Scalable adaptive algorithms for next-generation multiphase simulations

The accuracy of multiphysics simulations is strongly contingent up on the finest resolution of mesh used to resolve the interface. However, the increased resolution comes at a cost of inverting a larger matrix size. In this work, we propose algorithmic advances that aims to reduce the computational cost without compromising on the physics by selectively detecting the key regions of interest (droplets/filaments) that requires significantly higher resolution. The overall framework uses an adaptive octree-based mesh generator, which is integrated with PETSc's linear algebra solver. We demonstrate the scaling of the framework up to 114,688 processes on TACC Frontera. Finally we deploy the framework to simulate primary jet atomization on an \textit{equivalent} 35 trillion grid points - 64$\times$ greater than the state-of-the-art simulations.