Softened Lagrangian hydrodynamics for cosmology

A new approach to cosmological hydrodynamics is discussed that is based on a moving, quasi-Lagrangian mesh. The softened Lagrangian hydrodynamics (SLH) method utilizes a high-resolution Lagrangian hydrodynamic code combined with a low-resolution Eulerian solver to deal with severe mesh distortions. Most of the volume of a simulation is treated with the Lagrangian code and only in sites where the Lagrangian approach fails, due to mesh distortions, does the Eulerian part of the code step in. This approach utilizes a high-resolution gravity solver without use of TREE or P3M methods; Poisson's equation is solved on the moving baryonic mesh using a simple relaxation technique. The dark matter is included by means of the cloud-in-cell method on the Lagrangian mesh. All three components of the cosmological code--gravity, dark matter, and baryons--are thus treated selft-consistently with exactly the same resolution. The computer code based on the SLH approach is described in detail, and comparison with existing Eulerian and smooth particle hydrodynamics (SPH) codes is presented. For most purposes the SLH approach turns out to be the intermediate between Eulerian and SPH codes, but it outperforms both of these approaches in resolving caustics. Thus, it may turn out to be a valuable tool to study galaxy formation.