A 2D gyrofluid model for coupled toroidal ITG/ETG multiscale turbulence and its comparison to gyrokinetics*

To study cross-scale interactions and provide a practical test-bed for multi-rate and multi-scale algorithms, we have formulated a reduced 2D toroidal nonlinear gyrofluid model with full FLR effects via Bessel functions. A modified Poisson equation simulates the electron response at both ion and electron scales. These equations are implemented in a pseudo-spectral code with adaptive additive multi-rate Runge-Kutta time integration using the ARKODE[1] library, providing more robust time integration than a naive CFL-constrained RK stepper, with specified accuracy and IMEX hyperviscosity. Toroidal ITG mode linear growth rates are very close to 2D GENE gyrokinetic results for Cyclone-like parameters. Unlike Hasegawa-Mima like models, toroidal ITG and ETG modes are simultaneously unstable. Nonlinear simulations using this reduced model also closely match GENE toroidal ITG heat fluxes and even its nonlinear critical temperature gradient when using a particular closure. In the parameter regime in which the 2D approximation is justified, zonal flows are very strong. Multi-scale simulations are presented, qualitatively comparing 2D phenomena to published 3D results.

[1] A. C. Hindmarsh et al., ACM Transactions on Mathematical Software 31, 3 (2005).