Problems, Analysis, and Solutions of the Equations for Viscoelastic Flow
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After summarizing the basic equations, the type of the equations for the upper-convected Maxwell model and for the Jeffreys-type models is derived. It is shown that the corotational Maxwell model changes type which is unacceptable from a physical point of view. The Jeffreys-type models (including the Leonov model) have a drastic different type compared to the Maxwell models and are physically more appealing. Correct boundary conditions are briefly discussed for a linearized upper-convected Maxwell model. The boundary conditions for the Jeffreys models are shown to be equal to the boundary conditions for the Navier-Stokes equations, supplemented by boundary conditions for all the extra stresses at the inflow boundary. Jump conditions are derived for Jeffreys-type models. It is shown that in complex flows with sharp corners discontinuities may arise. Numerical methods are discussed that take into account the special type of the equations.
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