ADAPTIVE SMOOTHED PARTICLE HYDRODYNAMICS, WITH APPLICATION TO COSMOLOGY - METHODOLOGY

The development of a new smoothed particle hydrodynamics( SPH) method, called adaptive smoothed particle hydrodynamics (ASPH), generalized f or cosmology and coupled to the particle mesh (PM) method for solving the Poisson equation, for the gasdynamical simulation of galaxy and la rge-scale structure formation, will be described. The accurate numeric al simulation of the highly nonlinear phenomena of shocks and caustics which occur generically in the process of cosmological structure form ation requires enormous dynamic range and resolution. Existing numeric al methods require substantial modification in order to achieve the re quired resolution with current computer technology. The SPH method is a promising approach to this problem, since it is a Lagrangian numeric al hydrodynamics method which adjusts its resolution dynamically so as to keep track of the mass as it flows. However, in its standard form, SPH suffers from two deficiencies which are particularly acute in the presence of the kind of gravitational collapse and strong shocks whic h are generic to the dynamics of galaxy and large-scale structure form ation. The first deficiency results from the fact that the smoothing k ernel in standard SPH is isotropic, while gravitational collapse and s hock waves involve highly anisotropic volume changes. Hence, the abili ty of SPH to adjust its resolution dynamically so as to follow Lagrang ian fluid changes is limited by the mismatch between this isotropic sm oothing kernel and the inherent anisotropy of the flow. The ASPH metho d solves this problem by replacing the isotropic smoothing kernel of s tandard SPH, which is characterized by a scalar smoothing length h, by an anisotropic smoothing tensor H which adjusts dynamically so as to follow the changes of the local mean interparticle spacing with direct ion around each fluid element. The second deficiency of standard SPH r esults from the fact that artificial viscosity is necessary in order t o accommodate shocks, but this results in substantial and widespread a rtificial heating of gas which is undergoing supersonic collapse far f rom any shock. The ASPH method solves this problem by using the evolut ion of the anisotropic smoothing tensor H to track shocks by predictin g the occurrence of caustics in the now, and thereby to restrict the e ffect of artificial viscosity to just those fluid particles which are involved in the shock transition. The result of these two new features introduced by ASPH is a substantial increase in the resolving power o f the SPH method for the same total number of particles, without any c orresponding increase in computational run time. The new algorithms wh ich constitute the ASPH method are described here in detail. A series of tests of the method in one and two dimensions are presented. These include kinematical tests of the anisotropic smoothing algorithm and a comparison with that of standard SPH, as well as dynamical tests, inc luding the Reimann shock tube problem. A special emphasis is placed on the requirement that the method pass the stringent test of matching t he known, detailed solution of the cosmological pancake collapse probl em. Finally, we apply the ASPH method in two dimensions to simulate th e growth of large-scale structure from a spectrum of primordial densit y fluctuations in a hot dark matter model. The ASPH method succeeds in resolving the generic nonlinear structures and shocks in such a model in a calculation with fewer than 40 particles per pancake per dimensi on.