The Collapse of Interstellar Gas Clouds--II: An Analytical Study

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Abstract
The equations of hydrodynamics with gravitation are derived in an Eulerian form suitable for direct use in numerical methods. This form of the equations is particularly well suited for a simple derivation of analytical solutions for the case of linear wave flow. Linear wave flow solutions are obtained with a view to their subsequent use as checks of the numerical studies. It is thereby shown that integral checks of the motion can ascribe a misleading accuracy to the numerical methods—in particular an integral check may show that an error of less than 0.1 per cent is to be expected whereas a comparison with an analytical solution showed the existence of errors of about 100 per cent in the parameters of the solution near the centre of the gas cloud.

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