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738 Section 1
The research was partly supported by the Ministry of Science and Higher Education of the Russian Federation within
the framework of the state assignment (project Nos. 121030500137.5 and ����.�19.119051590004.5).
References
1. Belyaev V. A. Solving a Poisson equation with singularities by the least.squares collocation method // Numer.Anal.
Appl. 2020.V. 13, N. 3, P. 207.218.
Numerical simulation of a stabilizing Poiseuille.type polymer fluid flow in the channel with elliptical
cross.section
A. M. Blokhin1,2, B. V. Semisalov1
1Novosibirsk State University
2Sobolev Institute of Mathematics SB RAS
Email: blokhin@math.nsc.ru, vibis@ngs.ru
DOI 10.24412/cl.35065.2021.1.00.04
Stabilization of the Poiseuille.type flows of an incompressible viscoelastic polymer fluid is studied using
non.linear rheological relations from [1]. Channels of elliptical and circular cross.sections are considered. In [2]
it was shown that the corresponding stationary formulation admits three different solutions. The process of
stabilization of the flow after the jump of pressure gradient in the channel was simulated using the algorithm
from [3]. The stabilized flow shows which of the three solutions of the stationary problem is implemented in
practice. Simulations in a wide range of values of the physical parameters enable us to discover the effect of
"switching"the limiting solution of the non.stationary problem from one solution of the stationary equations
to another. The scenario of this switch is discussed in detail.
The research has been done under the financial support of the Russian Science Foundation (project No. 20.11.
20036)
References
1. Altukhov Yu. A., Gusev A. S., Pyshnograi G. V. Introduction to the Mesoscopic Theory of Flowing Polymer Systems.
Barnaul: Altai State Pedagogical Academy Press, 2012 [in Russian].
2. Blokhin, A.M., Semisalov, B. V. Simulation of the Stationary Nonisothermal MHD Flows of Polymeric Fluids in
Channels with Interior Heating Elements // J. Appl. Ind. Math.2020.V. 14. P. 222�241.
3. Semisalov B. V. Fast Nonlocal Algorithm for Solving Neumann�Dirichlet Boundary Value Problems with an Error
Control // Vychisl. Metody.Programmirovanie. 2016.V. 17, N. 4. P. 500�522 [in Russian].
The discontinuous shapeless particle methodfor quasi.linear transport
S. V. Bogomolov1, A. E. Kuvshinnikov2
1Lomonosov Moscow State University
2Keldysh Institute of Applied Mathematics RAS
Email: kuvsh90@yandex.ru
DOI 10.24412/cl.35065.2021.1.00.06
Simulation of gas dynamic problems deals with the appearance of discontinuities, more precisely, strong
gradients. The quality of computational methods is assessed primarily by their ability to convey this behavior
of a solution as adequately as possible. In our opinion, the discontinuous particle method [1.3] allows one to
cope with these difficulties better than alternative, traditionally more commonly used difference and finite
element methods. This is achieved because the particle method is based on the Lagrange approach, and this,
in turn, provides automatic mesh generation.
