General Implicit Runge-Kutta Integrators for Multifluid Gas-Dust Aerodynamic Drag

TL;DR

This paper introduces GIRK, a novel implicit Runge-Kutta integrator for efficient, accurate simulation of dust-gas interactions in hydrodynamical codes, especially with many dust grain sizes.

Contribution

The paper presents GIRK, a new integrator that combines analytical solutions with implicit Runge-Kutta methods, improving efficiency and accuracy in multifluid dust-gas simulations.

Findings

GIRK achieves linear complexity with multiple dust sizes.

The method demonstrates high accuracy and convergence in benchmark tests.

GIRK is easily integrated into existing hydrodynamical codes.

Abstract

The integration of aerodynamic drag is a fundamental step in simulating dust dynamics in hydrodynamical simulations. We propose a novel integration scheme, designed to be compatible with Strang splitting techniques, which allows for the straightforward integration of external forces and hydrodynamic fluxes in general-purpose hydrodynamic simulation codes. Moreover, this solver leverages an analytical solution to the problem of drag acceleration, ensuring linear complexity even in cases with multiple dust grain sizes, as opposed to the cubic scaling of methods that require a matrix inversion step. This new General Implicit Runge-Kutta integrator (GIRK) is evaluated using standard benchmarks for dust dynamics such as DUSTYBOX, DUSTYWAVE, and DUSTYSHOCK. The results demonstrate not only the accuracy of the method but also the expected scalings in terms of accuracy, convergence to equilibrium, and execution time. GIRK can be easily implemented in hydrodynamical simulations alongside hydrodynamical steps and external forces, and is especially useful in simulations with a large number of dust grain sizes.