Direct van der Waals Simulation: A First-Principles Framework for Phase-Transforming Fluids

<p dir="ltr">Flows involving phase transformation are central to many natural phenomena and engineering applications. Despite their importance, our understanding of such flows remains limited, in part due to the significant challenges they pose to computational methods. These flows involve non-equilibrium phase transitions, rapid changes in fluid properties over small spatial and temporal scales, and complex interactions between interfacial dynamics and turbulent boundary layers. To date, most multiphase models rely either on the assumption of thermodynamic equilibrium or on empirically calibrated mass transfer functions. As an alternative, the Navier-Stokes-Korteweg (NSK) equations, derived by coupling van der Waals theory of capillarity with a compressible flow model, offer a first-principles framework for modeling phase transformation and interfacial dynamics. However, despite their theoretical advantages, the NSK equations pose significant numerical challenges and have thus far been restricted to microscale problems with free boundaries. Here, we present the Direct van der Waals Simulation (DVS) framework. DVS augments the NSK equations with a thickened interface method, state-of-the-art multi-parameter equations of state, and residual-based stabilization schemes that account for the unique wave structures and interfacial dynamics. We demonstrate that the proposed computational framework is high-order accurate and capable of producing robust solutions under extreme flow conditions. The DVS framework is applied to simulate wall-bounded, phase-transforming fluids at engineering-relevant length scales. Our results show excellent agreement with both theoretical predictions and experimental data for highly unsteady, turbulent cavitating flows. We argue that the proposed computational framework not only enables predictive simulation but also opens a pathway toward a fundamental understanding of phase-transforming flows.</p>