We present a novel artificial viscosity for staggered Lagrangian schemes in 2D axi-symmetric r-z geometry on logically rectangular grids. The suggested viscous force is dissipative by construction, conserves both components of momentum, and preserves spherical symmetry on an equiangular polar grid. This method turns out to be robust and performs well for spherically symmetric problems on various grid types (symmetric, perturbed polar, rectangular), without any need for tinkering with problem-dependent or grid-dependent parameters. The results are compared with the outcome of the area-weighted approach using the popular tensor viscosity by Campbell and Shashkov. Copyright © 2014 John Wiley & Sons, Ltd.