FURTHER DISCUSSION OF NUMERICAL ERRORS IN CFD

The methods of estimating numerical errors given in an earlier paper are extended in directions that make them useful in actual CFD applications. In particular, the method of estimating convergence error (the error due to insufficient iteration) is extended to allow the possibility of complex eigenvalues; an ad hoc method that can be applied to any case is also given. For the discretization error, which arises from the numerical approximation of the differential equation(s), methods that can be used on non-uniform drids are presented; they can be extended to unstructured grids as well. The utility of these methods is demonstrated for linear problems as well as solutions of the Navier-Stokes equations. The examples show that the estimation of errors is neither difficult nor expensive.     

Theoretical investigation of the Renner-Teller effect in Δ electronic states of tetra-atomic molecules. 1. Variational calculation of vibronic structure in the 11Δg state of B2H2

A variational approach for the ab initio handling of the Renner-Teller effect in Δ electronic states of tetra-atomic molecules is presented. The model Hamiltonian involves four nuclear degrees of freedom which correlate for a linear nuclear arrangement with two doubly degenerate bending modes. The bond lengths are assumed to be kept fixed at their equilibrium values and the effect of end-over-end rotations is neglected. The kinetic energy operator and the general form of the potential surfaces employed allow in principle for a treatment of large amplitude bending vibrations. However, because of restrictions implied, such as neglect of coupling between bending and stretching vibrations and interactions with other electronic states, the approach is aimed primarily at molecules bending with relatively small amplitudes around their linear equilibrium geometries. Two algorithms are developed, one for symmetric acetylene-like (A-B-B-A) molecules, the other for asymmetric (A-B-C-D) species. The approach is applied to calculate the vibronic spectrum of the lowest lying excited state, ¹Δ_g, of B₂H₂, employing ab initio computed potential energy surfaces.