How to deal with discontinuous heterogeneous data in 2D geometry

I am trying to model two phase flow in a 2-D porous media. There are four types of sands in the domain and thus four different entry capillary pressure. The variation of the capillary pressure becomes steep and thus non differentiable at the interfaces(as indicated in the attached photo) hindering the convergence of model.

Please let me know how can I smoothen the variance of this pressure at the different interfaces. I have tried step function, but it apparently smoothens the parameter with respect to single dimension(i.e either t or x or y). I am looking for a function or method which could smoothen it at all the interfaces thus incorporating both x and y dimension.

Thanking you in anticipation