Scientific Computing Research Environments for the Mathematical Sciences

拟议的计算机集群将专门用于以下四个前沿研究项目：(i)多相单层动力学的数值模拟；（ii）狭窄动脉血流的随机模拟；(3)三维人体动脉树涡激振动和血流模拟；（iv）波传播的数值模拟在地球物理中的应用。单层项目将为设计表面活性剂的开发提供有价值和可靠的信息——单层形成材料用于新兴技术，如用于并行、低成本DNA测序的芯片实验室。狭窄动脉血流的随机模拟将导致确定性分析的有效机制的量化，并更好地理解具有输入不确定性的狭窄血流的流体动力学。利用有效的升力抑制流动控制方案对结构涡激振动进行参数化研究，可以在许多情况下减少和抑制涡激振动。对流体饱和多孔介质中波动传播的真实模拟将有助于更好地理解局部非均质性在流体压力、饱和度、渗透率、孔隙度和其他岩石物理性质中的作用。这四个项目旨在解决具有挑战性的科学问题，这些问题将导致创新的计算算法，在与多尺度面间动力学相关的复杂物理和数学特性方面的新发现，狭窄动脉和整个人体动脉树的血流基本动力学，地震波在油气储层中传播所遭受的衰减和分散现象。拟议的活动还将通过本科生、研究生以及博士后研究人员直接参与拟议的研究，并将并行计算纳入普渡大学的高级研究生课程，对教育产生重大影响。

The proposed computer cluster will be dedicated to the following four cutting-edge research projects: (i) Numerical Simulations of Multiphase Monolayer Dynamics; (ii) Stochastic Simulations of Blood Flow in Stenosed Arteries; (iii) Simulations of Vortex Induced Vibrations and of Blood Flow in 3-D Human Arterial Tree; and (iv) Numerical Simulations of Wave Propagation in Geophysical Applications. The monolayer project will provide valuable and reliable information for the development of designer surfactants---monolayer forming materials for emerging technologies such as lab-on-a-chip for parallel, low-cost DNA sequencing. The stochastic simulations of blood flow in stenosed arteries will lead to quantifications of valid regimes for deterministic analysis and a better understanding of the fluid dynamics of stenotic flows with input uncertainties. The proposed parametric study for vortex-induced vibration (VIV) of structures using an efficient lift suppression flow-control scheme will enable reduction and suppression of vortex-induced vibrations in many situations. Realistic simulations of wave propagations in fluid-saturated porous media will lead to a better understanding on the role played by local heterogeneities in fluid pressure andsaturation, permeability, porosity and other petrophysical properties at the mesoscopic scale. The four projects are aimed at challenging scientific problems that will lead to innovative computational algorithms, new discoveries in complex physical and mathematical properties related to the multiscale inter-facial dynamics, fundamental dynamics of blood flow in stenosed arteries and in the entire human arterial tree, the attenuation and dispersion phenomena suffered by seismic waves traveling in hydrocarbon reservoir formations. The proposed activities will also have significant impact on education through involvement of undergraduate and graduate students as well as postdoctoral researchers directly in the proposedresearch, and incorporation of parallel computing into advanced graduate courses at Purdue University.