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In this paper, the design and analysis of high order accurate IMEX finitevolume schemes for the compressible Euler-Poisson (EP) equations in thequasineutral limit is presented. As the quasineutral limit is singular for thegoverning equations, the time discretisation is tantamount to achieving anaccurate numerical method. To this end, the EP system is viewed as adifferential algebraic equation system (DAEs) via the method of lines. As aconsequence of this vantage point, high order linearly semi-implicit (SI) timediscretisation are realised by employing a novel combination of the directapproach used for implicit discretisation of DAEs and, two different classes ofIMEX-RK schemes: the additive and the multiplicative. For both the timediscretisation strategies, in order to account for rapid plasma oscillations inquasineutral regimes, the nonlinear Euler fluxes are split into two differentcombinations of stiff and non-stiff components. The high order scheme resultingfrom the additive approach is designated as a classical scheme while the onegenerated by the multiplicative approach possesses the asymptotic preserving(AP) property. Time discretisations for the classical and the AP schemes areperformed by standard IMEX-RK and SI-IMEX-RK methods, respectively so that thestiff terms are treated implicitly and the non-stiff ones explicitly. In orderto discretise in space a Rusanov-type central flux is used for the non-stiffpart, and simple central differencing for the stiff part. AP property is alsoestablished for the space-time fully-discrete scheme obtained using themultiplicative approach. Results of numerical experiments are presented, whichconfirm that the high order schemes based on the SI-IMEX-RK time discretisationachieve uniform second order convergence with respect to the Debye length andare AP in the quasineutral limit.

High Order Asymptotic Preserving and Classical Semi-implicit RK Schemes for the Euler-Poisson System in the Quasineutral Limit