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

In this talk, I will discuss the challenges of simulating a fluid flow in a rotating cube numerically and the limitations of current numerical schemes. I will then introduce a new class of higher-order time discretization schemes for the Navier-Stokes equations with non-periodic boundary conditions. The proposed 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. Several numerical examples demonstrating the advantages of the proposed schemes will be discussed, including the higher accuracy despite larger time steps for the high-order schemes compared to second-order.