New Variants of Deation Techniques for Pressure Correction in Bubbly Flow Problems 1
Jinyu Tang, C. Vuik, J. M. Burgerscentrum · 2007
For various applications, it is well-known that deated ICCG is an ecien t method to solve linear systems iteratively. This deated ICCG can also be used to solve linear systems with a singular coecien t matrix arising from a discretization of the Pois- son equation with Neumann boundary conditions and discontinuous coecien ts. The use of sparse subdomain deation vectors in this method appears to be very eectiv e. In this paper, we explain this in more detail by applying a spectral analysis with perturbed eigenvectors. Moreover, we introduce new variants of the deation technique, that can deal with the pressure-correction equation for two-phase o w problems and in particular bubbly o w problems. The rst variant is the deation technique with the so-called levelset deation vectors. In contrast to the standard subdomain deation vectors, those vectors are related to the location of the bubbles in the domain. Another deation variant uses the so-called levelset-subdomain deation vectors and prots of the advantages of both subdomain and levelset deation vectors. Numerical experiments show the good performance of these new deation variants. c 2007 European Society of Computational Methods in Sciences and Engineering