seminar

In this talk, I will talk about some essential improvements on the original scalar auxiliary variable(SAV) approach. The Generalized SAV approach(GSAV) enjoys the following remarkable properties: 1. The computational cost is half of the original SAV approach. 2. It can be used to construct high-order unconditionally stable schemes with rigorous error analysis. 3. The new approach is not limited to the gradient flow systems, it can be applied to general dissipative systems.

We combine this GSAV approach with a new consistent splitting scheme for the Navier-Stokes equations, and obtain, for the first time, a strongly unconditional stable, decoupled schemes with uniform second-order accuracy for the velocity and pressure.