An efficient algorithm for axisymmetrical 2D fluid

We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of multigrid method with respect to the number of grid points allowed us to use $256\times 256$ grid, where we could achieve solutions in several minutes. Time limitations due to nonlinearity of the system are partially avoided by using multi level grids. In other words the initial solution on $256\times 256$ grid was the extrapolated, steady solution from $128\times 128$ grid which allowed using ``long'' integration time steps. The fluid solver is used as the basis for hybrid codes for DC discharges.