On Nonlinear Approximations to Cosmic Problems with Mixed Boundary Conditions
Abstract
Nonlinear approximations to problems with mixed boundary conditions are useful for predicting large-scale streaming velocities from the density field, or vice-versa. We evaluate the schemes of Bernardeau bernardeau92, Gramann gramann93, and Nusser ηl nusser91, using smoothed density and velocity fields obtained from N-body simulations of a CDM universe. The approximation of Nusser ηl is overall the most accurate and robust. For Gaussian smoothing of 1000\ the mean error in the approximated relative density perturbation, δ, is smaller than 0.06, and the dispersion is 0.1. The \ error in the estimated velocity is smaller than 60, and the dispersion is 40. For smoothing of 500\ these numbers increase by about a factor 2 for δ< 4-5, but deteriorate at higher densities. The other approximations are comparable to those of Nusser ηl for smoothing of 1000, but are much less successful for the smaller smoothing of 500.
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