Improved Coupling of Hydrodynamics and Nuclear Reactions via Spectral Deferred Corrections

Simulations in stellar astrophysics involve the coupling of hydrodynamics and nuclear reactions under a wide variety of conditions, from simmering convective flows to explosive nucleosynthesis. Numerical techniques such as operator splitting (most notably Strang splitting) are usually employed to couple the physical processes, but this can affect the accuracy of the simulation, particularly when the burning is vigorous. Furthermore, Strang splitting does not have a straightforward extension to higher-order integration in time. We present a new temporal integration strategy based on spectral deferred corrections, and describe the second- and fourth-order implementations in the open source, finite-volume, compressible hydrodynamics code Castro. One notable advantage to these schemes is that they combine standard low-order discretizations for individual physical processes in a way that achieves an arbitrarily high order of accuracy. We demonstrate the improved accuracy of the new methods on several test problems of increasing complexity.