Because they lose tremendous amounts of mass, cool evolved stars are major sources of dust and molecules for the interstellar medium. Spectro-imaging of the dust-driven winds around these stars has enabled us to identify recurring nonspherical patterns (e.g. spirals, arcs, compressed wind). We use radiative-hydrodynamic simulations of dust-driven winds to study the imprints left in the wind by an orbiting stellar or sub-stellar companion. We designed 3D numerical setup to solve the wind dynamics beyond the dust condensation radius and follow the flow up to several hundreds of stellar radii. Non-uniform grids enable us to capture small scale features such as shocks or disks forming around the orbiting object. Depending on its mass and orbital parameters, we reproduced typical non-spherical features such as arcs, spirals, petals and orbital density enhancements, and identified patterns associated to eccentric orbits.

In the framework of the ERTBP, we study an example of the influence of secondary resonances over the long term stability of Trojan motions. By the integration of ensembles of orbits, we find various types of chaotic diffusion, slow and fast. We show that the distribution of escape times is bi-modular, corresponding to two populations of short and long escape times. The objects with long escape times produce a power-law tail in the distribution.

We are developing a spherical hybrid model to study how the solar wind interacts with the solar system bodies. In this brief status report we introduce some lessons from the spherical grid development and illustrate the usage of the new model by showing a preliminary test run.

The nonlinear saturation of the magnetorotational instability (MRI) is best studied through numerical MHD simulations. Recent results of simulations that adopt the local shearing box approximation, and fully global models that follow the entire disk, are described. Outstanding issues remain, such as a first-principles understanding of the dynamo processes that control saturation with no net magnetic flux. Important directions for future work include a better understanding of basic plasma processes, such as reconnection, dissipation, and particle acceleration, in the MHD turbulence driven by the MRI.

We developed a fast numerical scheme for solving ambipolar diffusion MHD equations with the strong coupling approximation, which can be written as the ideal MHD equations with an additional ambipolar diffusion term in the induction equation. The mass, momentum, magnetic fluxes due to the ideal MHD equations can be easily calculated by any Godunov-type schemes. Additional magnetic fluxes due to the ambipolar diffusion term are added in the magnetic fluxes, because of two same spatial gradients operated on the advection fluxes and the ambipolar diffusion term. In this way, we easily kept divergence-free magnetic fields using the constraint transport scheme. In order to overcome a small time step imposed by ambipolar diffusion, we used the super time stepping method. The resultant scheme is fast and robust enough to do the long term evolution of star formation simulations. We also proposed that the decay of alfen by ambipolar diffusion be a good test problem for our codes.