Аннотация:

For equations of the rheological mesoscopic Vinogradov-Pokrovskii model the boundary value problem is formulated that describes non-isothermal Poiseuille-type flows of a viscoelastic polymer fluid through the channel with the elliptic cross-section under the condition that the pressure gradient and the temperature of the channel's wall undergo rapid (impulse) changes. To solve the problem, we develop the numerical algorithm  based on the collocation method, the application of polynomial and rational approximations with respect to spatial variables and of finite-difference scheme for the time marching. The analysis of distributions of the fluid's velocity and temperature in the channel, as well as, of the time dependencies of fluid's flow and mean temperature is performed. The critical relations between the amplitudes and durations of impulses of the pressure gradient and of the temperature are computed. They are those values surpassing which leads to the divergence of the numerical solution that, as we suppose, can be associates with the destruction (the stability loss) of a Poiseuille-type flow.