Accelerating incompressible flow calculations using a quasi-implicit scheme: local and dual time stepping approaches

In this paper, a local time stepping approach is proposed for incompressible flow calculations using a quasi-implicit time discretization. Since the non-linear convection term is treated explicitly by this discretization, the convective part of the time step limit still applies. To effectively manage the convection stability limit, the locally calculated time step values are employed. These local time step values are calculated for elements, rather than on nodes to avoid unsymmetric matrices. To avoid any adverse impact of local time stepping on the transient solution, a dual time stepping approach is employed for time dependent problems. The results clearly show that a speed up of more than five times is possible using the local time stepping approach. Although the proposed local time stepping approach is employed for a finite element based spatial discretization, it is applicable to any other form of spatial discretization.