We present a new approach to simulating mixtures of gas and dust in smoothed particle hydrodynamics (SPH). We show how the two-fluid equations can be rewritten to describe a single-fluid mixture moving with the barycentric velocity, with each particl
e carrying a dust fraction. We show how this formulation can be implemented in SPH while preserving the conservation properties (i.e. conservation of mass of each phase, momentum and energy). We also show that the method solves two key issues with the two fluid approach: it avoids over-damping of the mixture when the drag is strong and prevents a problem with dust particles becoming trapped below the resolution of the gas. We also show how the general one-fluid formulation can be simplified in the limit of strong drag (i.e. small grains) to the usual SPH equations plus a diffusion equation for the evolution of the dust fraction that can be evolved explicitly and does not require any implicit timestepping. We present tests of the simplified formulation showing that it is accurate in the small grain/strong drag limit. We discuss some of the issues we have had to solve while developing this method and finally present a preliminary application to dust settling in protoplanetary discs.
We describe a simple method for simulating the dynamics of small grains in a dusty gas, relevant to micron-sized grains in the interstellar medium and grains of centimetre size and smaller in protoplanetary discs. The method involves solving one extr
a diffusion equation for the dust fraction in addition to the usual equations of hydrodynamics. This diffusion approximation for dust is valid when the dust stopping time is smaller than the computational timestep. We present a numerical implementation using Smoothed Particle Hydrodynamics (SPH) that is conservative, accurate and fast. It does not require any implicit timestepping and can be straightforwardly ported into existing 3D codes.
Aims: In order to understand the first stages of planet formation, when tiny grains aggregate to form planetesimals, one needs to simultaneously model grain growth, vertical settling and radial migration of dust in protoplanetary disks. In this study
, we implement an analytical prescription for grain growth into a 3D two-phase hydrodynamics code to understand its effects on the dust distribution in disks. Methods: Following the analytic derivation of Stepinski & Valageas (1997), which assumes that grains stick perfectly upon collision, we implement a convenient and fast method of following grain growth in our 3D, two-phase (gas+dust) SPH code. We then follow the evolution of the size and spatial distribution of a dust population in a classical T Tauri star disk. Results: We find that the grains go through various stages of growth due to the complex interplay between gas drag, dust dynamics, and growth. Grains initially grow rapidly as they settle to the mid-plane, then experience a fast radial migration with little growth through the bulk of the disk, and finally pile-up in the inner disk where they grow more efficiently. This results in a bimodal distribution of grain sizes. Using this simple prescription of grain growth, we find that grains reach decimetric sizes in 10^5 years in the inner disk and survive the fast migration phase.
We present the first results of the treatment of grain growth in our 3D, two-fluid (gas+dust) SPH code describing protoplanetary disks. We implement a scheme able to reproduce the variation of grain sizes caused by a variety of physical processes and
test it with the analytical expression of grain growth given by Stepinski & Valageas (1997) in simulations of a typical T Tauri disk around a one solar mass star. The results are in agreement with a turbulent growing process and validate the method. We are now able to simulate the grain growth process in a protoplanetary disk given by a more realistic physical description, currently under development. We discuss the implications of the combined effect of grain growth and dust vertical settling and radial migration on subsequent planetesimal formation.
We present the first results of the treatment of grain growth in our 3D, two-fluid (gas+dust) SPH code describing protoplanetary disks. We implement a scheme able to reproduce the variation of grain sizes caused by a variety of physical processes and
test it with the analytical expression of grain growth given by Stepinski & Valageas (1997) in simulations of a typical T Tauri disk around a one solar mass star. The results are in agreement with a turbulent growing process and validate the method. We are now able to simulate the grain growth process in a protoplanetary disk given by a more realistic physical description, currently under development. We discuss the implications of the combined effect of grain growth and dust vertical settling and radial migration on subsequent planetesimal formation.
