Nektar-Driftwave

Nektar-Driftwave solves the 2D Hasegawa-Wakatani equations describing drift-wave turbulence. The equations are, for vorticity \(\zeta \), number density perturbation \(n\), and electrostatic potential \(\phi \),

\begin{eqnarray} \frac {\partial \zeta }{\partial t}+[\phi , \zeta ] &=& \alpha (\phi -n)\\ \frac {\partial n}{\partial t} +[\phi ,n] &=& \alpha (\phi -n)-\kappa \frac {\partial \phi }{\partial y}, \end{eqnarray}

where \([a,b] \equiv \frac {\partial a}{\partial x} \frac {\partial b}{\partial y} - \frac {\partial a}{\partial y} \frac {\partial b}{\partial x}\).

In the above, \(\alpha \) is the adiabaticity operator (taken to be constant) and \(\kappa \) is the background density gradient scale length. The electrostatic potential is related to the vorticity by Poisson’s equation \(\nabla ^2 \phi = \zeta \).

The main system is implemented as an advection problem using a discontinuous Galerkin formulation which provides numerical stabilization meaning that the usual hyperviscosity term is not required. The Poisson solve is implemented in a continuous Galerkin formulation.

The example provided tracks the nonlinear evolution of an initial Gaussian spatial density perturbation to a turbulent quasi-steady state. See the internal report ref. [77] for a presentation of the output and a comparison with published results.

Nektar-Driftwave is publicly available at https://github.com/ExCALIBUR-NEPTUNE/nektar-driftwave.