/value

The present calculation method has no limitations but its convergence is slow. The current study can be used in fluid flow simulations for nuclear power applications in natural convection flows subjected to large temperature differences.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 4 January 2016

Mehdi Jamei and H Ghafouri

The purpose of this paper is to present a novel sequential implicit discontinuous Galerkin (DG) method for two-phase incompressible flow in porous media. It is based on…

Abstract

Purpose

The purpose of this paper is to present a novel sequential implicit discontinuous Galerkin (DG) method for two-phase incompressible flow in porous media. It is based on the wetting phase pressure-saturation formulation with Robin boundary condition (Klieber and Riviere, 2006) using H(div) velocity projection.

Design/methodology/approach

The local mass conservation and continuity of normal component of velocity across elements interfaces are enforced by a simple H(div) velocity projection in lowest order Raviart-Thomas (RT0) space. As further improvements, the authors use the weighted averages and the scaled penalties in spatial DG discretization. Moreover, the Chavent-Jaffre slope limiter, as a consistent non-oscillatory limiter, is used for saturation values to avoid the spurious oscillations.

Findings

The proposed model is verified by a pseudo 1D Buckley-Leverett problem in homogeneous media. Two homogeneous and heterogeneous quarter five-spot benchmark problems and a random permeable medium are used to show the accuracy of the method at capturing the sharp front and illustrate the impact of proposed improvements.

Research limitations/implications

The work illustrates incompressible two-phase flow behavior and the capillary pressure heterogeneity between different geological layers is assumed to be negligible.

Practical implications

The proposed model can efficiently be used for modeling of two-phase flow in secondary recovery of petroleum reservoirs and tracing the immiscible contamination in porous media.

Originality/value

The authors present an efficient sequential DG method for immiscible incompressible two-phase flow in porous media with improved performance for detection of sharp frontal interfaces and discontinuities.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 14 August 2017

Ming-min Liu, L.Z. Li and Jun Zhang

The purpose of this paper is to discuss a data interpolation method of curved surfaces from the point of dimension reduction and manifold learning.

Abstract

Purpose

The purpose of this paper is to discuss a data interpolation method of curved surfaces from the point of dimension reduction and manifold learning.

Design/methodology/approach

Instead of transmitting data of curved surfaces in 3D space directly, the method transmits data by unfolding 3D curved surfaces into 2D planes by manifold learning algorithms. The similarity between surface unfolding and manifold learning is discussed. Projection ability of several manifold learning algorithms is investigated to unfold curved surface. The algorithms’ efficiency and their influences on the accuracy of data transmission are investigated by three examples.

Findings

It is found that the data interpolations using manifold learning algorithms LLE, HLLE and LTSA are efficient and accurate.

Originality/value

The method can improve the accuracies of coupling data interpolation and fluid-structure interaction simulation involving curved surfaces.

Details

Multidiscipline Modeling in Materials and Structures, vol. 13 no. 2
Type: Research Article
ISSN: 1573-6105

Keywords

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Article
Publication date: 1 June 1994

Sang‐Ho Lee, Ted Blacker and Ted Belytschko

An enhanced L2 projection method for recovering accuratederivatives such as moments, or shears, from finite element solutions forC° plates is presented. In the enhanced…

Abstract

An enhanced L2 projection method for recovering accurate derivatives such as moments, or shears, from finite element solutions for C° plates is presented. In the enhanced global and local projections, the square of the residuals in the equilibrium equations is included. Results are compared with those of standard global and local projection methods. Numerical examples show that in the global projection, the enhanced technique improves the accuracy of projected solution significantly. In the local projection, the enhanced projection technique circumvents the numerical ill‐conditioning which occurs in some meshes, and usually recovers derivatives with better accuracy. These techniques are effective for both thin and thick plate problems, and can provide more reliable error estimates for mesh adaptivity.

Details

Engineering Computations, vol. 11 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 20 June 2019

Peter Wriggers and Wilhelm T. Rust

This paper aims to describe the application of the virtual element method (VEM) to contact problems between elastic bodies.

