Generalized conservation cells for finite volume calculations

This paper presents a new algorithm development involving a further generalization of the conservation cells used in all current time-marching Euler methods. At present the conservation cells which are used are fairly general, in that they can have an irregular spatial structure and in some unsteady applications may even move during the calculation. However, at present all computational grids share the feature that for time-accurate calculations the nodes at one computational time level all correspond to one physical time. This paper shows the consequences of relaxing this restriction, why it is useful or even necessary in some applications, how it is achieved computationally, the various effects on domains of dependence and numerical stability and some sample results to demonstrate the features discussed.