Resolution Considerations for Two-Dimensional High-Speed Droplet Impact Along a Rigid Wall

Mechanical loads produced from the impact of droplets on high-speed projectiles are important considerations for their operation. To accurately predict the pressure produced along the surface of the object during impact, it is important to correctly model the air/water interface of the droplet. Novel modeling approaches such as the Phase-Field model enable control of the (numerical) interface thickness. However, the interactions of the grid resolution and interface thickness with the resulting simulation results are not well understood. In this work, the resolution requirements for numerical simulations of a water droplet impacting a rigid wall at Mach 4 are computationally investigated in two dimensions. Numerical simulations are performed using a second-order accurate method with adaptive mesh refinement (AMR) and a consistent and conservative Phase-Field method. The extent to which the maximum wall pressure and its location depend on the choice of numerical interface thickness and resolution parameters (mesh size, levels of mesh refinement) is quantified. The work provides a comprehensive resolution study by investigating the convergence of the Phase-Field parameter, AMR levels, and grid size required for various flow problems to determine suitable numerical parameters for interface control provided by the Phase-Field mechanism.