Modeling surface tension in multi-species flows using a Roe solver with stiffened gas equation

Abstract

This paper presents a numerical method for simulating multi-species flows with surface tension, integrating a Roe-type Riemann solver, the gamma model, and the continuous surface force (CSF) model into a Navier–Stokes framework with a stiffened gas equation of state. In the present formulation, the fluids are treated as non-reacting species, and no phase change or mass transfer is considered. The approach resolves shock waves, contact discontinuities, and interfacial dynamics in conservative form. Validation encompasses a one-dimensional shock tube test, capturing discontinuities with errors below 2% using Van Leer and optimum symmetric polynomial-ratio expression limiters, and static droplet simulations in two dimensions and three dimensions, predicting pressure jumps within 10% of Young–Laplace theory. Parasitic currents, on the order of 10−2, persist as a numerical artifact despite mesh refinement, highlighting a limitation of the CSF implementation. Comparisons with analytical solutions and prior studies confirm robustness across diverse scenarios. This method achieves high accuracy and stability, offering potential for microfluidics, environmental flows, and industrial applications involving interfacial phenomena. Future work could mitigate parasitic currents through enhanced schemes and extend the model to dynamic multi-species flows.