Recent progress on asymptotic preserving finite-volume methods for fluid models in low-temperature partially-magnetized plasma applications involving instabilities.

Multi-fluid plasma models are able to represent the scale disparity between the different species within plasmas while being theoretically less expensive than kinetic approaches. Nevertheless, stability constraints, which imply that the time step must be smaller than the inverse of the electron plasma frequency and that the mesh size should be below the Debye length, are extremely restrictive and prevent finite volume method from outperforming PIC methods in terms of computational cost. We have recently proposed a series of so-called asymptotic preserving (AP) scheme that remains stable even when these conditions are not met and yield very accurate results even in the low Mach regime for the electrons. This approach thus allows for a significant reduction of the simulation time. Following the same path, we focus in this contribution on the extension to second order of these schemes while maintaining the AP properties, as well as introduce a well-balanced version of the scheme specifically designed to correctly balance the source terms and the convective parts of the equation. Special care is devoted to the implementation of boundary conditions. The approach is assessed through a thorough comparison to reference PIC simulation obtained via the LPPic code.