Reactive flows are at the heart of stellar evolution and explosions. Modeling these reactive flows can be challenging. Nuclear reaction networks are stiff, demanding implicit integration techniques and/or small timesteps to accurately capture the nucleosynthesis. Coupling reactions to hydrodynamics is often done via operator splitting, with the hydrodynamics update and reactive update each operating on the state evolved by the other process. In reactions where burning is energetic, operator splitting can breakdown, requiring small overall simulation timesteps to ensure accurate modeling of reactive flows. We demonstrate two other coupling methods, both built on the idea of spectral deferred corrections (SDC). The first method is built on the traditional SDC methodology, expressing the update as an integral over discrete time nodes, and extends straightforwardly to higher-order time-integration (e.g. fourth order). The second is a simplified version of the SDC method, that can reuse a lot of the infrastructure in place with an operator split code, but is limited to second order accuracy. We describe both methods, their implementation in the open source Castro simulation code, and show a range of test problems comparing these methods to the traditional operator split approach.
This work at Stony Brook was supported by DOE/Office of Nuclear Physics grant DE-FG02-87ER40317. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of Nuclear Physics, Scientific Discovery through Advanced Computing (SciDAC) program under Award Number DE-SC0017955. This research was supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration.