The Euler-Poisson (EP) system which is a macroscopic hydrodynamic model is commonly used in the mathematical and numerical modelling of plasma flows. The quasineutral limit is singular for the governing equations, therefore, the time discretisation is tantamount towards achieving an accurate numerical method.
In this talk we will present the design and analysis of high order accurate IMEX finite volume schemes for the compressible EP equations in the quasineutral limit the EP system. To this end the EP system is viewed as a differential algebraic equation system (DAEs) via static condensation. As a consequence of this vantage point, high order linearly semi-implicit (SI) time discretisations are realised by employing a novel combination of the direct approach used for implicit discretisation of DAEs and, two different classes of IMEX-RK schemes: the additive and the multiplicative. In order to discretise in space a Rusanov-type central flux is used for the non-stiff part, and simple central differencing for the stiff part. Both the time semi-discrete scheme and the space-time fully discrete scheme are shown to exhibit asymptotic preserving (AP) property. Results of numerical experiments will be showcased, which confirm that the high order schemes based on the SI-IMEX-RK time discretisation achieve uniform second
order convergence with respect to the Debye length and are AP in the quasineutral limit.
