Design of Provably Physical-Constraint-Preserving Methods for General Relativistic Hydrodynamics

Understand

The paper develops high-order physical-constraint-preserving (PCP) methods for general relativistic hydrodynamic (GRHD) equations, equipped with a general equation of state.

• Here the physical constraints, describing the admissible states of GRHD, are referred to the subluminal constraint on the fluid velocity and the positivity of the density, pressure and specific internal energy.
• Preserving these constraints is very important for robust computations, otherwise violating one of them will lead to the ill-posed problem and numerical instability.
• To overcome the difficulties arising from the inherent strong nonlinearity contained in the constraints, we derive an equivalent definition of the admissible states.