Abstract
The properties of a set of conservative positive rate equations, such as the collisional-radiative equations, are investigated. It is shown that the equations are positivity maintaining, and furthermore, converge uniformly onto a unique equilibrium state consistent with physical constraints. Two methods of integration are considered. The first involving eigenvector decomposition yields an exact solution, but is expensive in computer time, and cumbersome if the rate matrix is defective. A simple weighted finite difference approach may be integrated stiffly and unconditionally stably, and is therefore suitable for inclusion in multi-celled fluid codes. The improvement in accuracy obtained by weighting is investigated, and attention is drawn to the importance of a positivity-maintaining form.
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