Many formulations of Smoothed particle hydrodynamics exist but I am looking for a simple formulation that could handle the contact discontinuities found in 1D Sod's shock tube problem.

I have a recollection that an artificial thermal conductivity needs to be added to the energy equation.

There used to be 1D free code available online from NASA that had a suite of problems including Sod's shock tube but I can't locate that code now.