Robust 3 + 1-D simulations of BDNK causal relativistic viscous hydrodynamics

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 the hot, dense matter inside neutron stars and their mergers. I will present two independent mathematical formulations that enable stable and accurate simulations of the Bemfica–Disconzi–Noronha–Kovtun (BDNK) causal relativistic viscous-hydrodynamic theory in full 3 + 1 dimensions and on arbitrary spacetime backgrounds. Both schemes are hyperbolic, flux-conservative, and well-posed; one is a full first-order reduction with constraint-cleaning fields, while the other is a mixed-order formulation that forgoes cleaning and is both memory-efficient and markedly faster. After outlining the underlying ideas, the talk will concentrate on numerical evidence for robustness and reliability. We present convergence and shock-tube tests and reproduce two well-known semi-analytical solutions relevant to heavy-ion collisions, demonstrating that both codes converge and provide accurate results. We aim to develop a common, open codebase for studying both QGP dynamics and neutron-star mergers.