A New Convergence Acceleration Technique for Scramjet Flowfields

This paper outlines a new convergence acceleration de-signed to solve scramjet flowfields with zones of re-circulation. Named the “marching-window”, the algorithm consists of performing pseudo-time iterations on a minimal width subdomain composed of a sequence of cross-stream planes of nodes. The upstream boundary of the subdomain is positioned such that all nodes upstream exhibit a residual smaller than the user-specified convergence threshold. The advancement of the downstream boundary follows the advancement of the upstream boundary, except in zones of significant streamwise ellipticity where a streamwise ellipticity sensor ensures its continuous progress. Compared to the standard pseudo-time marching approach, the march-ing-window is here seen to decrease the work required for convergence by up to 24 times for supersonic flows with little streamwise ellipticity and by up to 8 times for supersonic flows with large streamwise separated regions. The memory requirements are observed to be reduced sixfold by not allocating memory to the nodes not included in the computational subdomain. The marching-window satisfies the same convergence criterion as the standard pseudo-time stepping methods, hence resulting in the same converged solution within the tolerance of the user-specified convergence threshold. The extension of the marching-window to the weakly-ionized Navier-Stokes equations is also discussed.