Effective vorticity-velocity formulations for three-dimensional incompressible viscous flows (Q1903816)

The main concern is an effective numerical solution of the kinematic Cauchy-Riemann equations for velocity, especially when the divergence- free condition for vorticity is violated due to numerical error. The mathematical formulation of a differential and an integral approaches are revisited. A novel projection of vorticity onto the divergence-free space and its application to the two approaches are studied. As an illustration of the differential approach, the three-dimensional lid-driven cavity problem is solved. The projection scheme is justified through numerical tests by comparing it to a new fully divergence-free scheme.