NONLINEAR HYDRODYNAMICS OF COSMOLOGICAL SHEETS .1. NUMERICAL TECHNIQUES AND TESTS

We present the numerical techniques and tests used to construct and va lidate a computer code designed to study the multidimensional nonlinea r hydrodynamics of large-scale sheet structures in the universe, espec ially the fragmentation of such structures under various instabilities . This code is composed of two codes, the hydrodynamical code ZEUS-2D and a particle-mesh code. The ZEUS-2D code solves the hydrodynamical e quations in two dimensions using explicit Eulerian finite-difference t echniques, with modification made to incorporate the expansion of the universe and the gas cooling due to Compton scattering, bremsstrahlung , and hydrogen and helium cooling. The particle-mesh code solves the e quation of motion for the collisionless dark matter. The code uses two -dimensional Cartesian coordinates with a nonuniform grid in one direc tion to provide high resolution for the sheet structures. A series of one-dimensional and two-dimensional linear perturbation tests are pres ented which are designed to test the hydro solver and the Poisson solv er with and without the expansion of the universe. We also present a r adiative shock wave test which is designed to ensure the code's capabi lity to handle radiative cooling properly. And finally a series of one -dimensional Zel'dovich pancake tests used to test the dark matter cod e and the hydro solver in the nonlinear regime are discussed and compa red with the results of Bond et al. (1984) and Shapiro & Struck-Marcel l (1985). Overall, the code is shown to produce accurate and stable re sults, which provide us a powerful tool to further our studies.