Numerical approximation of the Euler-Maxwell model in the quasineutral limit

International audienceWe derive and analyze an Asymptotic-Preserving scheme for the Euler-Maxwell system in the quasi-neutral limit. We prove that the linear stability condition on the time-step is independent of the scaled Debye length $\lambda$ when $\lambda \to 0$. Numerical validation performed on Riemann initial data and for a model Plasma Opening Switch device show that the AP-scheme is convergent to the Euler-Maxwell solution when $\Delta x/ \lambda \to 0$ where $\Delta x$ is the spatial discretization. But, when $\lambda /\Delta x \to 0$, the AP-scheme is consistent with the quasi-neutral Euler-Maxwell system. The scheme is also perfectly consistent with the Gauss equation. The possibility of using large time and space steps leads to several orders of magnitude reductions in computer time and storage

Coupled finite element–lattice Boltzmann analysis

A coupled finite element (FE) and lattice Boltzmann (LB) numerical scheme to model the deformation of a porous solid through which fluid flows could offer an attractive solution strategy. As a precursor to a complete simulator, we review the two methodologies and show an initial proof of concept for a coupling method solving one- and multi-dimensional diffusion problems. The accuracy and computational efficiency of the combined method is presented and compared for simple problems that offer analytical solutions. The effects of changing temporal discretisations and diffusivities at the FE–LB interface, as well as iterating towards convergence, are described. The results demonstrate for the first time a transfer of state variables across the FE–LB interface for this class of problems

Assessment of coupling conditions in water way intersections

We present a numerical assessment of coupling conditions in T-junction for water flow in open canals. The mathematical model is based on the well-established shallow water equations for open channel flows. In the present work, the emphasis is given to the description of coupling conditions at canal-to-canal intersections. The accurate prediction of these coupling conditions is essential in order to achieve good performance and reliable numerical simulations of water canals in networks. There exist several theoretical results for coupling conditions in a reduced geometry. The purpose of our work is to numerically verify these conditions for different water flow regimes. More precisely, we consider a local zooming of the T-junction resulting in a two-dimensional flow problem at the canals intersection. A high-order non-oscillatory method is used for solving the governing two-dimensional equations, and the water flow solutions are space-averaged over the junction areas. The obtained are thereafter, used for verification and comparison with the theoretical results. Verifications are conducted for two types of junctions, namely the 1-to-2 and 2-to-1 situations