2003/08/25 by Alexander N. Gorban, A. N. Gorban, P. A. Gorban +3 · 14 citations
Chemical Engineering · Engineering · Mathematics · Physics and Astronomy · #Computer science #Environmental science #Integrator #Legendre polynomials #Mathematical analysis #Mathematics #Numerical methods for differential equations #Phase Equilibria and Thermodynamics #Rheology and Fluid Dynamics Studies #Telecommunications #cond-mat #math-ph #math.MP #physics.comp-ph
paper · pdf · doi:10.1016/j.jnnfm.2003.12.005
published in Journal of Non-Newtonian Fluid Mechanics 120(1-3), 149-167 (Elsevier BV) · 40 pages, 3 figures, submitted to the Journal of Non-Newtonian Fluid Mechanics
arxiv created 2003/08/25 · openalex publication_date 2004/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A toolbox for the development and reduction of the dynamical models of nonequilibrium systems is presented. The main components of this toolbox are: Legendre integrators, dynamical postprocessing, and thermodynamic projector. Thermodynamic projector is the tool to transform almost arbitrary anzatz to a thermodynamically consistent model, the postprocessing is the cheapest way to improve the solution, obtained by the Legendre integrators. Legendre Integrators give the opportunity to solve linear equations instead of nonlinear ones for quasiequilibrium (MaxEnt) approximations. The essentially new element of this toolbox, the method of thermodynamic projector, is demonstrated on application to FENE-P model of polymer kinetic theory. The multy-peak model of polymer dynamics is developed. The simplest example, discussed in details, is the two peaks model for Gaussian manifold instability in polymer dynamics. This type of models opens a way to create the computational models for the "molecular individualism".