Orateur
Marie-helene Vignal
(Institut de Mathématiques de Toulouse, Université Toulouse 3 - Paul Sabatier)
Description
In this presentation, I will begin by explaining the objectives and underlying principles of asymptotic-preserving schemes. I will then focus on two specific cases: schemes that preserve the low Mach number limit for the Euler equations, and schemes that preserve the quasi-neutral limit for the Vlasov–Poisson equations. I will discuss the main challenges in simulating these problems numerically, and show how asymptotic-preserving schemes can overcome them. Such schemes are uniformly stable in the considered limit allowing time steps that do not tend to zero in the asymptotic regime. Moreover, they preserve the asymptotic limit, giving an accurate approximation of the corresponding reduced model in the limit.