arXiv:2602.10120v1 Announce Type: new
Abstract: We provide a numerical method for computing solutions to a free boundary problem arising from the equilibrium state of a floating drop. This numerical method is based on a Newton’s method for the underlying nonlinear boundary value problems, and at each iterative step a Chebyshev spectral collocation method is employed. The problems considered here are those that can be described by using generating curves, and include problems in $mathbb{R}^2$ and $mathbb{R}^3$.
The resulting nine-dimensional space of physical parameters is explored, and examples are given that highlight the potential energy of centrally located drops, wall-bound drops, and asymmetrical configurations in $mathbb{R}^2$. Non-uniqueness of solutions to the corresponding Euler-Lagrange equations is displayed, and also strong evidence of non-uniqueness of energy minimizers is given.