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
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
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
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U2 - 10.1016/j.jcp.2019.109184
DO - 10.1016/j.jcp.2019.109184
M3 - Article
AN - SCOPUS:85078064299
SN - 0021-9991
VL - 406
JO - Journal of Computational Physics
JF - Journal of Computational Physics
M1 - 109184
ER -