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A numerical solution of the Navier-Stokes equations using the finite element technique
C. Taylor,Paul Hood +1 more
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In this paper, two methods of finite element discretisation are presented, and a comparison of the effeciency of the methods associated with the solution of particular problems is made.Citations
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Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book
TL;DR: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software.
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Stabilized finite element methods. II: The incompressible Navier-Stokes equations
Leopoldo P. Franca,Sérgio Frey +1 more
TL;DR: Stabilized methods are proposed and analyzed for a linearized form of the incompressible Navier-Stokes equations, allowing any combination of velocity and continuous pressure interpolations and generalizing previous works restricted to low-order interpolations.
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An ‘upwind’ finite element scheme for two‐dimensional convective transport equation
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Coupling Fluid Flow with Porous Media Flow
TL;DR: This work proves existence of weak solutions and gives a complete analysis of a finite element scheme which allows a simulation of the coupled problem to be uncoupled into steps involving porous media and fluid flow subproblems.
References
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Boundary layer theory
TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.
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Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100
S. C. R. Dennis,Gau-Zu Chang +1 more
TL;DR: In this article, a finite-difference solution of the equations of motion for steady incompressible flow around a circular cylinder has been obtained for a range of Reynolds numbers from R = 5 to R = 100, where the wake length increases linearly with R over the whole range from the value, just below R = 7, at which it first appears.
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Analytical and numerical studies of the structure of steady separated flows
TL;DR: In this paper, an analytical solution, based on a linearized model, is obtained for an eddy bounded by a circular streamline, which reveals the flow development from a completely viscous eddy at low Reynolds number to an inviscid rotational core at high Reynolds number, in the manner envisaged by Batchelor.
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Curved, isoparametric, “quadrilateral” elements for finite element analysis
TL;DR: In this article, the theory of a new family of isoparametric elements for use in two-dimensional situations is described, and examples illustrating the accuracy improvement are included in the paper.