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A benchmark exercise for the modeling of vertical displacement events (VDEs)is presented and applied to the 3D nonlinear magneto-hydrodynamic codesM3D-C$^1$, JOREK and NIMROD. The simulations are based on a vertically unstableNSTX equilibrium enclosed by an axisymmetric resistive wall with rectangularcross section. A linear dependence of the linear VDE growth rates on theresistivity of the wall is recovered for sufficiently large wall conductivityand small temperatures in the open field line region. The benchmark resultsshow good agreement between the VDE growth rates obtained from linear NIMRODand M3D-C$^1$ simulations as well as from the linear phase of axisymmetricnonlinear JOREK, NIMROD and M3D-C$^1$ simulations. Axisymmetric nonlinearsimulations of a full VDE performed with the three codes are compared andexcellent agreement is found regarding plasma location and plasma currents aswell as eddy and halo currents in the wall.

Axisymmetric simulations of vertical displacement events in tokamaks: A benchmark of M3D-C$^1$, NIMROD and JOREK