Semi-implicit Red/Black Solver for Incompressible Navier-Stokes Equations on GPGPU

A novel Semi-Implicit Bicolor Navier-Stokes solver, inspired by red/black scheme for Poisson equation, was developed for simulating incompressible fluids on GPGPU. The solver was shown to be beneficial for simulating highly unsteady flows. Also, it allows more freedom in choice of time step because of the relaxed stability condition. Spatial discretization uses staggered grid and approximates convective terms with WENO scheme to capture the effects of convection-dominated flows. The computation is dominated by the Poisson solver, which uses matrix-free Preconditioned Conjugate Gradient algorithm. Several known matrix-free preconditioners were considered. Red/Black SSOR was found to be the most suitable matrix-free preconditioner for PCG, even though it is usually used as a main solver. A mixed precision modification, developed with sensitivity analysis, was shown to be beneficial for unsteady flows.