4 research outputs found
Three discontinuous Galerkin schemes for the anisotropic heat conduction equation on non-aligned grids
We present and discuss three discontinuous Galerkin (dG) discretizations for
the anisotropic heat conduction equation on non-aligned cylindrical grids. Our
most favourable scheme relies on a self-adjoint local dG (LDG) discretization
of the elliptic operator. It conserves the energy exactly and converges with
arbitrary order. The pollution by numerical perpendicular heat fluxes degrades
with superconvergence rates. We compare this scheme with aligned schemes that
are based on the flux-coordinate independent approach for the discretization of
parallel derivatives. Here, the dG method provides the necessary interpolation.
The first aligned discretization can be used in an explicit time-integrator.
However, the scheme violates conservation of energy and shows up stagnating
convergence rates for very high resolutions. We overcome this partly by using
the adjoint of the parallel derivative operator to construct a second
self-adjoint aligned scheme. This scheme preserves energy, but reveals
unphysical oscillations in the numerical tests, which result in a decreased
order of convergence. Both aligned schemes exhibit low numerical heat fluxes
into the perpendicular direction. We build our argumentation on various
numerical experiments on all three schemes for a general axisymmetric magnetic
field, which is closed by a comparison to the aligned finite difference (FD)
schemes of References [1,2
Magnetic flutter effect on validated edge turbulence simulations
Small magnetic fluctuations () are intrinsically
present in a magnetic confinement plasma due to turbulent currents. While the
perpendicular transport of particles and heat is typically dominated by
fluctuations of the electric field, the parallel stream of plasma is affected
by fluttering magnetic field lines. In particular through electrons, this
indirectly impacts the turbulence dynamics. Even in low beta conditions, we
find that turbulent transport can be reduced by more than a factor
2 when magnetic flutter is included in our validated edge turbulence
simulations of L-mode ASDEX Upgrade. The primary reason for this is the
stabilization of drift-Alfv\'en-waves, which reduces the phase shifts of
density and temperature fluctuations with respect to potential fluctuations.
This stabilization can be qualitatively explained by linear analytical theory,
and appreciably reinforced by the flutter nonlinearity. As a secondary effect,
the steeper temperature gradients and thus higher increase the impact
of the ion-temperature-gradient mode on overall turbulent transport. With
increasing beta, the stabilizing effect on turbulence increases,
balancing the destabilization by induction, until direct electromagnetic
perpendicular transport is triggered. We conclude that including flutter is
crucial for predictive edge turbulence simulations