Taming the “stiff stiffness” of pressure work and equilibration in numerical schemes for compressible multi-fluid flows

Designing models and schemes for compressible multi-fluid flow is often considered as challenging when dealing with contrasted equations of state, low volume fractions, or high compression expansion ratios. This due to the potentially severe stiffness pressure couplings, aggravated by (i) their quadratic multiplicity they connect all energy reservoirs (ii) entropy conditions be preserved on each fluid, (iii) unknown signs, (iv) potential “stiff stiffness”, defined in present work. Whether captured under pressure-equilibration pressure-relaxation models—where fluids respectively share a common undergo damped evolution towards pressure—the stiff terms have always required dedicated numerical approaches, sometimes mixed results depending specific applications. Some broad general guidelines are here proposed tame issues terms. The framework that pressure-equilibrated average-field (or Euler–Euler) models, discretized splitting momentum internal equations: this makes behave locally simple ODEs, amenable integration schemes. approach resorts (partly) exponential integrators provide explicit estimations implicit pressures. final scheme, though not robust would its fully version, displays vastly improved resilience stiffness. Numerical tests were carried out strenuous versions usual 1D shock tubes two-fluid mixtures air water (described ideal stiffened gases). In view excellent results, further more extreme considered: free vacuum shocks zero state (Noh’s test). At acoustic CFL values, was robustly simulated fractions from less than 10−12 up nearly 1. Similarly, states different 10−8, density factors across ranging between few hundreds hundredths choice dissipation fluid. All previously developed Geometry, Energy, Entropy Consistent (GEEC) scheme (Vazquez-Gonzalez et al., 2020).