Detailed modeling of plasmas for computational aerodynamics

As demonstrated by Parent, B., et al., ("Electron and Ion Transport Equations in Computational Weakly-Ionized Plasmadynamics," Journal of Computational Physics, Vol. 259, 2014, pp. 51-69), the computational efficiency of the drift-diffusion plasma model can be increased significantly by recasting the equations such that the potential is obtained fromOhm's law rather than Gauss's law and by adding source terms to the ion transport equations to ensure that Gauss's law is satisfied. Not only did doing so reduce the stiffness of the system, leading to faster convergence, but it also resulted in a higher resolution of the converged solution. The combined gains in convergence acceleration and resolution amounted to a hundredfold increase in computational efficiency when simulating nonneutral plasmas with significant quasi-neutral regions. In this paper, it is shown that such a recast of the drift-diffusion model has yet another advantage: its lack of stiffness permits the electron and ion transport equations to be integrated in coupled form along with the Favre-averaged Navier-Stokes equations. Test cases relevant to plasma aerodynamics (including nonneutral sheaths, magnetic field effects, and negative ions) demonstrate that the proposed coupled system of equations can be converged in essentially the same number of iterations as that describing nonionized flows while not sacrificing the generality of the drift-diffusion model.