Three dimensional simulation of high compressible flows using a subcycling algorithm for time integration

An algorithm to simulate 3-D high compressible flows using the finite element method and a multi-time-step integration technique with subcycles is presented in this work. An explicit two-step Taylor-Galerkin scheme is adopted to integrate in time continuum equations. When explicit schemes are used, the time steps must satisfy some stability conditions. If the smallest critical time-step is adopted uniformely for the whole domain, the integration scheme may consume a large amount of CPU time. Multi-time-step integration techniques are very suitable in these cases because elements and nodes are separated into several groups and a different time-step is assigned to each group. In this way, each group of elements is integrated with a time interval wich is much closer to the critical time steps of the elements in the group. This results in great computational savings, mainly when elements size and properties are very different, leading to significative differences of the local critical time steps values. Multi-time-steps integration techniques are also very useful in transient problems, taking into account that at the end of each subcycle, values of the unknowns at the same time level are obtained. The multi-time-step algorithm is applied to analyze the supersonic flow (Mach=8,5) past a sphere immersed in a non viscous flow, and results and computational performance are compared with those obtained when a uniformly time-step is used over the whole domain.