The Kratos Framework for Heterogeneous Astrophysical Simulations: Ray Tracing, Reacting Flow and Thermochemistry

TL;DR

This work presents Kratos, a GPU-optimized framework for heterogeneous astrophysical simulations that tightly couples thermochemistry, ray tracing, and radiation-matter interactions with hydrodynamics. It introduces a stoichiometry-aware reconstruction method that preserves elemental abundances without matrix inversions, along with a GPU-friendly LU decomposition for solving stiff thermochemical ODEs in a massively parallel setting. Comprehensive verifications using advection tests, Strömgren spheres, and detonation benchmarks demonstrate high accuracy, robust conservation, and substantial performance gains over CPU-based approaches. The combination of consistent microphysics, high-order advection, and efficient radiation transport enables realistic modeling of complex environments such as star-forming regions and explosive astrophysical events. The framework’s modular design, demonstrated scalability, and plan for future enhancements (scattering, polarization, and machine-learning accelerators) position Kratos as a powerful tool for studying coupled microphysical processes across diverse astrophysical contexts.

Abstract

Thermochemistry, ray-tracing radiation, and radiation-matter interactions are important processes which are computationally difficult to model in astrophysical simulations, addressed by introducing novel algorithms optimized for heterogeneous architectures in the Kratos framework. Key innovations include a stoichiometry-compatible reconstruction scheme for consistent chemical species advection, which ensures element conservation while avoiding matrix inversions, and a LU decomposition method specifically designed for multi-thread parallelization in order to solve stiff thermochemical ordinary differential equations with high efficiency. The framework also implements efficient ray-tracing techniques for radiation transport for radiation-matter interactions. Various verification tests, spanning from chemical advection, combustion, Strömgren spheres, and detonation dynamics, are conducted to demonstrate the accuracy and robustness of Kratos, with results closely matching semi-analytic solutions and benchmarks such as Cantera and the Shock and Detonation Toolbox. The modular design and performance optimizations position it as a versatile tool for studying coupled microphysical processes in the diverse environments of contemporary astrophysical studies.

Figures (8)

• Figure 1: Example of comparing $\delta l_\phi$ and $\delta l_R$ in cylindrical mesh, for the ray passing through a cell. This is a top-down view with $z$-related quantities omitted for clarity. Grey lines and curves indicate the excerpts of coordinate surfaces and boundaries of the cell concerned.
• Figure 2: Test example of ray tracing on a spherical polar grid, with the radiation flux (at unitary intensity in code units) incidented at a $\theta = \arctan(0.1)$ angle with the horizontal axis (§\ref{['sec:method-direct-rt']}). The shadow behind the central blank zone can be clearly observed.
• Figure 3: Test results of different advection schemes (see §\ref{['sec:verify-adv-spe']}). The advection results (in number density ratios relative to $n_{\rm tot}$) using different algorithms are presented in the upper two panels at $t=1$ for two representative species, compared to the exact solution in heavy solid lines. Note that the lines for PLM with and without stoichiometric corrections overlap each other. The bottom panel shows the violation of elemental abundance conservation in comparison to the exact solutions.
• Figure 4: Thermochemical reaction tests for the burning of molecular hydrogen with oxygen (§\ref{['sec:verify-0d']}), comparing the mixed-precision results (solid lines) with the ones (dashed lines). The upper panel exhibits the evolution of different variables (distinguished by line colors), including the mass fraction of chemical species (the left ordinate, in logarithm scale) and the temperature (the right ordinate, in linear scale), while the lower panel shows the relative differences of the mass fractions and the gas temperature.
• Figure 5: Hydrostatic profiles of the Strömgren sphere test using the fiducial set of parameters (see §\ref{['sec:verify-strom']}). The left four colormap panels, marked with the code unit lenght $l_0 = {\rm pc}$, show the slices at $z=0$ for mass density $\rho$, temperature $T$, ionizing photon flux $F$, and the mass fraction of neutral hydrogen $Y(\mathrm{H})$. The right panel illustrates the profiles along the radial line along the $z$-axis, comparing the results by (solid lines) with the semi-analytic solutions (dashed lines).