1. ASCI/Alliances Center for Astrophysical Thermonuclear Flashes Simulating Self-Gravitating Flows with FLASH P. M. Ricker, K. Olson, and F. X. Timmes Motivation: Self-gravity is important in the case of Type Ia supernovae, in which thermonuclear runaway disrupts an entire white dwarf star within a matter of seconds. It is also important in a wide variety of other dynamic astrophysical environments, ranging from merging neutron stars through the turbulent interstellar medium (with which supernova blast waves interact) to galaxies and clusters of galaxies. Also, incorporating self-gravity into the FLASH framework allows us to extend the framework to include non-hyperbolic equation solvers, which are necessary to enable FLASH to handle radiation and conduction as well as gravity. Technique: Incorporating self-gravity into FLASH requires two additions: solving the Poisson equation for the gravitational potential at every timestep, and applying time- and space-varying gravitational source terms to the momentum and energy equations. We have implemented the following Poisson solvers in FLASH 1.61: A multipole solver - Directly sums fields due to multipole moments of the interior matter distribution, up to some limiting multipole l max. This is particularly efficient for nearly-spherical, isolated situations like the supernova problem. A multigrid solver - Appropriate for more general mass distributions. Multigrid works efficiently on irregularly refined meshes using periodic or isolated boundaries. The latter case is handled using an image mass technique (James 1977). An FFT solver - Based on the Couchman (1991) P 3 M algorithm, this method efficiently computes the potential due to a collection of particles on an adaptive mesh. We are investigating this method as a complement to the above methods for future collisionless particle simulations (e.g., shock acceleration of cosmic rays). We have made the following modifications to FLASH to incorporate space-and time-varying gravitational source terms: We retain the potential at the previous timestep (  n-1 ) and use it with  n to estimate the time-advanced potential,  n+1. We use  n+1 to make second-order corrections to input states for the Riemann problems solved in the PPM hydrodynamics module, as described by Colella and Woodward (1984). Keeping old state variables within a consistent code framework requires us to implement a variable registration interface (included with FLASH 2.0). For the Riemann state modifications we require cell-averaged accelerations, which can be determined exactly from face-averaged potentials. However, the Poisson solvers give us cell-averaged potentials. Careful averaging of interpolants gives us the following second-order difference expression for the cell-averaged acceleration: In relaxation solvers (e.g., multigrid), we use the PARAMESH flux conservation routines to maintain consistency across jumps in mesh refinement. This is needed because field values on the low-refinement sides of such jumps are obtained through interpolation. For self-gravitating problems, in addition to refining the mesh using a second- derivative criterion, we refine blocks using the maximum density contrast  max  max{ |  -  avg |/  avg } in each block. This work has been supported by the U.S. Department of Energy under Grant No. B341495 to the Center for Astrophysical Thermonuclear Flashes at the University of Chicago. Left, time evolution of the kinetic, thermal, and potential energies for a stable Jeans mode simulated in 2D with FLASH 1.61 using the multigrid Poisson solver. Right, the dispersion relation derived for stable modes calculated with FLASH, compared against the analytic result (Jeans 1902). Time evolution of a slice from a 2D multimode Jeans-unstable calculation performed using FLASH 1.61 with the multigrid Poisson solver. Time evolution of a 3D isothermal sphere collapse problem performed using FLASH 1.61 with the multipole Poisson solver (cf. Foster & Chevalier 1993).