A Smooth Transition Approach Between the Vlasov-Poisson and the Euler-Poisson System

摘要

Plasma dynamics is characterized by a wide range of spatial and temporal scales. Typical examples include plasmas produced around hypersonic bodies, ion wind of corona discharges, magnetic fusion processes. Depending on conditions, kinetic models of Boltzmann type or macroscopic models are commonly used for plasma physics simulations. The most common kinetic model for plasmas is the Vlasov equation, coupled with the electromagnetic field equations. On the other hand, Euler or Navier-Stokes based models coupled with the Maxwell equations are used for describing equilibrium plasma flows. Even if fluid models are sufficiently accurate to describe many observed phenomena, however, for some of them, this choice is inadequate. In these cases, it turns out that a kinetic description is strictly necessary to correctly represent the solutions. In these circumstances, the most widely used numerical methods for solving the Vlasov equation are Particle-In-Cell (PIC) approaches. They have many advantages in terms of computational cost for large dimensional problems, for enforcing physical properties such as conservation laws and in terms of flexibility when handling with complex geometries. On the other hand, these methods involve a significant level of numerical noise and the convergence rate is in general quite slow. Moreover, in situations close to thermodynamical equilibrium, the cost of PIC methods or, more in general, direct Monte Carlo simulations increases. For this reason, domain decomposition techniques have been proposed in the recent past (see). Indeed, in many situations, the resolution of the kinetic equations in the whole computational domain is unnecessary because the fluid equations coupled with suitable equations for the electromagnetic fields provide a sufficiently accurate solution, except in small zones like shock layers or extremely rarefied regions where departure from thermodynamical equilibrium is strong.