01579nam a2200181 a 450000500170000000800400001710000150005724500980007226400160017033600090018633800200019552009050021550600460112085600660116694200090123299900130124195201430125420260901030408.0250101s2020    xx     o     000 0 eng d1 aJuan Zhang10aStructure-preserving, energy stable numerical schemes for a liquid thin film coarsening model 1barXivc2020  atext  aonline resource  aIn this paper, two finite difference numerical schemes are proposed and analyzed for the droplet liquid film model, with a singular Leonard-Jones energy potential involved. Both first and second order accurate temporal algorithms are considered. In the first order scheme, the convex potential and the surface diffusion terms are implicitly, while the concave potential term is updated explicitly. Furthermore, we provide a theoretical justification that this numerical algorithm has a unique solution, such that the positivity is always preserved for the phase variable at a point-wise level, so that a singularity is avoided in the scheme. In fact, the singular nature of the Leonard-Jones potential term around the value of 0 prevents the numerical solution reaching such singular value, so that the positivity structure is always preserved. Moreover, an unconditional energy stability of the nume0 aOpen access — freely available to read.40uhttps://arxiv.org/pdf/2012.11802v1yRead the full paper (PDF)  cERES  c703d703  001040738GENaMAINbMAINcSCICOMPd2026-09-01l0pYGE000964r2026-09-01 03:04:08uhttps://arxiv.org/pdf/2012.11802v1w2026-09-01yPAPER