Scientific Computing Research Environments for the Mathematical Sciences

拟议的计算机集群将致力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)狭窄动脉中血液流动的随机模拟；(Iii)涡流诱发振动和三维人体动脉树中血液流动的模拟；以及(Iv)地球物理应用中的波传播的数值模拟。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-用于新兴技术的单层形成材料，例如用于并行、低成本DNA测序的芯片实验室。对狭窄动脉中血流的随机模拟将有助于量化确定性分析的有效区域，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。采用有效的升力抑制流动控制方案对结构涡激振动(VIV)进行参数研究，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传播的真实模拟将有助于更好地理解局部非均质性在介观尺度上对流体压力和饱和度、渗透率、孔隙度等岩石物理性质所起的作用。这四个项目旨在挑战科学问题，这些问题将导致创新的计算算法，与多尺度界面动力学有关的复杂物理和数学特性的新发现，狭窄动脉和整个人类动脉树中血液流动的基本动力学，以及地震波在油气藏地层中传播时遭受的衰减和弥散现象。拟议的活动还将对教育产生重大影响，让本科生和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。

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.