Mathematical Sciences: Analytical and Numerical Studies of Viscoelastic Flows

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Viscoelastic flows exhibit behavior intermediate to that of an elastic solid and a viscous fluid. Although several models of viscoelastic flows are currently available, these models do not accurately describe the flows in all situations of interest. The proposed research will involve a comprehensive analysis of the mathematical behavior of the equations which govern both steady and transient viscoelastic flows. Classical numerical methods for the solutions of differential equations are difficult to employ in this problem because of the character of the governing equations and the nature of the singularities. Reliable numerical methods for viscoelastic flow simulation will be developed. Results may shed light on the validity and plausability of the constitutive models used. The future of materials processing will be strongly influenced by the ability to simulate viscoelastic flows. This work is concerned with the underpinnings of simulation.