For a numerical simulation paper, is it necessary to include boundary conditions and initial conditions in the paper?
Is it necessary to always include experimental validation for a numerical model?


Typically, yes, this is necessary. When you are going to publish an altered model (e.g., a more complex one), you need to demonstrate how the modifications play out in an experimental setup.


  Is it necessary to include the boundary condition and initial condition in the paper as well, or can I just refer to the previous paper/include in the appendix?


You may choose to either refer to your previous paper, or include them in your new paper (or do both). It is perfectly fine to refer to your previous publication, e.g., when you are trying to reduce the paper length, as long as the conditions are identical. However, when you want your new paper to be self-contained, or your previous paper was at a more obscure venue, it might be wise to include them in the new paper.


  Does it help if I include the simulation methodology in the paper? Or should I just put it in the appendix?


It is impossible to decide that without knowing the specifics, the journal's policy, and what is usual within your field.