  We present an efficient, fully conservative numerical scheme valid in the
entire range of highly to weakly compressible flows using a single-fluid four
equation approach together with multi-component thermodynamic models. The
approach can easily be included into existing finite volume methods on compact
stencils and enables handling of compressibility of all involved phases
including surface tension, cavitation and viscous effects. The mass fraction
(indicator function) is sharpened in the two-phase interface region using the
algebraic interface sharpening technique Tangent of Hyperbola for INterface
Capturing (THINC). The cell face reconstruction procedure for mass fractions
switches between an upwind-biased and a THINC-based scheme, along with proper
slope limiters and a suitable compression coefficient, respectively. For
additional sub-grid turbulence modeling, a fourth order central scheme is
included into the switching process, along with a modified discontinuity
sensor. The proposed All-Mach Riemann solver consistently merges the
thermodynamic relationship of the components into the reconstructed
thermodynamic variables (like density, internal energy), wherefore we call them
All Mach THINC-based Thermodynamic-Dependent Update (All-Mach THINC-TDU)
method. Both, liquid-gas and liquid-vapor interfaces can be sharpened. Surface
tension effects are taken into account by using a Continuum Surface Force (CSF)
model. An explicit, four stage low storage Runge Kutta method is used for time
integration. The proposed methodology is validated against a series of
reference cases, such as bubble oscillation,advection,deformation, shock-bubble
interaction, a vapor bubble collapse and a multi-component shear flow. Finally,
the approach is applied to simulate the three-dimensional primary break-up of a
turbulent diesel jet.
