A Landau-fluid closure for arbitrary frequency response

The kinetic Landau-fluid (LF) closure which can be regarded as the exact closure is derived. For Maxwellian plasma, the kinetic closure is the same as Hammett-Perkins closure in static limit and totally the same with Chang-Callen closure. A new LF closure for arbitrary frequency response constructed with harmonic average technique is presented in this paper. This new LF closure bridges the existing LF closures in the low and high frequency limits: it recovers Hammett-Perkins closure when weight coefficient κ = 0 and converges to Chang-Callen closure at high frequency when weight coefficient κ = 1. By picking an appropriate κ, the harmonic average closure contains both nonlocal transport and local transport and the resulting fluid response function of a three moment fluid model well matches the exact kinetic response function within the entire frequency range. On the computational side, a sum of diffusion-convection solves (SDCS) method is developed to facilitate numerical implementation of the harmonic average LF closure. By using SDCS method, good agreement is achieved for the response functions between driven initial-value simulations and matrix eigenvalue calculations within the BOUT++ framework. The harmonic average closure of shifted-Maxwellian is also outlined.