Acceleration of preconditioned Krylov solvers for bubbly flow problems

  • Authors:

  • Jok Man Tang;Kees Vuik

  • Affiliations:

  • Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics, Delft, The Netherlands;Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics, Delft, The Netherlands

  • Venue:
  • PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
  • Year:
  • 2007

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Abstract

We consider the linear system arising from discretization of the pressure Poisson equation with Neumann boundary conditions, derived from bubbly flow problems. In the literature, preconditioned Krylov iterative solvers are proposed, but they often suffer from slow convergence for relatively large and complex problems. We extend these traditional solvers with the so-called deflation technique, that accelerates the convergence substantially and has favorable parallel properties. Several numerical aspects are considered, such as the singularity of the coefficient matrix and the varying density field at each time step. We demonstrate theoretically that the resulting deflation method accelerates the convergence of the iterative process. Thereafter, this is also demonstrated numerically for 3-D bubbly flow applications, both with respect to the number of iterations and the computing time.