Solving the Bernoulli-Zel'dovich equation

Abstract

view Abstract Citations (9) References (11) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Solving the Bernoulli-Zel'dovich Equation Lachieze-Rey, M. Abstract The Zel'dovich approximation is very efficient in reconstructing the initial conditions (in the form of a displacement field, a deformation tensor, or the corresponding potential) from observational data, usually proper velocities. Recently it has been shown that this problem reduces to a differential equation for the velocity potential, the Bernouilli-Zel'dovich equation, and numerical methods were proposed to solve it. Here I derive an analytical solution to this equation which allows reconstruction without any numerical integration (except a spatial integration of the present velocity field which is the first step of any procedure). This allows the reconstruction of the initial potential at Lagrangian positions. I also propose an approximation which makes this method even more direct, allowing the reconstruction of the initial potential (Lagrangian or Eulerian) at Eulerian positions. Publication: The Astrophysical Journal Pub Date: April 1993 DOI: 10.1086/172486 Bibcode: 1993ApJ...407....1L Keywords: Bernoulli Theorem; Cosmology; Gravitational Fields; Universe; Astronomical Models; Lagrange Coordinates; Reconstruction; Astrophysics; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE; COSMOLOGY: THEORY; METHODS: ANALYTICAL full text sources ADS |