Particle Simulations in Fluid Dynamics and Molecular Dynamics

Krasny0107187研究人员为流体动力学和分子动力学中的粒子模拟开发了新的计算机算法，并利用这些算法研究重要的应用问题。主要的技术工具是一种新的自适应树编码算法，用于解决远程粒子相互作用背景下的N体问题。在该算法中，质点作用力或速度在直角坐标系中采用泰勒近似计算，所需的泰勒系数由递推关系计算。自适应特征包括分而治之的评估策略、非均匀矩形簇、变阶近似以及运行时在泰勒近似和直接求和之间的选择。为了最大限度地提高算法的准确性和效率，研究人员开发了一种选择代码中参数的最优策略。流体力学中需要研究的应用问题包括涡核中混沌动力学的开始，Kelvin-Helmholtz问题中涡片卷起和螺旋形成的高精度计算，以及涡环中的破裂和转变。这项工作的一个重要组成部分是将正则化粒子模拟与实验以及用有限差分格式计算的真实粘性流动进行比较。分子动力学要研究的应用问题涉及静电相互作用的势能和力场的计算。这项研究的结果影响到几个具有战略意义的国家利益领域，包括民用和军用航空和生物技术。航空领域的一个突出问题是飞机起飞和着陆时形成的尾涡尾迹的模拟。涡流尾迹对其他飞机是一个严重的危险，特别是在拥挤的机场。它规定了在给定跑道上起飞和降落之间的最短时间和距离，它是风切变的来源，已被认为与事故有关。该项目揭示了涡核的结构和动力学，这有助于航空工程师设计涡流尾迹补救系统。在生物技术领域，一个影响深远的问题是以物理上准确的方式模拟蛋白质折叠。事实上，这是利用人类基因组计划中收集的数据所需的下一步。该项目通过增强生物化学家用来研究蛋白质折叠的计算机算法做出了贡献。在教育和人力资源领域，研究人员为一年级理工科学生指导应用荣誉计算课程，开发新的科学计算研究生课程，并指导本科生、研究生和博士后的专业发展。

Krasny0107187 The investigator develops new computer algorithms forparticle simulations in fluid dynamics and molecular dynamics,and he employs the algorithms to study important applicationproblems. The main technical tool is a new adaptive treecodealgorithm for solving the N-body problem in the context oflong-range particle interactions. In this algorithm, the particleforces or velocities are evaluated using Taylor approximation inCartesian coordinates, and the necessary Taylor coefficients arecomputed by a recurrence relation. The adaptive features includea divide-and-conquer evaluation strategy, nonuniform rectangularclusters, variable order approximation, and a run-time choicebetween Taylor approximation and direct summation. Theinvestigator develops an optimal strategy for choosing theparameters in the code, in order to maximize the accuracy andefficiency of the algorithm. The application problems to bestudied in fluid dynamics include the onset of chaotic dynamicsin vortex cores, high precision computation of vortex sheetroll-up and spiral formation in the Kelvin-Helmholtz problem, andbreakdown and transition in vortex rings. An important componentof the work is to compare regularized particle simulations withexperiments and with genuine viscous flows computed by finitedifference schemes. The application problems to be studied inmolecular dynamics involve potential energy and force fieldevaluation for electrostatic interactions. The results of this research affect several areas ofstrategic national interest, including civil and militaryaviation and biotechnology. One outstanding problem in aviationis the simulation of the trailing vortex wake that forms behindan aircraft on takeoff and landing. The vortex wake is a serioushazard to other aircraft, especially in crowded airports. Itimposes a minimum time and distance between takeoffs and landingson a given runway, and it is a source of wind shear, which hasbeen implicated in accidents. The project sheds light on thestructure and dynamics of vortex cores, and this helpsaeronautical engineers in designing vortex wake remediationsystems. In the area of biotechnology, one far-reaching problemis to simulate protein folding in a physically accurate way. Thisis in fact the next step required to make use of the datacollected in the human genome project. The project contributes byenhancing the computer algorithms that are used by biochemists tostudy protein folding. In the area of education and humanresources, the investigator directs an applied honors calculuscourse for freshman science and engineering students, develops anew graduate course on scientific computing, and mentors theprofessional development of undergraduate and graduate studentsand postdocs.