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

Verification and Benchmarking of the Impurity Transport Solver

I.M. Ivanova-Stanik1, R. Stankiewicz1, R. Zagorski2

1 Institute of Plasma Physics and Laser Microfusion, EURATOM Association, Hery Str, 23, 01-497 Warsaw, Poland
2 EFDA-CSU, Garching, Boltzmannstr. 2,D-85748,Garching , Germany

The Impurity Transport Solver(ITS) was developed within the Integrated Tokamak Modelling Task Force (ITM-TF) Project (IMP#3). ITS solves the 1.5D transport equations for the density of each ionization state for each impurity. The equations are coupled by the ionization and recombination processes. The two numerical method of solving the system of equations are implemented into the code . The first one solves the equation successively for each ionisation stage of impurity. The time interval is split into two half subinterval . In the first half step the equation are solved starting from the low ionisation step to highest ionisation step. In the second half step the 1D equation are solved starting from highest ionisation stage to lowest one. In the second method the splitting methods is used. In the first half time step the 1D equation are solved without the term corresponding to ionisation and recombination. In the second half step only the terms corresponding to atomic processes is taken into account. After the second step the value of the solution closed to the boundary are corrected to satisfy the boundary conditions. The several numerical methods (solver) implemented into ETS can be used for solving each of the equations.

A procedure of verification of ITS for core plasma in tokamak is presented in this contribution. The conservation of particle is checked for both method and all solvers. In order to estimate the error of the solution obtained by various numerical procedures the manufactured solution method is used. The profiles of the density for each ionization state is assumed as given analytical function. Using the equations the artificial extra source term are calculated for which the analytical profiles are exact solution. The numerical solution of the equation with extra source terms are compared with analytical profiles. A series of numerical test has been used to qualified the numerical procedures.