On finite-difference approximations to steady-state solutions of the Navier-Stokes equations
A. Krzywicki (1968)
Colloquium Mathematicae
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Displaying similar documents to “On Numerical Methods for the Stokes Problem”
On finite-difference approximations to steady-state solutions of the Navier-Stokes equations
Analytical solution of Stokes flow near corners and applications to numerical solution of Navier-Stokes equations with high precision
Burda, Pavel, Novotný, Jaroslav, Šístek, Jakub
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We present analytical solution of the Stokes problem in 2D domains. This is then used to find the asymptotic behavior of the solution in the vicinity of corners, also for Navier-Stokes equations in 2D. We apply this to construct very precise numerical finite element solution.
Vorticity dynamics and numerical Resolution of Navier-Stokes Equations
Matania Ben-Artzi, Dalia Fishelov, Shlomo Trachtenberg (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We present a new methodology for the numerical resolution of the hydrodynamics of incompressible viscid newtonian fluids. It is based on the Navier-Stokes equations and we refer to it as the vorticity projection method. The method is robust enough to handle complex and convoluted configurations typical to the motion of biological structures in viscous fluids. Although the method is applicable to three dimensions, we address here in detail only the two dimensional case. We provide numerical...
On a new finite-difference scheme for the non-stationary Navier-Stokes equations
A. Krzywicki (1968)
Colloquium Mathematicae
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The Convergence of two Numerical Schemes for the Navier-Stokes Equations.
E. Fernandez-Cara, Mercedes M. Beltran (1987)
Numerische Mathematik
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Numerical simulation of a viscoelastic fluid with a preconditioned Schwarz method
Luís Borges, Adélia Sequeira (2008)
Banach Center Publications
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In this paper we apply a domain decomposition method to approach the solution of a non-Newtonian viscoelastic Oldroyd-B model. The numerical scheme is based on a fixed-point argument applied to the original non-linear system of partial differential equations decoupled into a Navier-Stokes system and a tensorial transport equation. Using a modified Schwarz algorithm, involving block preconditioners for the Navier-Stokes equations, the decoupled problems are solved iteratively. Numerical...
An application of the BDDC method to the Navier-Stokes equations in 3-D cavity
Hanek, Martin, Šístek, Jakub, Burda, Pavel
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We deal with numerical simulation of incompressible flow governed by the Navier-Stokes equations. The problem is discretised using the finite element method, and the arising system of nonlinear equations is solved by Picard iteration. We explore the applicability of the Balancing Domain Decomposition by Constraints (BDDC) method to nonsymmetric problems arising from such linearisation. One step of BDDC is applied as the preconditioner for the stabilized variant of the biconjugate gradient...
On a finite element method application in aeroelasticity
Sváček, Petr
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The subject of this paper is the numerical simulation of aeroelastic problems. The interaction of two-dimensional incompressible viscous flow and a vibrating airfoil is modelled. The solid airfoil, which can rotate around the elastic axis and oscillate in the vertical direction, is considered. The numerical simulation consists of the finite element solution of the Navier-Stokes equations coupled with the system of ordinary differential equations describing the airfoil motion. The stabilization...