Timothée David-Cléris

arXiv2026

Momentum-conserving self-gravity in the Phantom. Parallel dual tree traversal for the fast multipole method

Tree codes that approximate groups of distant particles with multipole expansions accelerate gravitational force calculations. While momentum-conserving fast multipole methods exist, parallelisation is non-trivial inside a modern SPH framework. We aim for a parallel momentum and angular momentum-conserving Cartesian multipole method for the computation of the gravitational force in smoothed particle hydrodynamics (SPH) with adaptive gravitational force softening in {\sc Phantom}. We modified Dehnen's original dual tree traversal algorithm to fit the parallel architecture of {\sc Phantom} by replicating the node-node interaction on the ancestors of each leaf node in the tree. While this notionally duplicates work, it greatly simplifies the parallelisation of the algorithm. We then recover the $\mathcal{O}(N)$ scaling of the algorithm by use of caches. We also adapt the tree opening criterion for adaptive softening lengths, such that all interactions within the softening kernel are handled pairwise (as in SPH) rather than with multipole expansions, also allowing the gravity calculation to be performed alongside the SPH force evaluation. We demonstrate that the new code conserves linear and angular momentum to machine precision while giving similar force accuracy and better computational performance to the previous (non-symmetric) self-gravity solver in Phantom. Our new fast multipole method is now the default for computing self-gravity in the public code.

astro-ph.IM↗

arXiv2026

Full one-fluid dusty gas with multiple grain species in SPH

We present a Smoothed Particle Hydrodynamics (SPH) implementation of the full one-fluid dusty gas algorithm for multiple dust species, generalising our previous terminal velocity approach to handle arbitrary drag regimes. By construction, mass, momentum, angular momentum, and energy are all conserved. We benchmark our method against a suite of tests -- DUSTYBOX, DUSTYWAVE, DUSTYSHOCK, DUSTYSETTLE, and DUSTYDISC -- each probing different aspects of the algorithm. Compared to the terminal velocity approximation, the full one-fluid approach incurs a computational cost increase of a factor of five to ten due to the added overhead of evolving the differential velocities and solving the drag terms implicitly. However, it accurately recovers analytic behaviour in regimes where the terminal velocity approximation fails. In such cases, errors from the terminal velocity approximation accumulate and propagate to other dust phases. We show that the stopping-time limiter commonly used in the terminal velocity approximation for numerical stability can substantially affect simulations containing large grains (Stokes numbers $\gtrsim 1$). While disabling the limiter leads to different outcomes, the discrepancy with the full one-fluid solution remains comparable, underscoring the importance of using a more general formulation for large grains. The full one-fluid formalism may be useful when including processes such as coagulation and fragmentation, where accurate treatment of large grains becomes essential. While the inability to model orbit-crossing dust trajectories remains a key limitation of the one-fluid formalism, this may eventually be addressed through the introduction of an effective dust pressure, mirroring how fluid models encapsulate microscopic velocity dispersion in gases.

astro-ph.EP↗