  We present the method of Direct van der Waals simulation (DVS) to study
computationally flows with liquid-vapor phase transformations. Our approach is
based on a novel discretization of the Navier-Stokes-Korteweg equations, that
couple flow dynamics with van der Waals' non-equilibrium thermodynamic theory
of phase transformations, and opens an opportunity for first-principles
simulation of a wide range of boiling and cavitating flows. The proposed
algorithm enables unprecedented simulations of the Navier-Stokes-Korteweg
equations involving cavitating flows at strongly under-critical conditions and
$\mathcal{O}(10^5)$ Reynolds number. The proposed technique provides a pathway
for fundamental understanding of phase-transforming flows with multiple
applications in science, engineering, and medicine.
