Flow Solver

The flow solver of FP utilises data produced by the grid generator, together with data read from an input file named FLOW.DAT, and proceeds to calculate the solution to the exact (or full) potential equation of inviscid compressible flow in three dimensions, by a method of finite-differences. The solution algorithm uses repeated iterations with 'over-relaxation'. The speed of overall convergence is improved by the facility to perform the relaxation scheme on three different levels of grid fineness. The finest grid (level 1) corresponds to the grid as produced by the grid generator. The middle grid (level 2) has half the numbers of grid intervals in each of the three coordinates (r,η,θ) of those in level 1. The coarsest grid (level 3) has the same number of grid intervals in the r and directions as those of the middle grid, but half the number of grid intervals in the direction of those of the middle grid (i.e. one quarter the number of grid intervals of those of the finest grid). The user controls the number of relaxation iterations carried out on each grid by means of parameters in the input file FLOW.DAT. A batch of successive iterations on a particular level of grid is termed a step. A typical run commences with one or two coarse-grid steps, continues with a middle-grid step and concludes with one or more fine grid steps. Each step typically comprises one hundred or more iterations. Full convergence (when changes in the computed flow can no longer be detected) typically requires two thousand or more iterations. As well as specifying a particular number of iterations for a step, it is also possible to impose convergence criteria, and to make the termination of the run (or step) dependent on the satisfaction of these criteria.