Multi-domain simulations of the time dependent Navier-Stokes equations: benchmark error analysis of some nesting procedures

This paper presents a benchmark error analysis of various approaches for treating multiple domain calculations within an anelastic finite difference model. One-way and two-way interactive nesting errors with and without temporal refinement are evaluated. The two-way interactive nesting approach is one where solutions between fine and coarse grid domains are matched through the simple post insertion of data. On the other hand, the equations can be matched by using the pressure defect correction approach. It is shown that, for the present model, the two-way interactive nesting method gives identical results to multi-domain solutions using the pressure defect correction approach. The present results indicate that in this type of analastic framework, a priori matching of the equations is equivalent to the a posteriori matching of the solutions. This result is attributed to the inflexible nature of the Neumann boundary conditions on the fine mesh pressure which need to be specified from the coarse mesh. Since a large number of meterological models employ the hydrostatic assumption, it is of interest to know of nesting errors attributable to this approximation. The results presented indicate essentially equivalent error levels for both the hydrostatic and nonhydrostatic systems of equations for the present case of airflow over an isolated mountain. It is shown how nesting technology can be used in a virtual sense to reduce the central memory requirements for large array sized numerical simulations. Nesting can be used in this sense to decompose the maximum memory working space required without affecting the results.