A PMAT dependence can also be applied to density to model a compressible flow. For such flows with variable overall density, Ansys Polyflow does not solve for the volume but rather solves the mass conservation equation. The overall density is either treated as an additional variable or algebraically substituted.

The treatment used depends on the nature of the term to be evaluated: if a gradient must be computed, then the density is considered as a variable; if an algebraic relationship must be computed, then the density is simply substituted. The resulting formulation is a mixed method with an increase in the number of unknown variables.

This solution procedure, however, has several advantages. The implementation is rather easy and, most importantly, it allows you to model an equation of state of any kind while still keeping the Newton-Raphson rate of convergence.

When the density varies, velocity is no longer divergence-free, as it is for incompressible flows. Since mass is conserved, the flow kinematics as well as the volume of the material may change dramatically.

For example, consider a problem in which the density decreases as chemical reactions proceed. In a confined geometry, the fluid will accelerate; in a free surface problem, large swelling ratios will be observed, and it may be useful to consider a gradual solution strategy using an evolution technique to introduce this nonlinearity.