Adaptive time-stepping algorithms for the scalar auxiliary variable scheme of Navier-Stokes equations

Adaptive time stepping is an important tool for controlling the simulation error and enhancing its efficiency in computational fluid dynamics. In this paper, we introduce two adaptive time-stepping algorithms based on the scalar auxiliary variable scheme for the Navier-Stokes equation. One way is to take equidistribution of energy decay to control the variance of the time steps, and in the other way, the relative error is involved to produce time steps. The numerical experiments show that the computational time is significantly saved by these methods.