Rates of convergence for viscous splitting of the Navier-Stokes equations
J. Thomas Beale,Andrew J. Majda +1 more
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In this paper, error estimates for splitting algorithms are developed which are uniform in the viscosity v as it becomes small for either two or three-dimensional fluid flow in all of space.Citations
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A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow
TL;DR: In this paper, the Lagrange-multiplier-based fictitious domain methods are combined with finite element approximations of the Navier-Stokes equations occurring in the global model to simulate incompressible viscous fluid flow past moving rigid bodies.
Book ChapterDOI
Finite element methods for incompressible viscous flow
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Zero Viscosity Limit for Analytic Solutions, of the Navier-Stokes Equation on a Half-Space.I. Existence for Euler and Prandtl Equations
TL;DR: In this article, the authors prove short time existence theorems for the Euler and Prandtl equations with analytic initial data in either two or three spatial dimensions, using abstract Cauchy-Kowalewski theorem.
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Zero Viscosity Limit for Analytic Solutions of the Navier-Stokes Equation on a Half-Space. II. Construction of the Navier-Stokes Solution
TL;DR: In this article, the Navier-Stokes solution is constructed through a composite asymptotic expansion involving the solutions of the Euler and Prandtl equations, plus an error term.
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Numerical study of slightly viscous flow
TL;DR: In this paper, a numerical method for solving the time-dependent Navier-Stokes equations in two space dimensions at high Reynolds number is presented, where the crux of the method lies in the numerical simulation of the process of vorticity generation and dispersal, using computer-generated pseudo-random numbers.
Journal ArticleDOI
Groups of diffeomorphisms and the motion of an incompressible fluid
David G. Ebin,Jerrold E. Marsden +1 more
TL;DR: In this article, the authors studied the manifold structure of certain groups of diffeomorphisms, and used this structure to obtain sharp existence and uniqueness theorems for the classical equations for an incompressible viscous and non-viscous fluid on a compact C^∞ riemannian, oriented n-manifold, possibly with boundary.