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Neumann Condition (neumann + condition)

Distribution by Scientific Domains

Mathematics and Statistics	50%

Selected Abstracts

Using vorticity to define conditions at multiple open boundaries for simulating flow in a simplified vortex settling basin

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2007
A. N. Ziaei
Abstract In this paper a method is developed to define multiple open boundary (OB) conditions in a simplified vortex settling basin (VSB). In this method, the normal component of the momentum equation is solved at the OBs, and tangential components of vorticity are calculated by solving vorticity transport equations only at the OBs. Then the tangential vorticity components are used to construct Neumann boundary conditions for tangential velocity components. Pressure is set to its ambient value, and the divergence-free condition is satisfied at these boundaries by employing the divergence as the Neumann condition for the normal-direction momentum equation. The 3-D incompressible Navier,Stokes equations in a primitive-variable form are solved using the SIMPLE algorithm. Grid-function convergence tests are utilized to verify the numerical results. The complicated laminar flow structure in the VSB is investigated, and preliminary assessment of two popular turbulence models, k,, and k,,, is conducted. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Pressure boundary condition for the time-dependent incompressible Navier,Stokes equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2006
R. L. Sani
Abstract In Gresho and Sani (Int. J. Numer. Methods Fluids 1987; 7:1111,1145; Incompressible Flow and the Finite Element Method, vol. 2. Wiley: New York, 2000) was proposed an important hypothesis regarding the pressure Poisson equation (PPE) for incompressible flow: Stated there but not proven was a so-called equivalence theorem (assertion) that stated/asserted that if the Navier,Stokes momentum equation is solved simultaneously with the PPE whose boundary condition (BC) is the Neumann condition obtained by applying the normal component of the momentum equation on the boundary on which the normal component of velocity is specified as a Dirichlet BC, the solution (u, p) would be exactly the same as if the ,primitive' equations, in which the PPE plus Neumann BC is replaced by the usual divergence-free constraint (, · u = 0), were solved instead. This issue is explored in sufficient detail in this paper so as to actually prove the theorem for at least some situations. Additionally, like the original/primitive equations that require no BC for the pressure, the new results establish the same thing when the PPE approach is employed. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Rotating incompressible flow with a pressure Neumann condition

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2006
Julio R. Claeyssen
Abstract This work considers the internal flow of an incompressible viscous fluid contained in a rectangular duct subject to a rotation. A direct velocity,pressure algorithm in primitive variables with a Neumann condition for the pressure is employed. The spatial discretization is made with finite central differences on a staggered grid. The pressure and velocity fields are directly updated without any iteration. Numerical simulations with several Reynolds numbers and rotation rates were performed for ducts of aspect ratios 2:1 and 8:1. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Energy decay for the wave equation with boundary and localized dissipations in exterior domains

MATHEMATISCHE NACHRICHTEN, Issue 7-8 2005
Jeong Ja Bae
Abstract We study a decay property of solutions for the wave equation with a localized dissipation and a boundary dissipation in an exterior domain , with the boundary ,, = ,0 , ,1, ,0 , ,1 = ,. We impose the homogeneous Dirichlet condition on ,0 and a dissipative Neumann condition on ,1. Further, we assume that a localized dissipation a(x)ut is effective near infinity and in a neighborhood of a certain part of the boundary ,0. Under these assumptions we derive an energy decay like E(t) , C(1 + t),1 and some related estimates. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

A three-dimensional vortex particle-in-cell method for vortex motions in the vicinity of a wall

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2001
Chung Ho Liu
Abstract A new vortex particle-in-cell method for the simulation of three-dimensional unsteady incompressible viscous flow is presented. The projection of the vortex strengths onto the mesh is based on volume interpolation. The convection of vorticity is treated as a Lagrangian move operation but one where the velocity of each particle is interpolated from an Eulerian mesh solution of velocity,Poisson equations. The change in vorticity due to diffusion is also computed on the Eulerian mesh and projected back to the particles. Where diffusive fluxes cause vorticity to enter a cell not already containing any particles new particles are created. The surface vorticity and the cancellation of tangential velocity at the plate are related by the Neumann conditions. The basic framework for implementation of the procedure is also introduced where the solution update comprises a sequence of two fractional steps. The method is applied to a problem where an unsteady boundary layer develops under the impact of a vortex ring and comparison is made with the experimental and numerical literature. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Finite energy solutions of self-adjoint elliptic mixed boundary value problems

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2010
Giles Auchmuty
Abstract This paper describes existence, uniqueness and special eigenfunction representations of H1 -solutions of second order, self-adjoint, elliptic equations with both interior and boundary source terms. The equations are posed on bounded regions with Dirichlet conditions on part of the boundary and Neumann conditions on the complement. The system is decomposed into separate problems defined on orthogonal subspaces of H1(,). One problem involves the equation with the interior source term and the Neumann data. The other problem just involves the homogeneous equation with Dirichlet data. Spectral representations of the solution operators for each of these problems are found. The solutions are described using bases that are, respectively, eigenfunctions of the differential operator with mixed null boundary conditions, and certain mixed Steklov eigenfunctions. These series converge strongly in H1(,). Necessary and sufficient conditions for the Dirichlet part of the boundary data to have a finite energy extension are described. The solutions for a problem that models a cylindrical capacitor is found explicitly. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Homogenization of elliptic problems with the Dirichlet and Neumann conditions imposed on varying subsets

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2007
Carmen Calvo-Jurado
Abstract We study the asymptotic behaviour of the solution un of a linear elliptic equation posed in a fixed domain ,. The solution un is assumed to satisfy a Dirichlet boundary condition on ,n, where ,n is an arbitrary sequence of subsets of ,,, and a Neumman boundary condition on the remainder of ,,. We obtain a representation of the limit problem which is stable by homogenization and where it appears a generalized Fourier boundary condition. We also prove a corrector result. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Global existence of solutions for non-small data to non-linear spherically symmetric thermoviscoelasticity

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2003
J. Gawinecki
Abstract We consider some initial,boundary value problems for non-linear equations of thermoviscoelasticity in the three-dimensional case. Since, we are interested to prove global existence we consider spherically symmetric problem. We examine the Neumann conditions for the temperature and either the Neumann or the Dirichlet boundary conditions for the elasticity equations. Using the energy method, we are able to obtain some energy estimates in appropriate Sobolev spaces enough to prove existence for all time without any restrictions on data. Due to the spherical symmetricity the constants in the above estimates increase with time so the existence for all finite times is proved only. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Iterated Neumann problem for the higher order Poisson equation

MATHEMATISCHE NACHRICHTEN, Issue 1-2 2006
H. Begehr
Abstract Rewriting the higher order Poisson equation ,nu = f in a plane domain as a system of Poisson equations it is immediately clear what boundary conditions may be prescribed in order to get (unique) solutions. Neumann conditions for the Poisson equation lead to higher-order Neumann (Neumann- n ) problems for ,nu = f . Extending the concept of Neumann functions for the Laplacian to Neumann functions for powers of the Laplacian leads to an explicit representation of the solution to the Neumann- n problem for ,nu = f . The representation formula provides the tool to treat more general partial differential equations with leading term ,nu in reducing them into some singular integral equations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]