An unconditionally stable rotational velocity-correction scheme for incompressible flows
We present an unconditionally stable splitting scheme for incompressible NavierStokes equations based on the rotational velocity-correction formulation. The main advantages of the scheme are: (i) it allows the use of time step sizes considerably larger than the widely-used semi-implicit type schemes: the time step size is only constrained by accuracy; (ii) it does not require the velocity and pressure approximation spaces to satisfy the usual infsup condition: in particular, the equal-order finite element/spectral element approximation spaces can be used; (iii) it only requires solving a pressure Poisson equation and a linear convectiondiffusion equation at each time step. Numerical tests indicate that the computational cost of the new scheme for each time step, under identical time step sizes, is even less expensive than the semi-implicit scheme with low element orders. Therefore, the total computational cost of the new scheme can be significantly less than the usual semi-implicit scheme.
velocity-correction scheme unconditional stability spectral element method navier-stokes equation