Topic/Type: 1.2 Fusion Plasmas (magnetic & inertial confinement), Poster

### Verification of the European Transport Solver for Transport Barrier

R. Stankiewicz1, D. P. Coster2, A. Figueiredo3, D. Kalupin4, G.Pereverzov2, M. Tokar5, D. Twar?g6, R. Zagorski4

1 Institute of Plasma Physics and Laser Microfusion, Euroatom Association, Warsaw, Poland
2 Max-Planck Institute fur Plasmaphysics, Euroatom-IPP Association, Garching,Germany
3 Centro de Fusade Nuclear, ITS Euroatom Association,Lisbone, Portugal
4 EFDA-CSU, Garching,Germany
5 Institute fur Energieforschung, Euroatom Association, Julich, Germany
6 The Henryk Niewodniczanski Institute of Nuclear Physics, Krakow, Poland

In the frame of European Integrated Tokamak Modeling Task Force the 1.5D transport code (ETS) has been developed. The several numerical methods (solvers) solving the transport equations has been incorporated into ETS. The verification of the ETS solvers for the strongly non linear stiff problem connected with the transport barrier dynamics is presented in the contribution. For the edge transport barrier the simple model of transport is assumed. The heat conductivity change abruptly when the temperature e-folding length $\small L$ approaches the critical value $\small L_{cr}$ ($\small k=k_{0}$ for $\small L> L_{cr}$ and $\small k=k_{1}\ll k_{0}$ for $\small L< L_{cr}$).

The method of verification is based on manufactured solution method. The analytical form of temperature profile $\small T(r, t)$ is constructed with following properties. The function is continuous and the continuity condition of the heat fluxes at critical point is satisfied. The time dependent critical point $\small r_{cr}(t)$ corresponding to jump of the heat conductivity is defined by the relation $\small L(r,t) = L_{cr}$. Moreover the temperature profile $\small T(r,t)$ is defined in such a way that $\small L(r,t)$ satisfy the condition: $\small L(r,t)> L_{cr}$ for $\small r< r_{cr}(t)$ and $\small L(r,t) for $\small r> r_{cr}(t)$. Using the assumed temperature profile, transport coefficients and geometrical coefficients also assumed as given analytical function the values of the source term at the mesh points can calculated at any time. With the calculated sources term the numerical solution can be find and compare with the analytical one. This the error produced by numerical method can be evaluated exactly. The various analytical profiles of the temperatures corresponding to various heating profiles has been analyzed. The described procedure takes consistently into account y the nonlinear coupling terms describing the heat exchange between electrons and ions due to the collision.