Abstract

Purpose

This paper aims to describe the application of the virtual element method (VEM) to contact problems between elastic bodies.

Design/methodology/approach

Polygonal elements with arbitrary shape allow a stable node-to-node contact enforcement. By adaptively adjusting the polygonal mesh, this methodology is extended to problems undergoing large frictional sliding.

Findings

The virtual element is well suited for large deformation contact problems. The issue of element stability for this specific application is discussed, and the capability of the method is demonstrated by means of numerical examples.

Originality/value

This work is completely new as this is the first time, as per the authors’ knowledge, the VEM is applied to large deformation contact.

Details

Engineering Computations, vol. 36 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 12 October 2012

Saeed Shamaghdari and S.K.Y. Nikravesh

The purpose of this paper is to present a nonlinear model along with stability analysis of a flexible supersonic flight vehicle system.

Abstract

Purpose

The purpose of this paper is to present a nonlinear model along with stability analysis of a flexible supersonic flight vehicle system.

Design/methodology/approach

The mathematical state space nonlinear model of the system is derived using Lagrangian approach such that the applied force, moment, and generalized force are all assumed to be nonlinear functions of the system states. The condition under which the system would be unstable is derived and when the system is stable, the region of attraction of the system equilibrium state is determined using the Lyapunov theory and sum of squares optimization method. The method is applied to a slender flexible body vehicle, which is referenced by the other researchers in the literature.

Findings

It is demonstrated that neglecting the nonlinearity in external force, moment and generalized force, as it was assumed by other researchers, can cause significant variations in stability conditions. Moreover, when the system is stable, it is shown analytically here that a reduction in dynamic pressure can make a larger region of attraction, and thus instability will occur in a larger angle of attack, greater angular velocity and elastic displacement.

Practical implications

In order to carefully study the behavior of aeroelastic flight vehicle, a nonlinear model and analysis is definitely necessary. Moreover, for the design of the airframe and/or control purposes, it is essential to investigate region of attraction of equilibrium state of the stable flight vehicle.

Originality/value

Current stability analysis methods for nonlinear elastic flight vehicles are unable to determine the state space region where the system is stable. Nonlinear modeling affects the determination of the stability region and instability condition. This paper presents a new approach to stability analysis of the nonlinear flexible flight vehicle. By determining the region of attraction when the system is stable, it is demonstrated analytically, in this research, that decreasing the dynamic pressure can produce larger region of attraction.

Details

Aircraft Engineering and Aerospace Technology, vol. 84 no. 6
Type: Research Article
ISSN: 0002-2667

Keywords

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Article
Publication date: 6 November 2017

Gholamreza Shobeyri and Mohammad Yourdkhani

The purpose of this paper is to develop an efficient and accurate mesh-less method to simulate free flows with continuous deformation in boundary positions.

Abstract

Purpose

The purpose of this paper is to develop an efficient and accurate mesh-less method to simulate free flows with continuous deformation in boundary positions.

Design/methodology/approach

A two-step pressure projection method in a Lagrangian form is used to solve the governing equations of mass and momentum conservation. In the first step, velocity field is calculated in which incompressibility is not enforced. In the second step, a pressure Poisson equation is applied to satisfy incompressibility conditions. The numerical proposed method is used for spatial discretization of the governing equations. Three benchmark-free surface problems, namely, dam break, solitary wave propagation and evolution of an elliptical bubble with available experimental results and analytical solutions, are used to test the accuracy of the proposed method. The results prove the accuracy of the method in simulating free surface problems.

Findings

The Voronoi diagram instead of kernel function summation can be used to estimate the particle or nodal volume concept in particle-based (mesh-less) methods for function approximation. This idea probably works well especially for highly irregular node distributions.

Originality/value

The continuous moving least squares shape functions are applied for function approximation, and the Voronoi diagram concept is also used to estimate region influence of computational nodal points or particle volumes. Combinations of these two concepts and finite differences formulation for first derivatives gives an accurate numerical model for Laplacian operator in the proposed method.

Details

Engineering Computations, vol. 34 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

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