A new class of higher-order decoupled schemes for the incompressible Navier-Stokes equations and applications to rotating dynamics

Abstract

A new class of time discretization schemes for the Navier-Stokes equations with non-periodic boundary conditions is constructed by combining the SAV approach for general dissipative systems in [15] and the consistent splitting schemes in [10]. The new schemes are unconditionally stable, only require solving linear equations with constant coefficients at each time step, and can be up to six-order accurate in time. With a Legendre-Galerkin method in space, the full discretized schemes can efficiently treat the Coriolis force implicitly. Delicate numerical simulations for highly complex rotating flows are presented to validate the new schemes.