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doi: 10.1002/fld.1650041102pmid: N/A
In this paper the pressure method for incompressible fluid flow simulation is extended and applied to the numerical simulation of compressible fluid flow. The governing equations, obtained from the physical principles of conservation of momentum, mass and energy, are first studied from a characteristic point of view. Then they are discretized with a semi‐implicit finite difference technique in such a fashion that stability is achieved independently of the speed of sound. The resulting algorithm is fast, accurate and particularly efficient in subsonic flow calculations. As an example, the computer simulation of the von Kármán vortex street is described and discussed.
Carey, Graham F.; Utku, Mehmet
doi: 10.1002/fld.1650041103pmid: N/A
A finite element method for solution of the stream function formulation of Stokes flow is developed. The method involves complete cubic non‐conforming (C0) triangular Hermite elements. This element fails the patch test. To correct the element and produce a convergent method we employ a penalty method to weakly enforce the desired continuity constraint on the normal derivative across the inter‐element boundaries. Successful use of the method is demonstrated to require reduced integration of the inter‐element penalty with a 1‐point Gauss rule. Error estimates relate the optimal choice of penalty parameter to mesh size and are corroborated by numerical convergence studies. The need for reduced integration is interpreted using rank relations for an associated hybrid method.
Albanese, R.; Grasso, F.; Meola, C.
doi: 10.1002/fld.1650041104pmid: N/A
In the present work the viscous (low Reynolds) flow in plane ducts confined by permeable walls has been studied. A simple model of the filtrating walls has been used, with the normal velocity component proportional to the pressure jump across the wall, resulting in a non‐standard boundary value Navier‐Stokes problem. A critical analysis of the appropriate boundary condition and pressure problem has led to the conclusions of employing a simple explicit finite volume approach, and of avoiding the use of higher order finite difference schemes. In this paper a special emphasis on the structure of the involved computational matrices has been given to illustrate the chosen algorithm. The latter yields a steady state solution that is second order accurate in space, and it has an accuracy in time of order ≤ Δt (the time step), due to the explicit treatment of the velocity boundary conditions along the membrane. The model has been tested to study the effects of the inlet/outlet conditions, Reynolds number and filtrating wall constant.
Löhner, R.; Morgan, K.; Zienkiewicz, O. C.
doi: 10.1002/fld.1650041105pmid: N/A
The difficulties experienced in the treatment of hyperbolic systems of equations by the finite element method (or other) spatial discretization procedures are well known. In this paper a temporal discretization precedes the spatial one which in principle is considered along the characteristics to achieve a self adjoint form. By a suitable expansion, the original co‐ordinates are preserved and combined with the use of a standard Galerkin process to achieve an accurate discretization. It is shown that the process is equivalent to the Taylor‐Galerkin methods of Donea.17 Several examples illustrate the accuracy and efficiency attainable in such problems as transport, shallow water equations, transonic flow etc.
Van Schaftingen, J. J.; Crochet, M. J.
doi: 10.1002/fld.1650041106pmid: N/A
The proficiency of available mixed methods for solving the flow of a Maxwell fluid is evaluated through their application to the same problem. The reasons for the usual degeneracy of the numerical results beyond some level of elasticity are investigated. The best‐performing technique is applied to the flow through an abrupt 4/1 contraction.
doi: 10.1002/fld.1650041107pmid: N/A
The aim of this contribution is to investigate the consistency and order of accuracy of different control surfaces used for finite area blade‐to‐blade flow calculations. The following cases will be treated: a hexagonal element, a trapezoidal element, a bitrapezoidal element and a quadrilateral element. Finally, the consistency conditions will be discussed and compared with respect to a cascade flow application.
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