Acceleration of preconditioned krylov solvers for bubbly flow problems

Abstract

We consider the linear system which arises from discretization of the pressure Poisson equation with Neumann boundary conditions, coming from bubbly flow problems. In literature, preconditioned Krylov iterative solvers are proposed, but these show slow convergence for relatively large and complex problems. We extend these traditional solvers with the so-called deflation technique, which accelerates the convergence substantially. Several numerical aspects are considered, like 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 computational time. © Springer-Verlag Berlin Heidelberg 2007.