Density estimators in particle hydrodynamics - DTFE versus regular SPH

We present the results of a study comparing density maps reconstructed by the Delaunay Tessellation Field Estimator (DTFE) and by regular SPH kernel-based techniques. The density maps are constructed from the outcome of an SPH particle hydrodynamics simulation of a multiphase interstellar medium. The comparison between the two methods clearly demonstrates the superior performance of the DTFE with respect to conventional SPH methods, in particular at locations where SPH appears to fail. Filamentary and sheetlike structures form telling examples. The DTFE is a fully self-adaptive technique for reconstructing continuous density fields from discrete particle distributions, and is based upon the corresponding Delaunay tessellation. Its principal asset is its complete independence of arbitrary smoothing functions and parameters specifying the properties of these. As a result it manages to faithfully reproduce the anisotropies of the local particle distribution and through its adaptive and local nature proves to be optimally suited for uncovering the full structural richness in the density distribution. Through the improvement in local density estimates, calculations invoking the DTFE will yield a much better representation of physical processes which depend on density. This will be crucial in the case of feedback processes, which play a major role in galaxy and star formation. The presented results form an encouraging step towards the application and insertion of the DTFE in astrophysical hydrocodes. We describe an outline for the construction of a particle hydrodynamics code in which the DTFE replaces kernel-based methods. Further discussion addresses the issue and possibilities for a moving grid-based hydrocode invoking the DTFE, and Delaunay tessellations, in an attempt to combine the virtues of the Eulerian and Lagrangian approaches