Stability and convergence analysis of rotational velocity correction methods for the Navier–Stokes equations

The velocity correction method has shown to be an effective approach for solving incompressible Navier–Stokes equations. It does not require the initial pressure and the inf-sup condition may not be needed. However, stability and convergence analyses have not been established for the nonlinear case. The challenge arises from the splitting associated with the nonlinear term and rotational term. In this paper, we carry out stability and convergence analysis of the first-order method in the nonlinear case. Our technique is a new Gauge–Uzawa formulation, which brings forth a telescoping symmetry into the rotational form. We also provide a stability proof for the second-order method in the linear case. Numerical results are provided for both first- and second-order methods.

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