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- W4387579511 abstract "The log-conformation formulation, although highly successful, was from the beginning formulated as a partial differential equation that contains an, for PDEs unusual, eigenvalue decomposition of the unknown field. To this day, most numerical implementations have been based on this or a similar eigenvalue decomposition, with Knechtges et al. (2014) being the only notable exception for two-dimensional flows. In this paper, we present an eigenvalue-free algorithm to compute the constitutive equation of the log-conformation formulation that works for two- and three-dimensional flows. Therefore, we first prove that the challenging terms in the constitutive equations are representable as a matrix function of a slightly modified matrix of the log-conformation field. We give a proof of equivalence of this term to the more common log-conformation formulations. Based on this formulation, we develop an eigenvalue-free algorithm to evaluate this matrix function. The resulting full formulation is first discretized using a finite volume method, and then tested on the confined cylinder and sedimenting sphere benchmarks." @default.
- W4387579511 created "2023-10-13" @default.
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- W4387579511 date "2023-10-01" @default.
- W4387579511 modified "2023-10-14" @default.
- W4387579511 title "An eigenvalue-free implementation of the log-conformation formulation" @default.
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- W4387579511 doi "https://doi.org/10.1016/j.jnnfm.2023.105133" @default.
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