A fully-implicit finite-volume method for multi-fluid reactive and collisional magnetized plasmas on unstructured meshes.

*(English)*Zbl 1349.76299Summary: We present a Finite Volume scheme for solving Maxwell’s equations coupled to magnetized multi-fluid plasma equations for reactive and collisional partially ionized flows on unstructured meshes. The inclusion of the displacement current allows for studying electromagnetic wave propagation in a plasma as well as charge separation effects beyond the standard magnetohydrodynamics (MHD) description, however, it leads to a very stiff system with characteristic velocities ranging from the speed of sound of the fluids up to the speed of light. In order to control the fulfillment of the elliptical constraints of the Maxwell’s equations, we use the hyperbolic divergence cleaning method. In this paper, we extend the latter method applying the CIR scheme with scaled numerical diffusion in order to balance those terms with the Maxwell flux vectors. For the fluids, we generalize the \(AUSM^{+}\)-up to multiple fluids of different species within the plasma. The fully implicit second-order method is first verified on the Hartmann flow (including comparison with its analytical solution), two ideal MHD cases with strong shocks, namely, Orszag-Tang and the MHD rotor, then validated on a much more challenging case, representing a two-fluid magnetic reconnection under solar chromospheric conditions. For the latter case, a comparison with pioneering results available in literature is provided.

##### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |

76W05 | Magnetohydrodynamics and electrohydrodynamics |

76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |

82C80 | Numerical methods of time-dependent statistical mechanics (MSC2010) |

82D10 | Statistical mechanics of plasmas |

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\textit{A. Alvarez Laguna} et al., J. Comput. Phys. 318, 252--276 (2016; Zbl 1349.76299)

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