Phase-Field/Discontinuity Capturing operator for direct van der Waals simulation (DVS)

TL;DR

This paper introduces a novel phase-field/discontinuity capturing operator for direct van der Waals simulation, improving stability and physical accuracy in modeling phase transitions and cavitating flows.

Contribution

The paper proposes the PF/DC operator to address limitations of classical DC operators in DVS, ensuring energy dissipation and physical realism.

Findings

PF/DC operator provides stable, accurate solutions in simulations.

Significant improvements over classical DC operators in cavitating flow.

Excellent agreement with experimental data in 3D flow simulations.

Abstract

Discontinuity capturing (DC) operators are commonly employed to numerically solve problems involving sharp gradients in the solution. Despite their success, the application of DC operators to the direct van der Waals simulation (DVS) remains challenging. The DVS framework models non-equilibrium phase transitions by admitting interfacial regions in which the derivative of pressure with respect to density is negative. In these regions, we demonstrate that classical DC operators may violate the free energy dissipation law and produce unphysical wave structures. To address this limitation, we propose the phase-field/discontinuity capturing (PF/DC) operator. Numerical results show that PF/DC yields stable and accurate solutions in both bulk fluids and interfacial regions. Finally, we apply the proposed method to simulate cavitating flow over a three-dimensional bluff body, obtaining excellent agreement with experimental data and significant improvements over results produced using classical DC operators.