Geodesic
Stationary solutions of equations describing the nonisothermal flow of an incompressible viscoelastic polymeric fluid
Matematičeskoe modelirovanie, Tome 28 (2016) no. 10, pp. 3-22.

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This work is dedicated to analysis and simulation of non-isothermal flow of an incompressible viscoelastic polymer fluid arising while manufacturing products from polymers by 3D printing. To this end a new rheological model was used accounting for the properties of macromolecular coil of solutions and melts of linear polymers, their anisotropy, viscosity and temperature impacts. A boundary value problem for quasilinear equation defining the velocity profile of polymer fluid through the tube with a rectangular cross-section was posed. The problem includes small parameters and nonlinear functional dependencies with large gradients that makes it difficult to perform numerical simulations. On the basis of approximations without saturation a new computational algorithm with enhanced properties of accuracy and stability was developed. It allows us to obtain numerical solutions in the wide range of values of problem parameters, including the cases of small thickness of channel.
Keywords: rheological model, boundary value problem, quasilinear equation, nonlocal numerical method, method without saturation. 
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A. M. Blokhin; B. V. Semisalov; A. S. Shevchenko. Stationary solutions of equations describing the nonisothermal flow of an incompressible viscoelastic polymeric fluid. Matematičeskoe modelirovanie, Tome 28 (2016) no. 10, pp. 3-22. http://geodesic.mathdoc.fr/item/MM_2016_28_10_a0/

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