01424nam a2200169 a 4500 20260901030408.0 250101s2020 xx o 000 0 eng d Juan Zhang Structure-preserving, energy stable numerical schemes for a liquid thin film coarsening model arXiv 2020 text online resource In 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 nume Open access — freely available to read. https://arxiv.org/pdf/2012.11802v1 Read the full paper (PDF) ERES 703 703 0 0 0 3 GEN MAIN MAIN SCICOMP 2026-09-01 0 YGE000964 2026-09-01 03:04:08 https://arxiv.org/pdf/2012.11802v1 2026-09-01 PAPER