Accuracy and Efficiency of Integration Methods for Modeling Reactions

The computational expense that comes with simulating complex astrophysical reacting flows is challenging. Reactions are stiff, and we typically model these systems using implicit integration methods. These methods require a Jacobian matrix, J = ∂f/∂y', to be calculated and stored at each time step, along with linear algebra operations, all of which are computationally expensive. This expense motivates exploring more economical explicit methods that do not store the Jacobian. The goal of this study is to investigate how accurate and efficient the explicit Runge-Kutta-Chebyshev (RKC) method is compared to the implicit VODE method applied to astrophysical reactive flows. These integrators are applied to simulate X-ray bursts arising from unstable thermonuclear burning of accreted fuel on the surface of neutron stars, and to the double detonation sub-Chandrasekhar model for Type Ia supernovae, occurring when a carbon-oxygen white dwarf accumulates sufficient helium to ignite at the surface. The code framework for these problems is contained within CASTRO and are ran at the NERSC Perlmutter supercomputer. The node hours used and the mass fractions of elements show the explicit RKC method outperforms the current implicit VODE method in this application. However, there is no noticeable difference when applied to detonations.