By Purushottam D. Gujrati, Arkady I. Leonov
Filling a niche within the literature and prepared to turn into the traditional during this box, this monograph starts off with a glance at computational viscoelastic fluid mechanics and stories of turbulent flows of dilute polymer recommendations. It then is going on talk about simulations of nanocomposites, polymerization kinetics, computational techniques for polymers and modeling polyelectrolytes. additional sections take care of tire optimization, irreversible phenomena in polymers, the hydrodynamics of synthetic and bacterial flagella in addition to modeling and simulation in liquid crystals.The result's valuable interpreting for polymer and theoretical chemists, chemists in undefined, fabrics scientists and plastics technologists.
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Additional info for Modeling and Simulation in Polymers
Therefore, Eqs. 1. Note that at each step of the iterative procedure, all nonlinear terms are known. Therefore, a procedure similar to the one described for the semi-implicit/explicit scheme can be applied. It is also worth noting that the last step in the full implicit scheme is the satisfaction of the divergence-free condition, which in spectral space can be enforced to machine accuracy. The implicit use of the continuity in the development of the Poisson equation for the pressure is not enough to guarantee with machine accuracy the satisfaction of the divergencefree condition due to approximation error involved in the solution of the Poisson equation caused by the coupling of the Chebyshev modes.
Thus, it is also important to examine the dependence of the extensional viscosity on the extensional rate and/or time, and the current data seem to support such a view. Beyond this correlation of model parameters with average macroscopic effects, such as represented by the overall drag reduction, one can ﬁnd in the detailed numerical results a wealth of additional information. 6, one can clearly see that with increasing viscoelasticity the turbulent velocity ﬂuctuations become more anisotropic.
99] have developed a simpler mapping that offers numerical advantages. This most recent idea is based on the Cayley–Hamilton theorem that is used to analytically relate the conformation tensor c to its logarithm tensor A. In fact, the process of updating c employs three simple successive mappings, each one of which is introduced to preserve a speciﬁc property of c : its boundness, its positive deﬁniteness, and (for computational convenience) the avoidance of underﬂow or overﬂow error in calculations.