Sub-grid scale characteristics of Godunov-based schemes for cavitating two-phase flows

Numerical accuracy of large-eddy simulations for cavitating flows decreases near discontinuities such as shock waves generated by vapor-bubble collapse, vapor-liquid phase boundaries, and complexities of solid boundaries. The errors can often be attributed to explicit sub-grid scale models. An alternative methodology, implicit large-eddy simulation, leverages the numerical discretization error of monotone, sharp-interface capturing schemes to mimic the physical dissipation rate. The characteristics of the numerical dissipation rate and implicit sub-grid scale are detailed for a class of high-order Godunov-based schemes for cavitating flows discretized in generalized curvilinear coordinates. Because variable reconstruction is performed locally, the scheme can capture both discontinuities and low Mach number features. Leading terms of modified equation analysis confirm the dissipative behaviors. A series of cases are undertaken including a two-phase shock tube, decaying homogeneous isotropic turbulence, and cavitating flow over a cylinder, which employs a sharp-interface immersed boundary method for compressible flow. The turbulence spectra, statistics and void fraction profiles show good agreement with direct numerical simulation.