A Landau Fluid Closure for Arbitrary Frequency and Its Implementation in Numerical Code

The perturbed heat flux and temperature for Landau damping case are calculated directly. The relationship between these two physical quantities is the same as Hammett-Perkins’ closure in low frequency limit. Another method to get Landau fluid (LF) closure, such as Chapman-Enskog-like (CEL) method, is analyzed. It shows that the CEL method produces the same closure as that of kinetic method only when background distribution is Maxwellian. To bridge the low and high frequency limit, the harmonic average form of kinetic LF closure is developed which shows that the transport is non-local both on space and time. The harmonic average closure depends on wave frequency and yields a better agreement with kinetic response function than that of Hammett-Perkins’ closure. The implementation in numerical code is also presented, based on an approximation by a sum of diffusion-convection solves (SDCS). The three moment Landau-fluid model has been implemented in the BOUT++ code using the SDCS method for the harmonic average form of LF closure. Good agreement has been obtained for the response function between driven initial-value calculations using this implementation and matrix eigenvalue calculations using SDCS implementation of the LF closure.