On level set modelling of bi‐fluid capillary flow

Abstract

SUMMARYWe consider the adaptation of a level set (LS) method for the simulation of capillary flows on unstructured meshes. The advection step is first analysed. In order not to lose accuracy, this step should be one order more accurate than the discretization of the velocity. We then compare different ways in choosing the LS velocity and in re-initializing the LS function between advection phases without losing too much accuracy. Applications to Rayleigh flows and to reorientation with contact angle are presented.

Adherence and bouncing of liquid droplets impacting on dry surfaces

“…This simple approach could have problems because the level-set function is not smooth near the wall resulting in inaccuracies in the calculation of interface curvature. A remedial measure is presented by Lesage et al (2007), where a different reinitialization method near the wall is proposed (we thank the reviewer for bringing this work to our attention). However, as our validation attempts show, this simple method is able to capture the transient dynamics of drop impact with acceptable fidelity.…”

An L∞–Lp mesh‐adaptive method for computing unsteady bi‐fluid flows

“…A discontinuity capturing scheme will theoretically and practically reach at best a first-order accuracy. The introduction of a level set opens the door to a higher-order accurate prediction of the color function, as analyzed in [15]. This property applies to the advection of a color function, but a priori not to the global multi-fluid model, since the issue of the accurate discretization of the discontinuous fluid properties in the momentum equations remains unaddressed.…”

“…In a classical manner, the level set function is then re-initialized by replacing it by a distance function n+1 , which is the signed distance to the set { n+1 = 0}. We refer to [15] for further details.…”

“…System of equations (6)- (7) is solved explicitly with a standard P 1 -P 1 projection finite element method as in [15]. The interface is advected by means of Equation (5), which is solved by a vertex-centered finite volume scheme [19].…”

“…The flow modeling relies on a level set formulation [16,17] of a two-fluid incompressible flow as introduced in [15].…”