A generalized modular grad-div Picard iteration for the incompressible Navier–Stokes equations

In this paper, we propose a generalized modular grad-div Picard iterative method for the stationary Navier–Stokes equations describing the motion of a viscous incompressible fluid. The innovative approach integrates an intrusive module into existing Navier–Stokes solver codes. This integration not only enhances the capability to handle problems with higher Reynolds numbers but also effectively mitigates solver failures and improves computational efficiency as the grad-div parameter increases. Furthermore, we provide analysis of stability and convergence. Finally, several numerical experiments are conducted to validate the theoretical findings and demonstrate the advantage of the proposed method.