Asymptotic Preserving IMEX Time Integrators for Low Mach Number Hydrodynamics and Quasi neutral Plasma

In this talk we consider some sound-proof models of the compressible Euler equations of atmospheric flows and the quasineutral model of the Euler-Poisson equations of plasma fluids. All these models can be obtained as singular limits of the governing hydrodynamic equations. Therefore, robust numerical approximation of the limits is a challenging task. We design and analyse numerical schemes for the singularly perturbed fluid equations in the so-called asymptotic preserving (AP) framework. For atmospheric flow equations the time discretisation is realised by using the additive implicit-explicit (IMEX) Runge-Kutta (RK) methods and the space discretisation by a finite volume technique. Uniform stability and accuracy throughout the asymptotic regime, and the compliance with the transition of governing equations are established for the proposed schemes. For the equations of plasma fluids a more general set of IMEX-RK methods called the semi- implicit (SI)-IMEX-RK methods are employed, where the PDEs are envisaged as differential algebraic equations (DAEs) via the method of lines. The proposed schemes are shown to be  asymptotically consistent with the singular limit. The results of numerical case studies demonstrate the robustness and efficacy of the schemes under consideration.