Modelling, Analysis and Computation in Viscoelasticity

粘弹性建模、分析和计算

• 批准号: 8712058
• 负责人: David Malkus
• 金额: $ 18.28万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-08-01 至 1990-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8712058&HistoricalAwards=false
• 关键词: Modelling; Analysis; Computation; Viscoelasticity

Viscoelastic materials with fading memory exhibit behavior that is intermediate between the nonlinear hyperbolic response of elastic materials and the strongly diffusive, parabolic response of viscous materials; they incorporate a subtle dissipative mechanism induced by the effects of fading memory. Understanding these effects is crucial to the proper design of computational methods for modeling both unsteady and steady viscoelastic flows. Analytical and computational techniques will be developed for unsteady problems by adapting methods from the study of hyperbolic conservation laws. Building upon the understanding of classical solutions and their breakdown, a study of weak solutions to the governing equations will be conducted using two approaches: the method of compensated compactness and the random choice method. The latter requires an understanding of the Riemann problem for viscoelastic flows; its solution is an essential ingredient for designing computational algorithms. These ideas will be used to broaden the scope of the established program of simulation of steady, two-dimensional viscoelastic flows, with the objective of resolving serious computational difficulties at high Weissenberg numbers. This research represents a program in scientific computation that unites methods from mathematical, computational, and engineering disciplines.

具有衰减记忆的粘弹性材料 这是中间的非线性双曲响应， 弹性材料和强扩散，抛物线响应 粘性材料;它们结合了一种微妙的耗散 记忆衰退的影响引起的机制。 理解 这些影响对于正确设计计算 非定常和定常粘弹性流动的建模方法。 将发展分析和计算技术 非定常问题的研究， 双曲守恒律 基于对以下问题的理解， 经典解及其分解，弱解的研究 控制方程的解将使用两个 方法：补偿紧性方法和随机 选择方法 后者需要了解 粘弹性流动的黎曼问题;其解是 设计计算算法的基本要素。 这些想法将被用来扩大既定的范围， 稳态二维粘弹模拟程序 流，目的是解决严重的计算问题， 高Weissenberg数的困难。 这项研究代表了科学计算的一个程序 它将数学、计算和 工程学科