Speaker
Description
In many applications, multiple physical scales, both small and large, coexist. This is the case for instance in fluid mechanics and plasma physics. Generally, the smaller scales, generically denoted by ε, have a significant impact on the cost of numerical simulations because, in the absence of specialized schemes, spatial and/or temporal discretizations must resolve the smallest of these scales. As a result, the development of efficient numerical methods for solving such multiscale problems constitutes a major computational challenge.
One way to perform numerical simulations of such models at a reasonable cost is to develop asymptotic-preserving schemes. These schemes are uniformly stable with respect to the parameter ε, making it possible to use meshes that are independent of the smallest scales present. They are said to be asymptotically stable in the limit ε → 0. Moreover, in regions where ε is very small, these schemes recover a discretization of the limiting model obtained as ε tends to zero. They are then said to be asymptotically consistent. Schemes that are both asymptotically stable and consistent are called asymptotic-preserving in the limit ε → 0, because they preserve this limit.
In this presentation, I will focus on a particular scheme that preserves the quasineutral limit for the Vlasov-Poisson equations. This work is a collaboration with Alain Blaustein (INRIA Lille), Giacomo Dimarco (University of Ferrara), and Francis Filbet (University of Toulouse). I will discuss the difficulties associated with this problem, particularly those related to its numerical simulation, and show how asymptotic-preserving schemes make it possible to overcome them.