Implicit-explicit Crank-Nicolson scheme for Oseen’s equation at excessive Reynolds quantity
Authors: Erik Burman, Deepika Garg, Johnny Guzman
Summary: On this paper we proceed the work on implicit-explicit (IMEX) time discretizations for the incompressible Oseen equations that we began in cite{BGG23} (E. Burman, D. Garg, J. Guzmàn, {emph{Implicit-explicit time discretization for Oseen’s equation at excessive Reynolds quantity with utility to fractional step strategies}}, SIAM J. Numer. Anal., 61, 2859–2886, 2023). The stress velocity coupling and the viscous phrases are handled implicitly, whereas the convection time period is handled explicitly utilizing extrapolation. Herein we deal with the implicit-explicit Crank-Nicolson methodology for time discretization. For the discretization in area we take into account finite factor strategies with stabilization on the gradient jumps. The stabilizing phrases ensures inf-sup stability for equal order interpolation and robustness at excessive Reynolds quantity. Beneath appropriate Courant situations we show stability of the implicit-explicit Crank-Nicolson scheme on this regime. The stabilization permits us to show error estimates of order O(hk+12+τ2). Right here h is the mesh parameter, ok the polynomial order and τ the time step. Lastly we talk about some fractional step strategies which can be implied by the IMEX scheme. Numerical examples are reported evaluating the completely different strategies when utilized to the Navier-Stokes’ equations
