Implicit-explicit time integration algorithms for the numerical simulation of blade/casing interactions

In order to solve fast dynamic problems, an explicit method is the most adapted. But for slower dynamics, an implicit method is more stable. Typical industrial problems are governed by high frequency, e.g. impact, during short time intervals and slower dynamics, e.g. spring-back, during other time intervals. The optimal solution is then to have both implicit algorithm and explicit methods readily available in the same code and to be able to switch automatically from one to the other. Criteria that decide when to shift from a method to another have been developed here. Implicit balanced restarting conditions that annihilate numerical oscillations resulting for an explicit calculation are also proposed.