Coronal holes and icosahedral symmetry: Part 3: Integration of the hydrodynamic equations

In continuation of our study of the application of group theory to the problem of solar wind expansion out of a system of coronal holes, this third paper deals with the formulation and subsequent numerical integration of the basic hydrodynamic equations. After calculating the metric coefficients and the corresponding Christoffel symbols, a description of a numerical procedure exploiting icosahedral symmetry and solutions of the equations are presented for several sets of boundary conditions. The properties of the resulting time-independent three-dimensional fields of number density, velocity and temperature of the solar wind are discussed, and the significance of such solutions, in particular for periods of solar activity maxima, is pointed out.