# Universal formulation of adiabatic equations of state in compresible finite-volume simultions

I code some finite element solver which should work for broad variety of materials (i.e. gas, liquid, solid, plasma) and large span of compressions resp. densities. I want to simulate things like shape-charge, implosion of nuclear bombs, and inertial confinement fusion.

I need some function which calculate pressure within my volume-element denpeding on its current shape (i.e. volume) assuming there is not transfer of material or heat from the element.

Basically want to some function $$p(V)$$

I was thinking to use equation of adiabatic process

$$p(V) = K/V^{\gamma}$$

where $$K$$ is constant as long there is no heat or mass transfer.

But I can imagine this will fail at high pressures, when pressure will rise sharply with minor changes of volume due to finite size of atoms (as described e.g. by Van_der_Waals_equation). Also there can be other phase changes like dissociation of electrons from atoms, which increase pressure and heat capacity.

Is there efficient way how to capture these effect using single general function?

It does not have to be very precise it is mostly just toy.