Linear relaxation to planar Travelling Waves in Inertial Confinement Fusion

We study linear stability of planar travelling waves for a scalar reaction-diffusion equation with non-linear anisotropic diffusion. The mathematical model is derived from the full thermo-hydrodynamical model describing the process of Inertial Confinement Fusion. We show that solutions of the Cauchy problem with physically relevant initial data become planar exponentially fast with rate s(\eps',k)>0, where \eps'=\frac{T_{min}}{T_{max}}\ll 1 is a small temperature ratio and $k\gg 1$ the transversal wrinkling wavenumber of perturbations. We rigorously recover in some particular limit (\eps',k)\rightarrow (0,+\infty) a dispersion relation s(\eps',k)\sim \gamma_0 k^{\alpha} previously computed heuristically and numerically in some physical models of Inertial Confinement Fusion

Contributions to the Mathematical Technology Transfer with Finite Volume Methods

[Abstract:] At the early 1980s, the research group in Mathematical Engineering, mat+i, started working on finite volume methods for the simulation of environmental issues concerning Galician rias (Spain). The focus was on the study of hyperbolic balance laws due to the presence of source terms related to the bathymetry. A correct treatment of these terms, an upwind discretization, was presented in [2, 7, 22]. The transfer of this knowledge has motivated the registration of the software Iber (http://www.iberaula.es). Latterly, under different research problems, we have been working on the development of a numerical algorithm for the resolution of Euler and Navier–Stokes equations. A hybrid projection finite volume/finite element method is employed making use of unstructured staggered grids (see [3, 9]). To attain second order of accuracy ADER methodology is employed [10]. On the other hand, with numerical simulation of gas transportation networks in view, a first-order well balanced finite volume scheme for the solution of a model, for the flow of a multicomponent gas in a pipe on non-flat topography, is introduced. The mathematical model consists of Euler equations, with source terms, coupled with the mass conservation equations of species. We propose a segregated scheme in which Euler and species equations are solved separately [6].The authors are indebted to E.F. Toro, from the Laboratory of Applied Mathematics, University of Trento, for the useful discussions on the subject. This project was partially supported by Spanish MECD, grant FPU13/00279; by Xunta de Galicia, grant PRE/2013/031; by Spanish MICINN projects MTM2013-43745-R and MTM2017-86459-R; by Xunta de Galicia and FEDER under project GRC2013-014 and by Fundación Barrié; by the Reganosa company.Xunta de Galicia; PRE/2013/031Xunta de Galicia; GRC2013-01

Waveform Modelling for the Laser Interferometer Space Antenna

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from communit

Nonlinear corrector for Reynolds‐averaged Navier‐Stokes equations

International audienceThe scope of this paper is to present a nonlinear error estimation and correction for Navier-Stokes and Reynolds-averaged Navier-Stokes equations. This nonlinear corrector enables better solution or functional output predictions at fixed mesh complexity and can be considered in a mesh adaptation process. After solving the problem at hand, a corrected solution is obtained by solving again the problem with an added source term. This source term is deduced from the evaluation of the residual of the numerical solution interpolated on the h/2 mesh. To avoid the generation of the h/2 mesh (which is prohibitive for realistic applications), the residual at each vertex is computed by local refinement only in the neighborhood of the considered vertex. One of the main feature of this approach is that it automatically takes into account all the properties of the considered numerical method. The numerical examples point out that it successfully improves solution predictions and yields a sharp estimate of the numerical error. Moreover, we demonstrate the superiority of the nonlinear corrector with respect to linear corrector that can be found in the literature