Lower and upper bounds for the Rayleigh conductivity of a perforation in a thick plate are usually derived from intuitive approximations and by physical reasoning. This paper addresses a mathematical justification of these approaches. As a byproduct of the rigorous handling of these issues, some improvements to previous bounds for axisymmetric holes are given as well as new estimates for tilted perforations. The main techniques are a proper use of the Dirichlet and Kelvin variational principlesin...
In this note, we give an overview of the authors’ paper [6] which deals with asymptotic consistency of a class of linearly implicit schemes for the compressible Euler equations. This class is based on a linearization of the nonlinear fluxes at a reference state and includes the scheme of Feistauer and Kučera [3] as well as the class of RS-IMEX schemes [8,5,1] as special cases. We prove that the linearization gives an asymptotically consistent solution in the low-Mach limit under the assumption of...
We present an efficient approach for reducing the statistical uncertainty
associated with direct Monte Carlo simulations of the Boltzmann equation.
As with previous variance-reduction approaches, the resulting relative
statistical uncertainty in hydrodynamic quantities (statistical uncertainty normalized by the
characteristic value of quantity of interest) is small
and independent of the magnitude of the deviation from equilibrium,
making the simulation of arbitrarily small deviations from equilibrium
possible....
We discuss a numerical formulation for the cell problem related to a homogenization approach for the study of wetting on micro rough surfaces. Regularity properties of the solution are described in details and it is shown that the problem is a convex one. Stability of the solution with respect to small changes of the cell bottom surface allows for an estimate of the numerical error, at least in two dimensions. Several benchmark experiments are presented and the reliability of the numerical solution...
FreeFem++ [11] is a software for the numerical solution of partial differential
equations. It is based on finite element method. The FreeFem++ platform aims at
facilitating teaching and basic research through prototyping. For the moment this platform
is restricted to the numerical simulations of problems which admit a variational
formulation. Our goal in this work is to evaluate the FreeFem++ tool on basic magnetic
equations arising in Fusion Plasma...