The Holy Grail

Art Taylor of Old Dominion University has suggested that the use of the already converged flow field in IIM should have increased stability properties, and thus it should be possible to increase the time step of each iteration. Increasing the time step would have the effect of lowering the number of iterations necessary to get a final answer.

We increased the time steps by factors of 2,4, and 8. In all cases, the answer converged to the correct AD value. The number of iterations was reduced by factors of 2, 4, and 4. Apparently, increasing the time step by a factor of 8 does not improve the convergence any more than a does a factor of 4. The figure below shows the derivative of ``coefficient of lift'' to ``angle of attach'' for each of these four timesteps.

We do not know if the CFL number can always be increased, but the technique certainly bears further consideration.