TY - JOUR

T1 - A variational level set methodology without reinitialization for the prediction of equilibrium interfaces over arbitrary solid surfaces

AU - Alamé, Karim

AU - Anantharamu, Sreevatsa

AU - Mahesh, Krishnan

PY - 2020/4/1

Y1 - 2020/4/1

N2 - A robust numerical methodology to predict equilibrium interfaces over arbitrary solid surfaces is developed. The kernel of the proposed method is the distance regularized level set equations (DRLSE) with techniques to incorporate the no-penetration and volume-conservation constraints. In this framework, we avoid reinitialization that is typically used in traditional level set methods. This allows for a more efficient algorithm since only one advection equation is solved, and avoids numerical error associated with the re-distancing step. A novel surface tension distribution, based on harmonic mean, is prescribed such that the zero level set has the correct liquid-solid surface tension value. This leads to a more accurate prediction of the triple contact point location. The method uses second-order central difference schemes which facilitates easy parallel implementation, and is validated by comparing to traditional level set methods for canonical problems. The application of the method in the context of Gibbs free energy minimization, to obtain liquid-air interfaces is validated against existing analytical solutions. The capability of the methodology to predict equilibrium shapes over both structured and realistic rough surfaces is demonstrated.

AB - A robust numerical methodology to predict equilibrium interfaces over arbitrary solid surfaces is developed. The kernel of the proposed method is the distance regularized level set equations (DRLSE) with techniques to incorporate the no-penetration and volume-conservation constraints. In this framework, we avoid reinitialization that is typically used in traditional level set methods. This allows for a more efficient algorithm since only one advection equation is solved, and avoids numerical error associated with the re-distancing step. A novel surface tension distribution, based on harmonic mean, is prescribed such that the zero level set has the correct liquid-solid surface tension value. This leads to a more accurate prediction of the triple contact point location. The method uses second-order central difference schemes which facilitates easy parallel implementation, and is validated by comparing to traditional level set methods for canonical problems. The application of the method in the context of Gibbs free energy minimization, to obtain liquid-air interfaces is validated against existing analytical solutions. The capability of the methodology to predict equilibrium shapes over both structured and realistic rough surfaces is demonstrated.

KW - Distance regularized level set equations

KW - Gibbs free energy minimization

KW - Level set method

KW - Multiphase

KW - Roughness

KW - Variational level set

UR - http://www.scopus.com/inward/record.url?scp=85078064299&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85078064299&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2019.109184

DO - 10.1016/j.jcp.2019.109184

M3 - Article

AN - SCOPUS:85078064299

VL - 406

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

M1 - 109184

ER -