New Variants of Deflation Techniques for Pressure Correction in Bubbly Flow Problems

Date of Online Publication: 27/10/2007
Keywords: deflation, conjugate gradient method, preconditioning, Poisson equation, symmetric positive semi-definite matrices, bubbly flow problems, level-set
Authors: J.M. Tang, C. Vuik
Pages: 227-249
For various applications, it is well-known that deflated ICCG is an efficient method to solve linear systems iteratively. This deflated ICCG can also be used to solve linear systems with a singular coefficient matrix arising from a discretization of the Poisson equation with Neumann boundary conditions and discontinuous coefficients. The use of sparse subdomain deflation vectors in this method appears to be very effective. In this paper, we explain this in more detail by applying a spectral analysis with perturbed eigenvectors.

Moreover, we introduce new variants of the deflation technique, that can deal with the pressure-correction equation for two-phase flow problems and in particular bubbly flow problems. The first variant is the deflation technique with the so-called levelset deflation vectors. In contrast to the standard subdomain deflation vectors, those vectors are related to the location of the bubbles in the domain. Another deflation variant uses the so-called levelset-subdomain deflation vectors and profits of the advantages of both subdomain and levelset deflation vectors. Numerical experiments show the good performance of these new deflation variants.

 

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