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Article

Alessandro Corsini, Franco Rispoli and Andrea Santoriello

An original finite element scheme for advection‐diffusion‐reaction problems is presented. The new method, called spotted Petrov‐Galerkin (SPG), is a quadratic…

Abstract

Purpose

An original finite element scheme for advection‐diffusion‐reaction problems is presented. The new method, called spotted Petrov‐Galerkin (SPG), is a quadratic Petrov‐Galerkin (PG) formulation developed for the solution of equations where either reaction (associated to zero‐order derivatives of the unknown) and/or advection (proportional to first‐order derivatives) dominates on diffusion (associated to second‐order derivatives). The addressed issues are turbulence and advective‐reactive features in modelling turbomachinery flows.

Design/methodology/approach

The present work addresses the definition of a new PG stabilization scheme for the reactive flow limit, formulated on a quadratic finite element space of approximation. We advocate the use of a higher order stabilized formulation that guarantees the best compromise between solution stability and accuracy. The formulation is first presented for linear scalar one‐dimensional advective‐diffusive‐reactive problems and then extended to quadrangular Q2 elements.

Findings

The proposed advective‐diffusive‐reactive PG formulation improves the solution accuracy with respect to a standard streamline driven stabilization schemes, e.g. the streamline upwind or Galerkin, in that it properly accounts for the boundary layer region flow phenomena in presence of non‐equilibrium effects.

Research limitations/implications

The numerical method here proposed has been designed for second‐order quadrangular finite‐elements. In particular, the Reynolds‐Averaged Navier‐Stokes equations with a non‐linear turbulence closure have been modelled using the stable mixed element pair Q2‐Q1.

Originality/value

This paper investigated the predicting capabilities of a finite element method stabilized formulation developed for the purpose of solving advection‐reaction‐diffusion problems. The new method, called SPG, demonstrates its suitability in solving the typical equations of turbulence eddy viscosity models.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 15 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Haruhiko Kohno

This paper aims to present an improved finite element method used for achieving faster convergence in simulations of incompressible fluid flows. For stable computations of…

Abstract

Purpose

This paper aims to present an improved finite element method used for achieving faster convergence in simulations of incompressible fluid flows. For stable computations of incompressible fluid flows, it is important to ensure that the flow field satisfies the equation of continuity in each element of a generally distorted mesh. The study aims to develop a numerical approach that satisfies this requirement based on the highly simplified marker-and-cell (HSMAC) method and increases computational speed by introducing a new algorithm into the simultaneous relaxation of velocity and pressure.

Design/methodology/approach

First, the paper shows that the classical HSMAC method is equivalent to a Jacobi-type method in terms of the simultaneous relaxation of velocity and pressure. Then, a Gauss–Seidel or successive over-relaxation (SOR)-type method is introduced in the Newton–Raphson iterations to take into account all the derivative terms in the first-order Taylor series expansion of a nodal-averaged error explicitly. Here, the nine-node quadrilateral (Q2–Q1) elements are used.

Findings

The new finite element approach based on the improved HSMAC algorithm is tested on fluid flow problems including the lid-driven square cavity flow and the flow past a circular cylinder. The results show significant improvement of the convergence property with the accuracy of the numerical solutions kept unchanged even on a highly distorted mesh.

Originality/value

To the best of the author’s knowledge, the idea of using the Gauss–Seidel or SOR method in the simultaneous relaxation procedure of the HSMAC method has not been proposed elsewhere.

Details

Engineering Computations, vol. 37 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

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Article

J.C. Cavendish, C.A. Hall and T.A. Porsching

We describe a new mathematical approach for deriving and solvingcovolume models of the three‐dimensional, incompressibleNavier—Stokes flow equations. The approach…

Abstract

We describe a new mathematical approach for deriving and solving covolume models of the three‐dimensional, incompressible Navier—Stokes flow equations. The approach integrates three technical components into a single modelling algorothm: automatic grid generation; covolume equation generation; dual variable reduction.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 4 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Mo‐Hwa Wang and Klaus‐Jürgen Bathe

The primitive variable finite element formulation is used in a straightforward manner to solve for two turbulent pipe flows. The solution is based on the use of the…

Abstract

The primitive variable finite element formulation is used in a straightforward manner to solve for two turbulent pipe flows. The solution is based on the use of the Nikuradse—van Driest mixing‐length formula but no special wall element is employed. The finite element solutions are compared with experimental results.

