A Redistribution-Based Volume-Preserving PLIC-VOF Technique

Abstract

Youngs' piecewise line interface construction/volume-of-fluid (PLIC-VOF) technique is an accurate tool for interface representation and intrinsic volume conservation for multiphase simulations. Direction splitting of the algorithm ensures stable performance up to Courant numbers of unity. However, baseline PLIC algorithms face an open problem of conservative volume advection in shearing velocity fields. Rather than modifying the advection equation of the baseline (Youngs PLIC-VOF) algorithm to achieve volume conservation for a limited range of solenoidal velocity fields, a coupling of the advection algorithm with a redistribution-based volume-correction routine is proposed here. The advantage of such a framework is that it decouples the prerequisite for mass conservation from the direction splitting of the advection equation. This happens because the advection is now made material-preserving up to machine accuracy for any velocity field, solenoidal or not. The volume-conservation property of the redistribution algorithm proposed here is established through stringent shear tests at a Courant number of unity, dam break simulations, and Rayleigh-Taylor instability. It is observed that the only mechanism through which such a formulation would violate volume conservation is by the addition of overall material source/sink terms to the advection equation.

Notes

¹Jetsam (“jettisoned goods”) and flotsam (“floating wreckage”) are stray regions of void generated within the primary phase due to the sweeping action of the interface through regions of void.

²Suborientations are ORIGINAL, ROTATED, REFLECTED, and REFLECTION OF ROTATED.

³The meaning of a nonstretching velocity field in this context is one which satisfies the operator−split form of the incompressibility condition, that is, and .