A Second-Order Accurate Implicit Scheme for Strongly Coupled Fluid Equations Applied to Fluid Electron Turbulence in a Magnetised Plasma

A computational method for treating fluid-type turbulence with strongly coupled equations is outlined and tested. Applied to drift wave turbulence in a magnetised plasma, it is generalisable to other systems. Coupling operators are treated with the second-order accurate scheme DIRK2, in which only values at the current time step are needed to advance the system. Turbulent advection, small-scale dissipation, and weak forcing terms are split apart and treated independently, so that the overall scheme is still first order. Nevertheless, the part that is not second order is that which needs to be resolved in any case. Strict convergence and error testing shows the new scheme to outperform the implicit one previously used with drift wave turbulence by a significant margin.