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 Matem. Mod., 2016, Volume 28, Number 10, Pages 3–22 (Mi mm3773)

Stationary solutions of equations describing the nonisothermal flow of an incompressible viscoelastic polymeric fluid

A. M. Blokhinab, B. V. Semisalovbc, A. S. Shevchenkod

a Sobolev Institute of Mathematics, Novosibirsk
b Novosibirsk State University, Novosibirsk
c Design Technological Institute of Digital Techniques, Novosibirsk
d Rubtsovsk Institute (branch) of Altai State University, Rubtsovsk

Abstract: 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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Citation: A. M. Blokhin, B. V. Semisalov, A. S. Shevchenko, “Stationary solutions of equations describing the nonisothermal flow of an incompressible viscoelastic polymeric fluid”, Matem. Mod., 28:10 (2016), 3–22

Citation in format AMSBIB
\Bibitem{BloSemShe16} \by A.~M.~Blokhin, B.~V.~Semisalov, A.~S.~Shevchenko \paper Stationary solutions of equations describing the nonisothermal flow of an incompressible viscoelastic polymeric fluid \jour Matem. Mod. \yr 2016 \vol 28 \issue 10 \pages 3--22 \mathnet{http://mi.mathnet.ru/mm3773} \elib{http://elibrary.ru/item.asp?id=28119108} 

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This publication is cited in the following articles:
1. A. M. Blokhin, A. S. Rudometova, “Stationary currents of a weakly conducting incompressible polymeric fluid between coaxial cylinders”, J. Appl. Industr. Math., 11:4 (2017), 486–493
2. A. M. Blokhin, E. A. Kruglova, B. V. Semisalov, “Steady-state flow of an incompressible viscoelastic polymer fluid between two coaxial cylinders”, Comput. Math. Math. Phys., 57:7 (2017), 1181–1193
3. A. M. Blokhin, E. A. Kruglova, B. V. Semisalov, “Estimation of two error components in the numerical solution to the problem of nonisothermal flow of polymer fluid between two coaxial cylinders”, Comput. Math. Math. Phys., 58:7 (2018), 1099–1115
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