11:25 to 12:35 Computational MHD: A model problem for widely separated time and space scales (Chair: R Rosner) The numerical simulaton of the dynamics of magnetized plasmas is among the most challenging problems in computational physics. Strongly magnetized plasmas are characterized widely separated space and time scales, and by extreme anisoptopy. All of these issues affect the design of algorithms. The fundamental mathematical description requires the simultaneous solution of the 6-dimensional kinetic equation along with Maxwell's equations. This is impossible in all but the very simplest cases, so reduced fluid models can be derived by taking velocity moments of the kinetic equation and assuming a closure condition. Different closure assumptions result in different fluid models. MHD is the simplest of these, although by no means universally applicable. MHD appears to be an excellent model for the dynamics of stellar interiors, where the problem reduces to computing large Reynolds' number turbulence. Memory and speed limitations of even the most powerful computer then dictate a further reduction by means of averaging and statistical closures to capture the effect of the sub-grid scale dynamics on the long wave length motions. There is no concensus on the form of these closures. For the case of low density, high temperature, strongly magnetized plasmas, as occur in laboratory fusion experiments, MHD is clearly not a good model on the smallest scales, and the closure problem becomes one of characterizing non-local kinetic effects in a local transport formalism. This is also an unsolved problem, so in both cases it can be said that there is no agreement on what equations to solve. Because of the differing plasma parameters in these 2 cases, different algorithms must be applied. The audience is already familiar with techniques for computing MHD turbulence. Here we will primarily be concerned with methods developed to simulate ther long time scale dynamics of highly magnetized plasmas, as occur in fusion plasmas and the solar corona. Methods of spatial and temporal differencing will be discussed, and examples of the computed dynamics of laboratory and coronal plasmas will be given. Limitations on the scope of simulations for the foreseeable future will be given. Perhaps some of the issues discussed here will also prove to be useful for stellar interiors. INI 1 15:30 to 16:40 Planetary convection and dynamos (Chair: N Weiss) The past decade has seen enormous progress in numerical modelling of planetary dynamos. In this talk I will review some of this work, the numerical techniques that are used, and some of the physics that makes this problem so difficult. I will also compare and contrast the situation in planets versus other astrophysical objects, and try to explain why quite different numerical techniques are often used in the planetary context. INI 1 16:40 to 17:05 DNS of anisotropic MHD flows (Chair: N Weiss) We will present preliminary results of the direct numerical simulation of the incompressible MHD problem. The system is forced at large-scale and an external magnetic field $B_0 \hat{z}$ is applied. Anisotropy is studied in terms of the decomposition group for rotation in $3D$, the so-called $SO(3)$ group. Similarities and differences with the anisotropic pure hydrodynamical case will be discussed. INI 1 17:05 to 17:30 Convective instabilities in pre-runaway white dwarfs (Chair: N Weiss) Studying the evolution of the convective burning process before and during the thermonuclear runaway in a white dwarf is crucial in order to measure the enrichment of the hydrogen envelope by convective overshoot. Recent numerical simulations, that start when the temperature at the base of the envelope is close to 10^8 K, show that in a few hundreds seconds the temperature grows up to 2 10^8 K. At this time the runaway takes place. Our simulations, performed by running a high order of accuracy code, with low numerical viscosity, show that care must be taken in the choice of the initial and boundary conditions. We have observed, in fact, the onset of fast convective instabilities that are driven by boundary effects and affect the dynamics of the pre-runaway phase. We plan, as a next step, to take the initial equilibrium with a peak of temperature close to 10^7 K, that corresponds to earlier and less unstable phase of the white dwarf evolution. INI 1