1 research outputs found
Stability analysis of a singlerate and multirate predictor-corrector scheme for overlapping grids
We use matrix stability analysis for a singlerate and multirate
predictor-corrector scheme (PC) used to solve the incompressible Navier-Stokes
equations (INSE) in overlapping grids. By simplifying the stability analysis
with the unsteady heat equation in 1D, we demonstrate that, as expected, the
stability of the PC scheme increases with increase in the resolution and
overlap of subdomains. For singlerate timestepping, we also find that the
high-order PC scheme is stable when the number of corrector iterations () is
odd. This difference in the stability of odd- and even- is novel and has not
been demonstrated in the literature for overlapping grid-based methods. We
address the odd-even behavior in the stability of the PC scheme by modifying
the last corrector iterate, which leads to a scheme whose stability increases
monotonically with . For multirate timestepping, we observe that the
stability of the PC scheme depends on the timestep ratio (). For
, even- is more stable than odd-. For , even- is
more stable than odd- for a small nondimensional timestep size and the
odd-even behavior vanishes as the timestep size increases. The stability
analysis presented in this work gives novel insight into a high-order temporal
discretization for ODEs and PDEs, and has helped us develop an improved PC
scheme for solving the incompressible Navier-Stokes equations.Comment: 34 pages, 18 figure