An asymptotically correct implicit-explicit time integration scheme for finite volume radiation-hydrodynamics

Area of Science:

• Astrophysical fluid dynamics
• Computational physics
• Numerical methods

Background:

• Radiation-hydrodynamics (RHD) simulations are computationally intensive due to vast differences in timescales and process importance.
• Existing numerical methods struggle to efficiently handle these broad ranges across computational domains.

Purpose of the Study:

• To introduce a novel implicit-explicit numerical method for non-relativistic RHD.
• To address the challenges of broad timescales and varying process importance in RHD simulations.
• To develop a method suitable for modern high-performance computing architectures.

Main Methods:

• Developed an implicit-explicit RHD scheme based on moments.
• Ensured machine-precision conservation of energy and momentum.
• Implemented the method in the GPU-accelerated RHD code, quokka.

Main Results:

• The method achieves machine-precision conservation of energy and momentum.
• It requires minimal communication, suitable for massively parallel and GPU systems.
• Demonstrated asymptotic accuracy in streaming, static diffusion, dynamic diffusion, and asymptotic diffusion regimes.
• Successfully passed a wide range of numerical tests.

Conclusions:

• The new implicit-explicit RHD method offers a robust and efficient solution for complex astrophysical simulations.
• Its design makes it highly suitable for adaptive mesh refinement and massively parallel computing environments.
• The method accurately handles various physical regimes, including unresolved photon mean-free paths.