Spectral-like methods to model dynamic gas-liquid interface deformation

For the modeling of unsteady flow in boundary layers near a gas-liquid interface, driven by for example surface tension gradients, a set of less conventional elementary functions is proposed which can be used in spectral element methods. It is proposed to eliminate pressure from the governing equations by spatial integration over closed contours. By selecting contours that cross the interface the dynamic stress boundary condition is easily accounted for. A fully closed solution method is obtained. If the thickness of free surface boundary layers is negligible, it is proposed to use generalized coordinates to describe the gas-liquid interface. The resulting Euler-Lagrange equations yield a reduced computational complexity as well as simplicity of conception, elucidating the physics involved. A fully closed solution method is obtained.