Finite element solution of flow problems with mixed-time integration

A mixed-time integration method that had been developed for the finite element analysis of structural and thermal dynamics has been implemented for the study of both steady and unsteady fluid mechanics problems. The method to be discussed is capable of partitioning the domain into implicit and explicit regions in an attempt to capitalize on the desirable properties of each method, namely the stability and accuracy of the implicit method, and the manageable computational resource demands of an explicit method. In addition, the explicit region is further divided into subregions, each of which may have a different time step that is governed by the local stability criterion of an explicit method. To demonstrate the applicability of these methods to equation systems that govern fluid flow, several examples are presented. These include one- and two-dimensional advection of a cosine hill, as well as two-dimensional steady and unsteady inviscid, compressible flow problems. These examples will be used to show the favorable features of a multi-time integration method, such as a reduction in CPU time, which can be directly attributed to the differing time steps used in the various subregions.