AUTHORS: Alexander Blokhin, Ekaterina Kruglova, Boris Semisalov

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ABSTRACT: Numerical simulation of the non isothermal flow of viscoelastic polymeric liquid between two coaxial cylinders has been done on the basis of the rheological mesoscopic Pokrovskii Vinogradov model. Boundary value problem for the nonlinear equation determining the velocity profile is posed. For solving it a pseudospectral numerical algorithm of increased accuracy based on Chebyshev approximations has been designed. The stationary numerical solutions of the posed problem are obtained for wide range of values of physical parameters and for record low values of the radius 𝑟𝑟0 of inner cylinder. A posteriori estimates of the truncation and round-off errors of the algorithm has been derived. Numerical analysis of these errors depending on the number of grid nodes and on the values of radius 𝑟𝑟0 is also performed

KEYWORDS: Polymeric liquid, Pokrovskii Vinorgadov model, Chebyshev approximation, algorithm without saturation, pseudospectral method, stabilization method, truncation error, round-off error

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