On the use of Galerkin-Eckhaus method to study the nonlinear regime of Marangoni-Benard instabilities in an evaporating liquid layer

摘要

We investigate theoretically Marangoni-Benard instability in an evaporating liquid layer surmounted by its vapor and an inert gas. A Galerkin-Eckhaus method, based on a slaving principle and an iterative algorithm, and a direct finite element method are used to determine the evaporation rate above the convective threshold. Both methods provide precise quantitative results, even far from the linear stability threshold.