A semi-implicit and unconditionally stable approximation of the surface tension in two-phase fluids

Abstract We focus on the energy conservation of two-phase fluids, where the change in kinetic energy is balanced by the gravitational potential and the surface energy related to surface tension. We introduce an unconditionally stable approximation in the sense that the total energy does not increase with any time step. An analysis is presented to prove the unconditional stability property of the scheme, and numerical results are given to confirming the analysis.