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## Selected Abstracts

### Shape reconstruction of an inverse boundary value problem of two-dimensional Navier,Stokes equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2010
Wenjing Yan
Abstract This paper is concerned with the problem of the shape reconstruction of two-dimensional flows governed by the Navier,Stokes equations. Our objective is to derive a regularized Gauss,Newton method using the corresponding operator equation in which the unknown is the geometric domain. The theoretical foundation for the Gauss,Newton method is given by establishing the differentiability of the initial boundary value problem with respect to the boundary curve in the sense of a domain derivative. The numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible. Copyright © 2009 John Wiley & Sons, Ltd. [source]

### Finite volume method with zonal-embedded grids for cylindrical coordinates

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2006
Yong Kweon Suh
Abstract A zonal-embedded-grid technique has been developed for computation of the two-dimensional Navier,Stokes equations with cylindrical coordinates. As is well known, the conventional regular grid system gives very small grid spacings in the azimuthal direction so it requires a very small time step for a stable numerical solution when the explicit method is used. The fundamental idea of the zonal-embedded-grid technique is that the number of azimuthal grids can be made small near the origin of the coordinates so that the grid size is more uniformly distributed over the domain than with the conventional regular-grid system. The code developed using this technique combined with the explicit, finite-volume method was then applied to calculation of the asymmetric swirl flows and Lamb's multi-polar vortex flows within a full circle and the spin-up flows within a semi-circle. It was shown that the zonal-embedded grids allow a time step far larger than the conventional regular grids. For the case of the Lamb's multi-polar vortex flows, the code was validated by comparing the calculated results with the exact solutions. For the case of the semi-circle spin-up flows, the experimental results were used for the verification. It was seen that the numerical results were in good agreement with the experimental results both qualitatively and quantitatively. Copyright © 2006 John Wiley & Sons, Ltd. [source]

### Coupled lubrication and Stokes flow finite elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2003
Matthew S. Stay
Abstract A method is developed for performing a local reduction of the governing physics for fluid problems with domains that contain a combination of narrow and non-narrow regions, and the computational accuracy and performance of the method are measured. In the narrow regions of the domain, where the fluid is assumed to have no inertia and the domain height and curvature are assumed small, lubrication, or Reynolds, theory is used locally to reduce the two-dimensional Navier,Stokes equations to the one-dimensional Reynolds equation while retaining a high degree of accuracy in the overall solution. The Reynolds equation is coupled to the governing momentum and mass equations of the non-narrow region with boundary conditions on the mass and momentum flux. The localized reduction technique, termed ,stitching,' is demonstrated on Stokes flow for various geometries of the hydrodynamic journal bearing,a non-trivial test problem for which a known analytical solution is available. The computational advantage of the coupled Stokes,Reynolds method is illustrated on an industrially applicable fully-flooded deformable-roll coating example. The examples in this paper are limited to two-dimensional Stokes flow, but extension to three-dimensional and Navier,Stokes flow is possible. Copyright © 2003 John Wiley & Sons, Ltd. [source]

### On the uniqueness of the solution of the two-dimensional Navier,Stokes equation with a Dirac mass as initial vorticity

MATHEMATISCHE NACHRICHTEN, Issue 14 2005
Isabelle Gallagher
Abstract We propose two different proofs of the fact that Oseen's vortex is the unique solution of the two-dimensional Navier,Stokes equation with a Dirac mass as initial vorticity. The first argument, due to C. E. Wayne and the second named author, is based on an entropy estimate for the vorticity equation in self-similar variables. The second proof is new and relies on symmetrization techniques for parabolic equations. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

### On the long-time stability of the Crank,Nicolson scheme for the 2D Navier,Stokes equations

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2007
Florentina Tone
Abstract In this article we study the stability for all positive time of the Crank,Nicolson scheme for the two-dimensional Navier,Stokes equations. More precisely, we consider the Crank,Nicolson time discretization together with a general spatial discretization, and with the aid of the discrete Gronwall lemma and of the discrete uniform Gronwall lemma we prove that the numerical scheme is stable, provided a CFL-type condition is satisfied. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 [source]