Roe Solver with Entropy Corrector for Uncertain Hyperbolic Systems

International audienceThis paper deals with intrusive Galerkin projection methods with Roe-type solver for uncertain hyperbolic systems using a finite volume discretization in physical space and a piecewise continuous representation at the stochastic level. The aim of this paper is to design a cost-effective adaptation of the deterministic Dubois and Mehlman corrector to avoid entropy-violating shocks in the presence of sonic points. The adaptation relies on an estimate of the eigenvalues and eigenvectors of the Galerkin Jacobian matrix of the deterministic system of the stochastic modes of the solution and on a correspondence between these approximate eigenvalues and eigenvectors for the intermediate states considered at the interface. Some indicators are derived to decide where a correction is needed, thereby reducing considerably the computational costs. The effectiveness of the proposed corrector is assessed on the Burgers and Euler equations including sonic points

Reported reasons for not using a mosquito net when one is available: a review of the published literature

Background: A review of the barriers to mosquito net use in malaria-endemic countries has yet to be presented in the published literature despite considerable research interest in this area. This paper partly addresses this gap by reviewing one component of the evidence base; namely, published research pertaining to self-reported reasons for not using a mosquito net among net 'owning' individuals. It was anticipated that the review findings would potentially inform an intervention or range of interventions best suited to promoting greater net use amongst this group. Method. Studies were sought via a search of the Medline database. The key inclusion criteria were: that study participants could be identified as owning a mosquito net or having a mosquito net available for use; that these participants on one or more occasions were identified or self-reported as not using the mosquito net; and that reasons for not using the mosquito net were reported. Studies meeting these criteria were included irrespective of mosquito net type. Results: A total of 22 studies met the inclusion criteria. Discomfort, primarily due to heat, and perceived (low) mosquito density were the most widely identified reason for non-use. Social factors, such as sleeping elsewhere, or not sleeping at all, were also reported across studies as were technical factors related to mosquito net use (i.e. not being able to hang a mosquito net or finding it inconvenient to hang) and the temporary unavailability of a normally available mosquito net (primarily due to someone else using it). However, confidence in the reported findings was substantially undermined by a range of methodological limitations and a dearth of dedicated research investigation. Conclusions: The findings of this review should be considered highly tentative until such time as greater quantities of dedicated, well-designed and reported studies are available in the published literature. The current evidence-base is not sufficient in scope or quality to reliably inform mosquito net promoting interventions or campaigns targeted at individuals who own, but do not (reliably) use, mosquito nets

Computing the Matrix Sign and Absolute Value Functions

International audienceWe present two algorithms for the computation of the matrixsign and absolute value functions.Both algorithms avoid a complete diagonalisation of thematrix, but they however require some informations regarding the eigenvalues location.The first algorithm consists in a sequence of polynomial iterations based on appropriate estimates of the eigenvalues, andconverging to the matrix sign if all the eigenvalues are real.Convergence is obtained within a finite number of steps when the eigenvalues are exactly known.Nevertheless, we present a second approach for the computation of the matrix sign and absolute value functions, when the eigenvalues are exactly known.This approach is based on the resolution of an interpolation problem, can handle the case of complex eigenvalues and appears to be faster than the iterative approach

Influence of interfacial pressure on the hyperbolicity of the two-fluid model

International audienceThe two-fluid Model, widely used in the modeling of two phase flows, generally fails to be hyperbolic in its basic formulation.However, it is well known that interfacial forces, bringing new differential terms to the system can make the model hyperbolic.This paper details the effects interfacial pressure has on the hyperbolicity of the two-fluid model, in the general case of two compressiblephases. We characterise the location and topology of the non hyperbolic regions and propose a closure law for the interfacial pressure to makes the system hyperbolic

Strong convergence of nonlinear finite volumemethods for linear hyperbolic systems

International audienceUnlike finite elements methods, finite volume methods are far fromhaving a clear functional analytic setting allowing the proof of generalconvergence results. In, compactness methods were used to deriveconvergence results for the Laplace equation on fairly general meshes.The weak convergence of nonlinear finite volume methods for linear hy-perbolic systems was proven in using the Banach-Alaoglu compactnesstheorem. It allowed the use of general $L^2$ initial data which is consistent with the continuous theory based on the $L^2$ Fourier transform.To our knowledge this was the first convergence results applicable to nondifferentiable initial data. However this weak convergence result seems not optimal with regard of numerical simulations. In this paper we prove that the convergence is indeed strong for a wide class of possibly nonlinear upwinding schemes. The context of our study being multidimensional, we cannot use the spaces $L^1$ and $BV$ classically encountered in the study of 1$D$ hyperbolic systems. We propose instead the use of generalised p-variation function, initially introduced by Wiener and first studied by Young. Thesespaces are compactly embedded in $L^p$. They can therefore fitinto the $L^2$ framework imposed by Brenner obstruction result. Usingestimates of the quadratic variation of the finite volume approximationswe prove the compactness of the sequence of approximations and deducethe strong convergence of the numerical method.We finally discuss the applicability of this approach to nonlinear hyper-bolic systems

Numerical Simulation of an Incompressible Two-Fluid Model

International audienc

Comparison of upwind and centered schemes for low mach number flows

International audienc