High order asymptotic-preserving penalized numerical schemes for the Euler-Poisson system in the quasineutral limit

In this work, we focus on developing a new class of numerical methods able to handle both quasineutrality and charge separation in plasmas. At large temporal and spatial scales, plasmas tend to be quasineutral, meaning that the local net charge density is nearly zero. However, when the scale at which one observes the plasma dynamics is smaller than the characteristic distance over which the electric field and charges are typically screened, then quasineutrality breaks down. In such regimes, standard numerical methods face severe stability constraints, rendering them practically unusable. To address this issue, in this work, we introduce and analyze a new class of finite volume penalized-IMEX Runge-Kutta methods for the Euler-Poisson system, specifically designed to handle the quasineutral limit. We show that, these proposed schemes are uniformly stable with respect to the Debye length and degenerate into high order methods as the quasineutral limit is approached. Several numerical tests confirm that this new class of methods exhibits the desired properties.