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This paper presents improvement and performance evaluation of the “perturbation source method”, which is one of the Monte Carlo perturbation techniques. The formerly proposed perturbation source method was first-order accurate, although it is known that the method can be easily extended to an exact perturbation method. A transport equation for calculating an exact flux difference caused by a perturbation is solved. A perturbation particle representing a flux difference is explicitly transported in the perturbed system, instead of in the unperturbed system. The source term of the transport equation is defined by the unperturbed flux and the cross section (or optical parameter) changes. The unperturbed flux is provided by an “on-the-fly” technique during the course of the ordinary fixed source calculation for the unperturbed system. A set of perturbation particle is started at the collision point in the perturbed region and tracked until death. For a perturbation in a smaller portion of the whole domain, the efficiency of the perturbation source method can be improved by using a virtual scattering coefficient or cross section in the perturbed region, forcing collisions. Performance is evaluated by comparing the proposed method to other Monte Carlo perturbation methods. Numerical tests performed for a particle transport in a two-dimensional geometry reveal that the perturbation source method is less effective than the correlated sampling method for a perturbation in a larger portion of the whole domain. However, for a perturbation in a smaller portion, the perturbation source method outperforms the correlated sampling method. The efficiency depends strongly on the adjustment of the new virtual scattering coefficient or cross section.

We present in this paper a spectrally accurate numerical method for computing the spherical/vector spherical harmonic expansion of a function/vector field with given (elemental) nodal values on a spherical surface. Built upon suitable analytic formulas for dealing with the involved highly oscillatory integrands, the method is robust for high mode expansions. We apply the numerical method to the simulation of three-dimensional acoustic and electromagnetic multiple scattering problems. Various numerical evidences show that the high accuracy can be achieved within reasonable computational time. This also paves the way for spectral-element discretization of 3D scattering problems reduced by spherical transparent boundary conditions based on the Dirichlet-to-Neumann map.

International audience; The shallow water magnetohydrodynamic system involves several families of physically relevant steady states. In this paper we design a well-balanced numerical scheme for the one-dimensional shallow water magnetohydrodynamic system with topography, that resolves exactly a large range of steady states. Two variants are proposed with slightly different families of preserved steady states. They are obtained by a generalized hydrostatic reconstruction algorithm involving the magnetic field and with a cutoff parameter to remove singularities. The solver is positive in height and semi-discrete entropy satisfying, which ensures the robustness of the method.

International audience; Homogenization of a thin micro-structure yields effective jump conditions that incorporate the geometrical features of the scatterers. These jump conditions apply across a thin but nonzero thickness interface whose interior is disregarded. This paper aims (i) to propose a numerical method able to handle the jump conditions in order to simulate the homogenized problem in the time domain, (ii) to inspect the validity of the homogenized problem when compared to the real one. For this purpose, we adapt the Explicit Simplified Interface Method originally developed for standard jump conditions across a zero-thickness interface. Doing so allows us to handle arbitrary-shaped interfaces on a Cartesian grid with the same efficiency and accuracy of the numerical scheme than those obtained in an homogeneous medium. Numerical experiments are performed to test the properties of the numerical method and to inspect the validity of the homogenization problem.

The e ciency of algorithms for solving nonlinear equations is a measure of comparison between di erent iterative methods. In the case of scalar equations two parameters are considered as it is well-known, but frequently in recent literature inaccurate generalizations combining these parameters are used when solving systems of nonlinear equations. Our goal in this paper is to clarify the concept of the e ciency in the multi-dimensional case. To do it we present a detailed de nition of the computational e ciency. The relation between the e ciency parameters in scalar and vectorial cases is analyzed in detail and tested in two numerical examples

Parametric vibrations can be observed in cable-stayed bridges due to periodic excitations caused by a deck or a pylon. The vibrations are described by an ordinary differential equation with periodic coefficients. The paper focuses on random excitations, i.e. on the excitation amplitude and the excitation frequency which are two random variables. The excitation frequency ωL is discretized to a finite sequence of representative points, ωL,i Therefore, the problem is (conditionally) formulated and solved as a one-dimensional polynomial chaos expansion generated by the random excitation amplitude. The presented numerical analysis is focused on a real situation for which the problem of parametric resonance was observed (a cable of the Ben-Ahin bridge). The results obtained by the use of the conditional polynomial chaos approximations are compared with the ones based on the Monte Carlo simulation (truly two-dimensional, not conditional one). The convergence of both methods is discussed. It is found that the conditional polynomial chaos can yield a better convergence then the Monte Carlo simulation, especially if resonant vibrations are probable.

International audience; In this paper we develop and study numerically a model to describe some aspects of sound propagation in the human lung, considered as a deformable and viscoelastic porous medium(the parenchyma) with millions of alveoli filled with air. Transmission of sound through the lung above 1 kHz is known to be highly frequency-dependent. We pursue the key idea that the viscoelastic parenchyma structure is highly heterogeneous on the small scale ε and use two-scale homogenization techniques to derive effective acoustic equations for asymptotically small ε. This process turns out to introduce new memory effects. The effective material parameters are determined from the solution of frequency-dependent micro-structure cell problems. We propose a numerical approach to investigate the sound propagation in the homogenized parenchyma using a Discontinuous Galerkin formulation.Numerical examples are presented.

A crucial property of second order fluid models is the behaviour of the fluid level at the boundaries. Two cases have been considered: the reflecting and the absorbing boundary. This paper presents an approach for the stationary analysis of second order fluid models with any combination of boundary behaviours. The proposed approach is based on the solution of a linear system whose coefficients are obtained from a matrix exponent. A practical example demonstrates the suitability of the technique in performance modeling.

WOS: 000252955800001, In order to enhance heat transfer between primary surface and the environment, radiating extended surfaces are commonly utilized. Especially in the case of large temperature differences, variable thermal conductivity has a strong effect on performance of such a surface. In this paper, variational iteration method is used to analyze convective straight and radial fins with temperature-dependent thermal conductivity. In order to show the efficiency of variational iteration method (VIM), the results obtained from VIM analysis are compared with previously obtained results using Adomian decomposition method (ADM) and the results from finite element analysis. VIM produces analytical expressions for the solution of nonlinear differential equations. However, these expressions obtained from VIM must be tested with respect to the results obtained from a reliable numerical method or analytical solution. This work assures that VIM is a promising method for the analysis of convective straight and radial fin problems. Copyright (C) 2007.