Details

Engineering Computations, vol. 6 no. 4
Type: Research Article
ISSN: 0264-4401

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Article

Habib Sammouda, Ali Belghith and Claude Surry

The aim of the present investigation was to study numerically the transient of thermal convection in a square cavity filled with low‐Prandtl‐number fluids. The flow is…

Abstract

The aim of the present investigation was to study numerically the transient of thermal convection in a square cavity filled with low‐Prandtl‐number fluids. The flow is driven by the horizontal temperature gradient between the vertical walls maintained at different temperatures. Two‐dimensional equations of conservation and energy are solved using a finite element method and a fractional step time. The discrete equations systems are solved in the lap of each element‐mesh with the aim of verifying the Boussinesq hypothesis locally. To compare our results with the earlier predictions, we have chosen the fluids for Prandtl‐numbers 0.001, 0.005 and 0.01 and with Grashof numbers up to 1 × 107. To predict the steady state solutions with an oscillary transient period, the results are reduced in terms of the time series average Nusselt‐number at the vertical walls, the velocity at the center of the cavity and near right boundary. In addition, the isotherms and the velocity field are produced with the aim of showing the main circulation and particularly the weak circulations at the corners of the cavity.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 9 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

William J. Weida and Franklin L. Gertcher

Foreign military sales agreements amounted to over 19.5 billion dollars in fiscal year 1982, while the US actually delivered $9 billion in weapons. The US and the Soviet…

Abstract

Foreign military sales agreements amounted to over 19.5 billion dollars in fiscal year 1982, while the US actually delivered $9 billion in weapons. The US and the Soviet Union are the largest arms suppliers in the world, with about 75 per cent of the global export market. France, and then Great Britain, follow with 12 per cent and 5 per cent, respectively. Italy and Israel also export significant dollar amounts of weapons. There is considerable public debate over the wisdom of US participation in this market. Of particular concern is the increased availability of highly sophisticated weapons systems in third world nations.

Details

International Journal of Social Economics, vol. 13 no. 1/2
Type: Research Article
ISSN: 0306-8293

Abstract

The paper published below was prepared by Taylor Ostrander for Frank Knight’s course, Economic Theory, Economics 301, during the Fall 1933 quarter.

Details

Documents from F. Taylor Ostrander
Type: Book
ISBN: 978-0-76231-165-1

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Article

M.A. KAAZ

The theory of pursuit games is obviously fragmentary at present. We know that general determinability of such games is incompatible with analysis, based on the principle…

Abstract

The theory of pursuit games is obviously fragmentary at present. We know that general determinability of such games is incompatible with analysis, based on the principle of time continuity; but we also witness some reasonably successful probing on a smaller scale. The problem is one of existence of winning strategies for quite general sets and spaces. It will be shown here that in one case, where multivalued strategies are used, such strategies must necessarily be subclasses of Polish spaces and in the other, the monovalued case, the loser's set either has to be a first category set in the sense of Baire or an ideal, but in any case a kind of small set. This paper is meant to provide a common topological basis for the appreciation of more recent results.

Details

Kybernetes, vol. 3 no. 4
Type: Research Article
ISSN: 0368-492X

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Article

Muhammad Syukri Salleh and Masudul A. Choudhury

The concept of sustainable development used in this paper is one of generating and maintaining development as a process through the interactions between social and…

Abstract

The concept of sustainable development used in this paper is one of generating and maintaining development as a process through the interactions between social and economic forces. On the side of the social factors influencing development, the focus here is on the human element, which is variously displayed in the process concept. Sometimes, this factor is simply the human resources treated as technologically induced capital, and in which case, the generation of growth is seen as attainment of efficiency derived from the use of human capital. But the more important human factor in sustainable development is the establishment of social justice, moral entitlement and endogeneity of ethics as cause and effect in the process itself. These factors emanate from the premise of human self‐actualization in various ways, and they augment the development process by increasing returns to knowledge as an indigenous experience. Thus, ethics and morality in development constitute the sustaining factors of a development paradigm that becomes truly authentic, not imposed. Among the scenarios of such ethical and moral elements of development is the endogenous role of Islamic values towards describing its socio‐scientific world view.

Details

Humanomics, vol. 12 no. 3
Type: Research Article
ISSN: 0828-8666

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Article

N. Lidbro

THE determination of the shape and position of the various constructional elements in an aircraft must be based on principles different from those used in the case of an…

Abstract

THE determination of the shape and position of the various constructional elements in an aircraft must be based on principles different from those used in the case of an ordinary machine such as, for example, a lathe. In the latter case, the position of the parts in relation to each other can be given by measurements to existing plane base surfaces and centre lines. In aircraft work, on the other hand, where such base surfaces and centre lines are lacking, an attempt was made from the beginning to work with certain imaginary base planes named according to their position in the aircraft, such as datum plane, plane of symmetry, wing datum plane, and so on. This was unsatisfactory, however, and now the conception of co‐ordinates forms the basis for dimensioning.

Details

Aircraft Engineering and Aerospace Technology, vol. 28 no. 11
Type: Research Article
ISSN: 0002-2667

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