Are Numerical Simulations Reliable? Proposed Improvements and Tests

Abstract

When one builds a code to simulate numerically a process, the first concern is the range of validity of the results. This can be accessed empirically, though the results can be misleading if the tests are too naive. For particle-mesh codes simulating the gravitational clustering, an analytical theory has been proposed in Bouchet et al. 1985. It yields the numerical dispersion relation of the system in the linear regime, and thus describes how the linear growth rate is affected by the discretisation. The theoretical predictions are in agreement with the results of actual numerical experiments: both show that the results of standart particle-mesh codes should not be trusted at distances smaller than 6 to 8 grid-spacing Δx (depending on the detail of the algorithm).