Momentum control volumes for finite difference codes

The integration of the Navier-Stokes equations in finite difference codes is considered. First, the surface integral technique is described using momentum control volumes. Then, attention is focused on the problem of the spherical expansion of a gas. The difference equations are analyzed to see why the numerical calculation does not preserve spherical symmetry. Then general, yet simple, techniques are proposed for reducing the errors that break the symmetry. Numerical results demonstrate the utility of the techniques proposed here. Finally, questions of accuracy and stability of the integration for nonuniform meshes are considered.