Protoplanetary disks — the gas-and-dust disks around young stars where planets form — have complex thermodynamics driven by gas, dust, and radiation. This paper presents a new simulation method that evolves the energies of gas, radiation, and multiple dust species together. The method is built into the PLUTO hydrodynamics code and is designed to capture how absorption, emission, and collisions move energy between these components in a self-consistent way.

The authors treat each dust size as a separate, pressureless fluid that can also diffuse. Treating dust this way lets the code follow grain settling toward the disk midplane and trapping in pressure bumps, both of which change how the disk is illuminated. Radiation is handled with a frequency-integrated moment method called M1, and the authors use the reduced speed of light approximation to speed up the calculations. Time integration combines implicit handling of stiff source terms (the fast energy exchanges) with explicit transport; an iterative Newton–Raphson solver with algebraic simplifications speeds up the implicit steps.

This approach matters because many previous hydrodynamic models used simple shortcuts for thermodynamics, for example assuming a fixed temperature structure or a prescribed cooling time. Those shortcuts miss effects like the dust and gas temperatures decoupling in the disk atmosphere, or changes in midplane temperature when large grains settle or concentrate. By evolving gas, dust, and radiation together and letting dust move independently, the new scheme can capture changes in disk illumination and thermal relaxation that influence disk structure and planet–disk interactions.

The paper checks the method with a suite of test problems and includes a demonstrative application related to sublimation in disks. The tests verify that the code handles the intended energy and momentum exchanges and the advection and diffusion of multiple dust species. The authors also point out that this tool can help address open questions about how spiral arms, turbulence, gaps carved by planets, and dust concentration shape observable disk features.