MODELING OF NONISOTHERMAL VISCOELASTIC FLOWS

The modelling of non-isothermal flow of viscoelastic materials using d ifferential constitutive equations is investigated. The approach is ba sed on the concept of a slip tensor describing the nonaffine motion of the stress-carrying structure of the fluid. By specifying a slip tens or and the elastic behaviour of the structure, the constitutive model is determined. This slip tensor also appears in the energy equation an d thus, for a given constitutive model, the form of the energy equatio n is known. Besides the partitioning between dissipated and elasticall y stored energy, also the difference between entropy and energy elasti city is discussed. Numerical simulations are based on a stabilized Dis continuous Galerkin method to solve the mass, momentum and constitutiv e equations and a Streamline Upwind Petrov-Galerkin formulation to sol ve the energy equation. Coupling is achieved by a fixed point iteratio n. The flow around a confined cylinder is investigated, showing differ ences between viscous and viscoelastic modelling, and between limiting cases of viscoelastic modelling. (C) 1997 Elsevier Science B.V.