  An algorithm of particle-in-cell simulations is described and tested to aid
further the actual design of simple vircators working on axially symmetric
modes. The methods of correction of the numerical solution, have been chosen
and jointly tested, allow the stable simulation of the fast nonlinear multiflow
dynamics of virtual cathode formation and evolution, as well as the fields
generated by the virtual cathode. The selected combination of the correction
methods can be straightforwardly generalized to the case of axially
nonsymmetric modes, while the parameters of these correction methods can be
widely used to improve an agreement between the simulation predictions and the
experimental data.
