**Topic/Type**:
2.4 Gyro-kinetic and gyro-fluid methods, Oral

**
W. Arter ^{1}, M. A. Barnes^{1}, C. M. Roach^{1}, N. J. Hammer^{2}, R. Hatzky^{2}
**

*
^{1} EURATOM/UKAEA Fusion Association^{2} High Level Support Team (HLST), Max-Planck-Institut f\"ur Plasmaphysik
*

GS2 is a time-dependent 5-D gyrokinetic fluid code extensively

validated for fusion work and widely used on HPC facilities for the

simulation of plasma turbulence, in particular for predicting tokamak transport.

Inefficiencies identified in a previous study

by Belli [1] will be addressed by a programme of work designed ultimately

to deliver improvements in GS2 accuracy and speed of execution.

Belli showed that two related issues, choice of (1) discretisation and (2)

solver for the Boltzmann

equation, needed to be addressed. These issues are common to a wide set of

compute-intensive transport

codes, including software for neutron transport [2] and radiative transport [3].

However, the plasma problem is

more general since aside from its nonlinearity, in the language of radiation

transport it is highly anisotropic, whereas most transport problems have no

or weak anisotropy and algorithms tend to exploit this property to produce

so-called multi-group energy discretisations.

Discontinuous Galerkin (DG) schemes are relatively new. However, DG

has been successfully implemented in the commercially available

Attila\textregistered [4] software for solving the (linear) Boltzmann equation.

DG has the important property for HPC that each element has data which is

minimally coupled to other elements.

Results for DG applied to a 1-D model

advection problem are compared with those from a number of popular, high

order schemes, and demonstrate the good accuracy of the method. Results for a 2-D

model Boltzmann test problem will also be presented.

Work partly funded by UK EPSRC and EURATOM

[1] E.A. Belli. \textit{Studies of Numerical Algorithms for Gyrokinetics and

the Effects of Shaping on Plasma Turbulence}.

PhD thesis, Princeton University, 2006.

{\tt http://w3.pppl.gov/~hammett/gyrofluid/papers/2006/thesis-belli.pdf}.

[2] M.L. Adams and E.W.~Larsen.

\textit{Progress in Nuclear Energy}, 40(1):3--159, 2002.

[3] E.~Meinkohn, G.~Kanschat, R.~Rannacher, and R.~Wehrse.

In J\"ager, W. and Rannacher, R. and

Warnatz, J., editors, \textit{Reactive Flows, Diffusion and Transport}, pages

485--526. Springer, 2007.

[4] Transpire Inc., http://www.transpireinc.com/