Speaker
Description
Relativistic viscous hydrodynamics is the workhorse for modeling the quark–gluon plasma (QGP) created in high-energy heavy-ion collisions and could play an equally crucial role in understanding hot, dense matter in neutron stars and their mergers. In contrast to commonly used Israel–Stewart–type (IS) theories, which can exhibit acausal behavior, we consider the Bemfica–Disconzi–Noronha–Kovtun (BDNK) formulation, equipped with well-defined causality conditions that are convenient for numerical implementation. We present two independent formulations that enable stable and accurate 3+1D simulations of the BDNK causal relativistic viscous hydrodynamic theory on arbitrary curved spacetimes. Both schemes are rigorously shown to be flux-conservative, strongly hyperbolic, locally well-posed, and mutually equivalent: one is a full first-order reduction augmented with auxiliary fields to enforce constraints, while the other is a mixed-order formulation that forgoes these fields and is more memory-efficient and markedly faster. We outline the underlying ideas and present a comprehensive validation of our numerical implementation through a suite of tests. Convergence and accuracy are demonstrated across all cases, including systems with semi-analytical solutions relevant to heavy-ion collisions and shock-tube benchmarks, with direct comparisons to standard IS-based approaches. In the low-viscosity limit, the code recovers stationary ideal-hydrodynamic solutions, including Bondi–Michel spherical accretion and equilibrium Kerr torus configurations, with negligible deviations from stationarity. We report progress toward developing a unified, open-source, performance-portable, GPU-ready codebase for simulating relativistic viscous fluids across QGP and astrophysical regimes.
