A time-dependent boundary-integral algorithm for nonlinear interfacial waves - Guan, Xin; Vanden-Broeck, Jean-Marc (Computers & fluids, 2025)
A boundary-integral algorithm based on an Eulerian or mixed Eulerian–Lagrangian description is presented for simulating two-dimensional unsteady nonlinear interfacial waves. It uses the tangent angle and the density-weighted velocity potential as primary unknowns, with the arclength used to parameterize the interface. Therefore, overhanging waves can be readily simulated. Cauchy’s integral formula is used to solve Laplace’s equation efficiently and accurately, for waves on deep water, finite-depth water or bottom topography. The numerical scheme is neutrally stable and conserves energy with superior accuracy. No significant numerical stiffness is observed, allowing for very long-term simulations of various physical scenarios. •A novel numerical algorithm for two-dimensional unsteady interfacial waves is presented.•An Eulerian or mixed Eulerian–Lagrangian formulation is used with arclength to parameterize interface.•Overhanging waves can be simulated.