Building a Cosmological Hydrodynamic Code: Consistency Condition, Moving Mesh Gravity, and SLH-P 3M

Abstract

Building a self-gravitating hydrodynamic code as a combination of a hydrodynamic solver and a gravity solver is discussed. We show that straightforward combining those two solvers generally leads to a code that does not conserve energy locally, and instead a special Consistency Condition ought to be satisfied. A particular example of combining Softened Lagrangian Hydrodynamics (SLH) with a P3M gravity solver is used to demonstrate the effect of the Consistency Condition for a self-gravitating hydrodynamic code. The need to supplement the SLH method with the P3M gravity solver arose because the Moving Mesh Gravity solver, used in conjunction with the SLH method previously, was found to produce inaccurated results. We also show that most existing cosmological hydrodynamic codes implicitly satisfy the Consistency Condition.Comment: postscript figures (except fig.10-12) are included; the full paper including color gif versions of fig.10-12 is available via anonymous ftp at ftp://ftp@arcturus.mit.edu/Preprints/slhp3m.ftp.tar.gz and fig.10-12 together with all color gifs are avaliable at the same address as slhp3m.complement.tar.g