Artificial viscosity model to mitigate numerical artefacts at fluid interfaces with surface tension

The numerical onset of parasitic and spurious artefacts in the vicinity of fluid interfaces with surface tension is an important and well-recognised problem with respect to the accuracy and numerical stability of interfacial flow simulations. Issues of particular interest are spurious capillary waves, which are spatially underresolved by the computational mesh yet impose very restrictive time-step requirements, as well as parasitic currents, typically the result of a numerically unbalanced curvature evaluation. We present an artificial viscosity model to mitigate numerical artefacts at surface-tension-dominated interfaces without adversely affecting the accuracy of the physical solution. The proposed methodology computes an additional interfacial shear stress term, including an interface viscosity, based on the local flow data and fluid properties that reduces the impact of numerical artefacts and dissipates underresolved small scale interface movements. Furthermore, the presented methodology can be readily applied to model surface shear viscosity, for instance to simulate the dissipative effect of surface-active substances adsorbed at the interface. The presented analysis of numerical test cases demonstrates the efficacy of the proposed methodology in diminishing the adverse impact of parasitic and spurious interfacial artefacts on the convergence and stability of the numerical solution algorithm as well as on the overall accuracy of the simulation results.