Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7061281 | Journal of Non-Newtonian Fluid Mechanics | 2015 | 28 Pages |
Abstract
The aim of this paper is to find a generalization of the previously made considerations to three dimensions, such that a monolithic Newton-Raphson solver based on the log-conformation formulation can be implemented also in this case. The underlying idea is analogous to the two-dimensional case, to replace the eigenvalue decomposition in the constitutive equation by an analytically more “well-behaved” term and to rely on the eigenvalue decomposition only for the actual computation. Furthermore, in order to demonstrate the practicality of the proposed method, numerical results of the newly derived formulation are presented in the case of the sedimenting sphere and ellipsoid benchmarks for the Oldroyd-B and Giesekus models. It is found that the expected quadratic convergence of Newton's method can be achieved.
Related Topics
Physical Sciences and Engineering
Chemical Engineering
Fluid Flow and Transfer Processes
Authors
Philipp Knechtges,