A Conservative Second-Order Difference Scheme for Curvilinear Coordinates - Part One - Assignment of Variables on a Staggered Grid
A conservative second-order difference scheme for solving the equations of ideal hydrodynamics is described. Although it is capable of dealing with general orthogonal curvilinear coordinates, it was mainly developed for calculating the axisymmetric collapse of rotating stellar cores in spherical coordinates.The basic features of the scheme are: (i) variables are assigned to "volume centers" of the computational cells and not to "geometrical cell centers" as usual; (ii) the spatial discretization is of second-order accuracy and includes monotonicity constraints; (iii) advectional changes are calculated by using a "volume advection scheme" instead of evaluating interface integrals of the advection fluxes; (iv) the time evolution is described by an explicit, second-order accurate discretization (v) a moving non-equidistant, staggered grid can be used. In addition a Poisson solver for axially symmetric mass distributions is incorporated into the scheme. In this paper it is demonstrated that for the simple but important test problem of a spherical dust collapse the proposed difference scheme avoids the pitfalls occurring whenever a discretization scheme originally developed for straight coordinates is applied to curvilinear Eulerian coordinates in a straightforward way.
Astronomy and Astrophysics
- Pub Date:
- June 1989