[Paper Review] Sensitivity of Simulations of Double Detonation Type Ia Supernova to Integration Methodology

M. Zingale, Zhi Chen+5 more|arXiv (Cornell University)|Sep 4, 2023

Gamma-ray bursts and supernovaePhysics and Astronomy3 citations

TL;DR

This paper investigates the sensitivity of double detonation Type Ia supernova simulations to numerical integration and coupling methods between hydrodynamics and nuclear reactions. Using a GPU-accelerated, open-source framework in Castro, it demonstrates that simplified spectral deferred corrections (SDC) outperforms traditional Strang splitting, enabling accurate, efficient nucleosynthesis and dynamics without requiring reaction rate limiting or sub-timestep integration, even during extreme temperature spikes at carbon detonation ignition.

ABSTRACT

We study the coupling of hydrodynamics and reactions in simulations of the double detonation model for Type Ia supernovae. When assessing the convergence of simulations, the focus is usually on spatial resolution; however, the method of coupling the physics together as well as the tolerances used in integrating a reaction network also play an important role. In this paper, we explore how the choices made in both coupling and integrating the reaction portion of a simulation (operator / Strang splitting vs.\ the simplified spectral deferred corrections method we introduced previously) influences the accuracy, efficiency, and the nucleosynthesis of simulations of double detonations. We find no need to limit reaction rates or reduce the simulation timestep to the reaction timescale. The entire simulation methodology used here is GPU-accelerated and made freely available as part of the Castro simulation code.

Motivation & Objective

• To assess how integration and coupling methodologies affect the accuracy, efficiency, and nucleosynthesis in double detonation Type Ia supernova simulations.
• To compare operator splitting (Strang) with simplified spectral deferred corrections (SDC) in coupling hydrodynamics and nuclear reaction networks.
• To determine whether limiting reaction rates or reducing timesteps to reaction timescales is necessary for convergence.
• To evaluate the performance of the SDC method in handling extreme conditions, such as rapid temperature increases during carbon detonation ignition.
• To enable high-fidelity, large-scale 3D simulations by demonstrating robustness and efficiency of the SDC approach in a GPU-accelerated, open-source framework.

Proposed method

• The study employs the Castro simulation code, which uses a finite-volume, block-structured adaptive mesh refinement (AMR) approach to solve the compressible Euler equations with reactive and gravitational source terms.
• Hydrodynamics is advanced explicitly in time using a Courant-limited timestep, while nuclear reactions are integrated implicitly using either Strang splitting or simplified SDC.
• The simplified SDC method enables second-order accuracy in time by iteratively correcting the reaction update across multiple substeps, improving consistency with hydrodynamic evolution.
• The reaction network is solved using the VODE ODE integrator with options for analytic or numerical Jacobians, and the system uses an equation of state based on Helmholtz free energy (Helmholtz EOS).
• All simulations are GPU-accelerated and made freely available as part of the open-source Castro and AMReX-Astro software stack.
• The framework supports large reaction networks via pynucastro and enables multi-point ignition and iron-group nucleosynthesis studies in 3D.

Experimental results

Research questions

• RQ1 How does the choice between Strang splitting and simplified SDC affect the accuracy and convergence of nucleosynthesis in double detonation SN Ia simulations?
• RQ2 Is it necessary to limit reaction rates or reduce the hydrodynamics timestep to the reaction timescale to achieve numerical convergence?
• RQ3 How does the SDC method perform during the extreme temperature rise at carbon detonation ignition, where nuclear statistical equilibrium (NSE) is established?
• RQ4 Can the simplified SDC framework be extended to include NSE approximations in a second-order, consistent manner during high-temperature burns?
• RQ5 What is the computational cost and scalability of 3D double detonation simulations using the SDC method on modern exascale architectures?

Key findings

• The simplified SDC method achieves second-order accuracy in time and provides superior convergence in both dynamics and nucleosynthesis compared to Strang splitting.
• No need to limit reaction rates or reduce the hydrodynamics timestep to the reaction timescale was found; simulations converged robustly even with large timesteps.
• During carbon detonation ignition, where temperature can rise from 3×10⁹ K to 6×10⁹ K in a single timestep, the SDC method maintained stability and accuracy without requiring sub-timestep integration.
• The ODE integrator performed better with numerical Jacobians during high-temperature phases, and the authors are exploring adaptive switching between analytic and numerical Jacobians.
• The framework enables large-scale 3D simulations: a 20 km resolution 3D simulation on OLCF Frontier requires ~10⁴ node-hours across 1024 GPUs, making it feasible for future studies.
• The entire simulation methodology, including reaction network infrastructure and initial models, is open-source and publicly available via GitHub repositories.