Capturing Composite Waves in Non-convex Special Relativistic Hydrodynamics

We deal with the numerical approximation of the complex structure in special relativistic hydrodynamics (SRHD) when the system is closed with a non-convex equation of state (EOS). We consider a recently introduced phenomenological EOS (Ibáñez et al. in MNRAS 476:1100, 2018) that mimics the loss of classical behavior when the fluid enters into a non-convex—thermodynamically—region in the relativistic regime. We introduce a flux formulation to approximate the solution of Riemann problems in SRHD such that the non-classical dynamics is detected and well resolved. We also design a strategy to recover primitive variables based on iterative procedures and present a detailed analysis providing a sufficient condition to ensure convergence. We propose a set of Riemann problems in one and two dimensions including blast waves, colliding slabs and expanding slabs, illustrating the strong complex dynamics arising in non-convex SRHD.