Grid Adaptive Algorithms for the Solution of the Euler Equations on Irregular Grids.
by J. Pike.
Journal of Computational Physics, Vol 71, No 1, pp. 194-223, July 1987.

Summary.
The effect of grid irregularity on the accuracy of algorithms for one-dimensional unsteady flow is investigated. It is shown how standard second order accurate algorithms for equally spaced grids may be extended to act as first order accurate algorithms on an irregular grid. The loss of accuracy on irregular grids is found to cause a significant reduction in the quality of the results. To obtain solutions comparable in quality with second order accurate algorithms on equally spaced grids, a class of second order accurate algorithms is derived, which are conservative and compatable on randomly spaced grids. They are shown to give solutions similar in quality to those obtainable on equally spaced grids.

Comment.
When calculating compressible flows, the accuracy of the solution depends on both the calculating algorithm used, and the type of grid on which the solution is performed. For many algorithms, the accuracy of the algorthm is stated assuming that the grid is regularly spaced, neglecting the errors or oscellations that sudden changes in grid size can cause in the solution. The algorithms developed in the present paper demonstrate how to amend current algorithms to regain second order accuracy on general one-dimensional irregular grids. When applied to calculations in two and three dimensions, the algorithms will then compensate for changes in cell size, but they will not compensate for the skewness or non-rectangularity in the cell which can occur. This gives increased freedom, but not complete freedom in the grid specification.

Availability
Obtainable from the Journal of Computational Physics
or email J A C K @ J A C K P I KE . C O . U K

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Last amended:Dec 2013.