  In this work, the van der Waals fluid model, a diffuse-interface model for
liquid-vapor two-phase flows, is numerically investigated. The thermodynamic
properties of the van der Waals fluid are first studied. Dimensional analysis
is performed to identify the control parameters for the system. An
entropy-stable numerical scheme and isogeometric analysis are utilized to
discretize the governing equations for numerical simulations. The steady state
solution at low Rayleigh number is presented, demonstrating the capability of
the model in describing liquid-vapor phase transitions. Next, two-dimensional
nucleate and film boiling are simulated, showing the applicability of the model
in different regimes of boiling. In the last, the heat transport property of
the van der Waals model is numerically investigated. The scaling law for the
Nusselt number with respect to the Rayleigh number in the van der Waals model
is obtained by performing a suite of high-resolution simulations.
