Context :

Aims : We present global 3D MHD simulations of disks of gas and solids , aiming at developing models that can be used to study various scenarios of planet formation and planet-disk interaction in turbulent accretion disks .

Methods : We employ the Pencil Code , a 3D high-order finite-difference MHD code using Cartesian coordinates .
We solve the equations of ideal MHD with a local isothermal equation of state .
Planets and stars are treated as particles evolved with an N -body scheme .
Solid boulders are treated as individual superparticles that couple to the gas through a drag force that is linear in the local relative velocity between gas and particle .

Results : We find that Cartesian grids are well-suited for accretion disk problems .
The disk-in-a-box models based on Cartesian grids presented here develop and sustain MHD turbulence , in good agreement with published results achieved with cylindrical codes.We investigate the dependence of the magnetorotational instability on disk scale height , finding evidence that the turbulence generated by the magnetorotational instability grows with thermal pressure .
The turbulent stresses depend on the thermal pressure obeying a power law of 0.24 \pm 0.03 , compatible with the value of 0.25 found in shearing box calculations .
The ratio of Maxwell to Reynolds stresses decreases with increasing temperature , dropping from 5 to 1 when the sound speed was raised by a factor 4 , maintaing the same field strength .
We also study the dynamics of solid boulders in the hydromagnetic turbulence , by making use of 10 ^ { 6 } Lagrangian particles embedded in the Eulerian grid .
The effective diffusion provided by the turbulence prevents settling of the solids in a infinitesimally thin layer , forming instead a layer of solids of finite vertical thickness .
The measured scale height of this diffusion-supported layer of solids implies turbulent vertical diffusion coefficients with globally averaged Schmidt numbers of 1.0 \pm 0.2 for a model with \alpha \approx 10 ^ { -3 } and 0.78 \pm 0.06 for a model with \alpha \approx 10 ^ { -1 } .
That is , the vertical turbulent diffusion acting on the solids phase is comparable to the turbulent viscosity acting on the gas phase .
The average bulk density of solids in the turbulent flow is quite low ( \rho _ { p } = 6.0 \times 10 ^ { -11 } { kg m ^ { -3 } } ) , but in the high pressure regions , significant overdensities are observed , where the solid-to-gas ratio reached values as great as 85 , corresponding to 4 orders of magnitude higher than the initial interstellar value of 0.01

Conclusions :