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Number Limit (number + limit)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

Exponential finite elements for diffusion,advection problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2005
Abbas El-Zein
Abstract A new finite element method for the solution of the diffusion,advection equation is proposed. The method uses non-isoparametric exponentially-varying interpolation functions, based on exact, one- and two-dimensional solutions of the Laplace-transformed differential equation. Two eight-noded elements are developed and tested for convergence, stability, Peclet number limit, anisotropy, material heterogeneity, Dirichlet and Neumann boundary conditions and tolerance for mesh distortions. Their performance is compared to that of conventional, eight- and 12-noded polynomial elements. The exponential element based on two-dimensional analytical solutions fails basic tests of convergence. The one based on one-dimensional solutions performs particularly well. It reduces by about 75% the number of elements and degrees of freedom required for convergence, yielding an error that is one order of magnitude smaller than that of the eight-noded polynomial element. The exponential element is stable and robust under relatively high degrees of heterogeneity, anisotropy and mesh distortions. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Modelling and simulation of fires in vehicle tunnels

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2004
I. Gasser
Abstract Applying a low-Mach asymptotic for the compressible Navier,Stokes equations, we derive a new fluid dynamics model,which should be capable to model large temperature differences in combination with the low-Mach number limit. The model is used to simulate fires in vehicle tunnels, where the standard Boussinesq-approximation for the incompressible Navier,Stokes seems to be inappropriate due to the high temperatures developing in the tunnel. The model is implemented using a modified finite-difference approach for the incompressible Navier,Stokes equations and tested in some realistic fire events. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Nonlinear simulations of magnetic Taylor-Couette flow with currentfree helical magnetic fields

ASTRONOMISCHE NACHRICHTEN, Issue 9 2006
J. Szklarski
Abstract Themagnetorotational instability (MRI) in cylindrical Taylor-Couette flow with external helical magnetic field is simulated for infinite and finite aspect ratios. We solve the MHD equations in their small Prandtl number limit and confirm with timedependent nonlinear simulations that the additional toroidal component of the magnetic field reduces the critical Reynolds number from O (106) (axial field only) to O (103) for liquid metals with their small magnetic Prandtl number. Computing the saturated state we obtain velocity amplitudes which help designing proper experimental setups. Experiments with liquid gallium require axial field ,50 Gauss and axial current ,4 kA for the toroidal field. It is sufficient that the vertical velocity uz of the flow can be measured with a precision of 0.1 mm/s. We also show that the endplates enclosing the cylinders do not destroy the traveling wave instability which can be observed as presented in earlier studies. For TC containers without and with endplates the angular momentum transport of the MRI instability is shown as to be outwards. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Hydrodynamic limits with shock waves of the Boltzmann equation

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 3 2005
Shi-Hsien Yu
We show that piecewise smooth solutions with shocks of the Euler equations in gas dynamics can be obtained as the zero Knudsen number limit of solutions of the Boltzmann equation for hard sphere collision model. The construction of the Boltzmann solutions is done in two steps. First we introduce a generalized Hilbert expansion with shock layer correction to construct approximations to the solutions of the Boltzmann equations with small Knudsen numbers. We then apply the recently developed macro-micro decomposition and energy method for Boltzmann shock layers to construct the exact Boltzmann solutions through the stability analysis. © 2004 Wiley Periodicals, Inc. [source]