Mathematical Sciences: Analytical and Numerical Studies of Viscoelastic Flows

粘弹性流动表现出的行为介于 弹性固体和粘性流体。 虽然有几种型号的 粘弹性流动是目前可用的，这些模型不 准确描述所有感兴趣的情况下的流量。 的 拟议的研究将涉及全面分析 数学行为的方程，这两个稳定的 和瞬态粘弹性流动。 经典数值方法 因为微分方程的解很难 在这个问题上，由于政府的性质， 方程和奇点的性质。 可靠 粘弹性流动模拟的数值方法将是 开发 结果可能揭示的有效性和 本构模型的合理性。 材料加工的未来将是强有力的 受模拟粘弹性流动能力的影响。 这 这项工作涉及模拟的基础。

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.