Ambipolar diffusion and drift in computational weakly-ionized plasmadynamics

Modeling of ambipolar diffusion and drift taking place within a weakly-ionized fluid can lead to some convergence difficulties when the ion conservation equation and the electric field potential equation are solved consecutively. A novel formulation of the ion flow rate is proposed here that reduces the computing effort to reach convergence by a factor of 10 or more. It is shown that by recasting the ion flow rate in terms of drift and ambipolar diffusion components, the sensitivity to the electric field is reduced hence alleviating the stiffness of the system of equations and permitting significantly faster convergence. What makes the method particularly appealing is that (i) it yields faster convergence without affecting the accuracy of the converged solution and (ii) it is not restricted to specific discretization or relaxation schemes and can hence be readily implemented in existing flow solvers. Because it is developed in general form (i.e. applicable to a multicomponent plasma in the simultaneous presence of electric current and magnetic and electric fields), the method is notably well-suited to simulate ambipolar diffusion within ionized multi-species flow solvers and is recommended for all flowfields as long as the plasma remains weakly-ionized and quasi-neutral.

► A new form of the ion conservation equation is proposed for a multicomponent plasma.
► The proposed ion equation consists of drift and ambipolar diffusion terms.
► The proposed equation is obtained without modifying the physical model.
► This is shown to reduce the computing effort by ten times or more.
► The method proposed is applicable in the presence of current and magnetic field.