The Effect of Boundary Conditions within Pressure Convection–Diffusion Preconditioners

We explore choices of boundary conditions within pressure convection–diffusion preconditioners for the incompressible Navier–Stokes equations. While these methods have been shown to be efficient, choosing the proper boundary conditions for the preconditioning operator is not well understood. In this paper, we first explore the effect of having “ideal” boundary conditions within the preconditioner. While not computationally feasible, the ideal boundary condition results highlight the importance of suitable boundary conditions. The remainder of the paper explores somewhat more practical approximations to the ideal conditions based on ILU factorizations and probing [5]. ∗This work was supported by Sandia National Labs. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC0494AL85000. †This work was supported by Sandia National Labs. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC0494AL85000. ‡This work was supported by Sandia National Labs. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC0494AL85000. §Sandia National Laboratories, PO Box 969, MS 9159, Livermore, CA 94551, [email protected]. ¶Department of Computer Science, University of Illinois at Urbana-Champaign, 201 N Goodwin Ave, Urbana, IL 61801, [email protected]. ‖Sandia National Laboratories, PO Box 969, MS 9159, Livermore, CA 94551, [email protected].