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An energy stable finite element scheme within arbitrary Lagrangian Eulerian(ALE) framework is derived for simulating the dynamics of millimetric dropletsin contact with solid surfaces. Supporting surfaces considered may exhibitnon--homogeneous properties which are incorporated into system throughgeneralized Navier boundary conditions (GNBC). Numerical scheme is constructedsuch that the counterpart of (continuous) energy balance holds on the discretelevel. This ensures that no spurious energy is introduced into the discretesystem, i.e. the discrete formulation is stable in the energy norm. The newlyproposed scheme is numerically validated to confirm the theoreticalpredictions. Of a particular interest is the case of droplet on anon-homogeneous inclined surface. This case shows the capabilities of thescheme to capture the complex droplet dynamics (sliding and rolling) whilemaintaining stability during the long time simulation.

Energy stable finite element scheme for simulating flow dynamics of droplets on non-homogeneous surfaces