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Article
Publication date: 1 February 1995

S. Sivaloganathan and J.M. Stockie

The purpose of this paper is twofold. Firstly, to present a detailedaccount of the generalized Lagrangian formulation of Hui and Zhao, in whichthe stream function ζ and…

Abstract

The purpose of this paper is twofold. Firstly, to present a detailed account of the generalized Lagrangian formulation of Hui and Zhao, in which the stream function ζ and Lagrangian distance λ, are used as independent variables, and secondly to assess and compare the performance of various flux limiters in this formulation with their corresponding performance in the Eulerian formulation. The generalized Lagrangian formulation is obtained by a transformation from the cartesian co‐ordinates (x, y) to the Lagrangian co‐ordinates (λ, ζ). In this manner, the number of independent variables for steady, 3‐D flow is reduced from four to three, placing this formulation on the same footing as the Eulerian formulation even for steady flows (as opposed to the conventional Lagrangian formulation which apparently still requires four independent variables even for steady flows). The generalized Lagrangian formulation with the Godunov scheme (using flux limiters) appears to have distinct advantages over the corresponding Eulerian formulation, particularly with respect to accuracy. Furthermore, the method requires no grid generation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 5 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 30 October 2018

Farhoud Kalateh and Ali Koosheh

This paper aims to propose a new smoothed particle hydrodynamics (SPH)-finite element (FE) algorithm to study fluid–structure interaction (FSI) problems.

Abstract

Purpose

This paper aims to propose a new smoothed particle hydrodynamics (SPH)-finite element (FE) algorithm to study fluid–structure interaction (FSI) problems.

Design/methodology/approach

The fluid domain is discretized based on the theory of SPH), and solid part is solved through FE method, similar to other SPH-FE methods in the previous studies. Instead of master-slave technique, the interpolating (kernel) functions of immersed boundary method are implemented to couple fluid and solid domains. The procedure of modeling completely follows the classic IB framework where forces and velocities are transferred between interacting parts. Three benchmark FSI problems are simulated and the results are compared with those of similar numerical and experimental works.

Findings

The proposed SPH-FE algorithm with promising and acceptable results can be utilized as a reliable method to simulate FSI problems.

Originality/value

Contrary to most SPH-FE algorithms, the calculation of contact force is not required at interacting boundaries and no iterative process is proposed to calculate forces, velocities and positions at new time step.

Details

Engineering Computations, vol. 35 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 1 January 2006

Eugeniusz Kurgan and Paweł Schmidt

Distribution of the electric potential and current density in the electrode of the proton exchange membrane fuel cell.

Abstract

Purpose

Distribution of the electric potential and current density in the electrode of the proton exchange membrane fuel cell.

Design/methodology/approach

Multicomponent model based on Maxwell‐Stefan equations is used to formulate generalized Fick's law. Next, mass conservation laws for gas components and equation of continuity for current density vector are formulated.

Findings

The problem is expressed by three non‐linear partial differential equations in total molar contraction of the gas mixture, oxygen and water vapor concentration describing multicomponent Maxwell‐Stefan mass transport and fourth equation for electric potential distribution. The final system of partial differential equations describing the problem is highly non‐linear and mutually coupled not only directly but also through the non‐linear boundary condition and is solved by finite element method.

Research limitations/implications

There are some convergence problems for some sets of the material parameters. Only one part of the fuel cell was modeled.

Practical implications

This approach allows one to calculate all important parameters required to develop and design the practical systems as well to optimize the performance from the geometrical and material parameters point of view.

Originality/value

The presented approach combines distribution of mass transport using Maxwell‐Stefan model and electric potential described by Laplace equation.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 25 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

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