Implementation of a Two-Dimensional Unsplit Volume of Fluid Interface-Capturing Method for Multi-Fluid Compressible Flows in the FLASH Code

We present an implementation of the volume-of-fluid (VOF) method to model multiple immiscible compressible fluid species within the FLASH code’s unsplit hydrodynamics solver. FLASH is a highly capable, parallel, adaptive-mesh refinement, finite-volume Eulerian hydrodynamics and magnetohydrodynamic code with extended physics capabilities. FLASH assumes a Dalton mix of the species within each computational cell, and advects the corresponding mass fractions with the flow, resulting in the mixing of species across contact discontinuities. In VOF, species are assumed to occupy distinct volumes whose interfaces may cut the computational cells and are assumed to be in mechanical equilibrium with a single velocity field shared by all species. Special care needs to be taken to allow for the compressibility of the different species and for the modeling of shocks and discontinuities in the flow, maintaining sharp interfaces between species even at contact discontinuities. Additional considerations are also necessary within a dimensionally unsplit formulation to prevent fluxing the same volume into multiple cells. We highlight the capabilities of this VOF implementation in FLASH for simple gamma-law equations of state (EOS); the formulation is readily extended to tabulated EOS for simulations of high-energy-density physics and laser-driven experiments.