000			01424nam a2200169 a 4500
005			20260901030408.0
008			250101s2020 xx o 000 0 eng d
100	1		_aJuan Zhang
245	1	0	_aStructure-preserving, energy stable numerical schemes for a liquid thin film coarsening model
264		1	_barXiv _c2020
336			_atext
338			_aonline resource
520			_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 nume
506	0		_aOpen access — freely available to read.
856	4	0	_uhttps://arxiv.org/pdf/2012.11802v1 _yRead the full paper (PDF)
942			_cERES
999			_c703 _d703