Mathematical Sciences: Creeping Flows Through Hollow Boundaries and Stenotic Pipes

该研究项目将研究流经空心边界和狭窄管道的慢粘性流体的行为。虽然这些问题中的方程是线性的，但由于边缘奇异性和混合边界条件，出现了很大的困难。除了分析工作外，研究还将考虑这些流动问题在无限域中的数值解。由于力奇异性的缓慢代数衰减，有限差分格式已被证明对无限域是不切实际的。这项工作应该会导致对一类涉及不完全边界的问题采取统一的方法。研究结果对聚合物挤出过程等涉及流经双连续边界的低雷诺数流动的情况具有实际意义。

This research program will study the behavior of slow viscows flows through hollow boundaries and stenobic pipes. Although the equations in these problems are linear, significant difficulties occur due to edge singularities and mixed boundary conditions. In addition to analytical work, the research will also consider the numerical solution of these flow problems in infinite domains. Finite difference schemes have proved impractical for infinite domains because of the slow algebraic decay of the force singularity. This work should lead to a unified approach to a class of problems involving incomplete boundaries. The results will have practical implications in situations, such as polymer extrusion processes, which involve low Reynolds number flows past dicontinuous boundaries.