Simulating flow over superhydrophobic surfaces at high $Re$ and high gas fractions using octree discretizations*

Superhydrophobic surfaces have demonstrated high drag reductions in turbulent flows. However, simulating the high gas fractions and high $Re$ typical of naval applications remains challenging, as very sharp gradients arise near the transitions between no-slip regions and gas-liquid interfaces. To achieve accurate yet computationally manageable simulations, we use adaptive octree discretizations in distributed environments, building on the parallel level-set schemes of Mirzadeh et al. (2016), using {\tt p4est} (2011), and extending the work of Egan et al. (2021). We thus leverage performant multicore systems and scalable linear solvers. We simulate SHS structures consisting of streamwise gratings and discretize the computational domain with 6-by-2-by-3 octrees, enforcing a wide band of the smallest cells layering the walls to capture local phenomena. Our simulation approach enables relatively rapid exploration of the parameter space up to gas fractions of 93.75\% and shows how flow properties, including Reynolds stresses, mean momentum advection, and vortical structures, are affected by gas fraction and Reynolds number. In this conference contribution, we will present flow results as well as the numerical tools and algorithms that have enabled our simulations.