Improving the speed and accuracy of projection-type incompressible flow solvers

Superseding so-called first-generation incompressible flow solvers of the projection type (based on Taylor–Galerkin advection, second-order pressure damping and element-based data structures), the current, second-generation solvers (based on high-order upwind advection, fourth-order pressure damping and edge-based data structures) have now been in use for half a decade and have proven remarkably robust and efficient for many large-scale problems. In order to achieve higher accuracy and speed, these solvers have recently been enhanced in a variety of ways: (a) substepping for advection, (b) implicit treatment of advective terms via SGS and GMRES-LU-SGS iterative solvers, (c) fully implicit, time-accurate advancement of pressure and velocities, and (d) linelet preconditioning for the pressure-Poisson equation. The combined effect of these third-generation improvements leads to speedups of the order of O(1:5−1:10), with similar or even better temporal accuracy, as demonstrated on a variety of academic and industrial problems.