Accelerated convergence of Euler solutions using time inclining

The use of time inclining for accelerating the convergence to steady state of inviscid-flow computations is examined. This technique, which was originally developed for the efficient computation of time-accurate rotorstator interactions, is based upon a local inclination in time of the computational cells. For convergence acceleration, these inclinations are chosen so as to balance the time-step restrictions for upwind- and downwind-running pressure waves. The inclusion of time inclining into Ni's Lax-Wendroff-type integration scheme is diseased in detail, both in terms of the additional transformations required as well as the selection of inclining parameters for near-optimal convergence rates. The technique is very easy to implement due to its local character and thus makes it an ideal candidate for structured as well as unstructured grid calculation procedures. The effectiveness of time inclining is demonstrated in two dimensions with freestream Mach numbers ranging from 0.2 to 3.0. The results show that although the steady-state accuracy is not affected by inclining, the convergence rate can be more than doubled.