Sub-timing in fluid flow and transport simulations

A sub-time stepping method is described for computational fluid dynamics problems that utilize implicit-type time marching procedures to resolve transients. In this method, small time-step sizes are used in portions of a domain where interest and activity is high, with larger time-step sizes being applied in other locations. The sub-time step is an integral portion of a larger time step––i.e., multiple sub-time steps over a sub-timed part of a domain add up to the time interval of the full time step used over the remainder of the domain. The technique is particularly suitable for extensive simulations where large portions of a domain are temporally over-discretized. The principles underlying implementation of the implicit sub-timing procedure, the computational effort in relation to conventional implicit time-stepping methods, and an analysis of the effects of sub-timing on the matrix structure are presented. Feasibility and applicability of the implicit sub-timing method is demonstrated through three proof-of-the-concept example problems. These examples include implementation of implicit sub-timing to one-dimensional as well as two-dimensional flow and solute transport problems.