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Time Scheme (time + scheme)

Distribution by Scientific Domains
Engineering50%

Selected Abstracts

A discrete splitting finite element method for numerical simulations of incompressible Navier,Stokes flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005
Kenn K. Q. Zhang
Abstract The presence of the pressure and the convection terms in incompressible Navier,Stokes equations makes their numerical simulation a challenging task. The indefinite system as a consequence of the absence of the pressure in continuity equation is ill-conditioned. This difficulty has been overcome by various splitting techniques, but these techniques incur the ambiguity of numerical boundary conditions for the pressure as well as for the intermediate velocity (whenever introduced). We present a new and straightforward discrete splitting technique which never resorts to numerical boundary conditions. The non-linear convection term can be treated by four different approaches, and here we present a new linear implicit time scheme. These two new techniques are implemented with a finite element method and numerical verifications are made. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Continuation of travelling-wave solutions of the Navier,Stokes equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2006
Isabel Mercader
Abstract An efficient way of obtaining travelling waves in a periodic fluid system is described and tested. We search for steady states in a reference frame travelling at the wave phase velocity using a first-order pseudospectral semi-implicit time scheme adapted to carry out the Newton's iterations. The method is compared to a standard Newton,Raphson solver and is shown to be highly efficient in performing this task, even when high-resolution grids are used. This method is well suited to three-dimensional calculations in cylindrical or spherical geometries. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Towards a consistent numerical compressible non-hydrostatic model using generalized Hamiltonian tools

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 635 2008
Almut Gassmann
Abstract A set of compressible non-hydrostatic equations for a turbulence-averaged model atmosphere comprising dry air and water in three phases plus precipitating fluxes is presented, in which common approximations are introduced in such a way that no inconsistencies occur in the associated budget equations for energy, mass and Ertel's potential vorticity. These conservation properties are a prerequisite for any climate simulation or NWP model. It is shown that a Poisson bracket form for the ideal fluid part of the full-physics equation set can be found, while turbulent friction and diabatic heating are added as separate ,dissipative' terms. This Poisson bracket is represented as a sum of a two-fold antisymmetric triple bracket (a Nambu bracket represented as helicity bracket) plus two antisymmetric brackets (so-called mass and thermodynamic brackets of the Poisson type). The advantage of this approach is that the given conservation properties and the structure of the brackets provide a good strategy for the construction of their discrete analogues. It is shown how discrete brackets are constructed to retain their antisymmetric properties throughout the spatial discretisation process, and a method is demonstrated how the time scheme can also be incorporated in this philosophy. Copyright © 2008 Royal Meteorological Society [source]

Numerical time schemes for an ocean-related system of PDEs

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2006
M. Petcu
Abstract In this article we consider a system of equations related to the ,-primitive equations of the ocean and the atmosphere, linearized around a stratified flow, and we supplement the equations with transparent boundary conditions. We study the stability of different numerical schemes and we show that for each case, letting the vertical viscosity , go to 0, the stability conditions are the same as the classical CFL conditions for the transport equation. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 [source]