Numerical Algorithms for the Detection and Simulation of Surface Water Waves

地表水波检测和模拟的数值算法

• 批准号: 0810958
• 负责人: David Nicholls
• 金额: $ 14.25万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0810958&HistoricalAwards=false
• 关键词: Numerical; Algorithms; Detection; Simulation; Surface

The generation, propagation, and energetic transport of ocean wavesplay a crucial role in many technologies including near-shorewatercraft navigation, the design of deep-sea oil-drilling rigs, andthe generation and propagation of tsunamis. However, the fundamentaltechnologies for the remote detection and measurement of thesenonlinear waves are based upon the scattering of linear acoustic orelectromagnetic radiation from the surface or bulk of the fluid. Notsurprisingly, the state-of-the-art in theory, approximation, andnumerical simulation of these two disparate wave phenomena is quitedifferent. In this proposal the Principal Investigator (PI) advocatesthe development of a unified computational approach to these twoproblems with the goal of producing a set of highly accurate, stable,and error-controllable numerical algorithms for the detection,simulation, and evaluation of waves on the surface of large bodies ofwater. Over the past ten years the PI has developed a set of stable,high-accuracy Boundary Perturbation (BP) algorithms for the study ofboth traveling ocean waves and scattering returns from irregularlyshaped obstacles. These BP algorithms each involve an independentperturbation parameter and the PI proposes to investigate a strategyof coupling these two disparate algorithms by linking theseparameters, thus realizing huge computational savings. Additionally,the PI proposes to significantly extend and improve existing BPalgorithms for the simulation of linear waves in the high-frequencyregime. In short, the Geometric Optics solution points the way to asolution Ansatz which can be represented with a frequency-independentnumber of unknowns. The PI, in collaboration with F. Reitich, hasdemonstrated how this Ansatz coupled to classical BP methods can beused to compute high-frequency scattering returns from shallowsurfaces with enormous computational savings. In this proposal the PIadvocates the further development of these algorithms to incorporatethe scenario of multiple reflections.The generation and propagation properties of ocean waves are crucialin many technologies including watercraft navigation, design ofdeep-sea oil-drilling rigs, and the study of tsunamis. However, themethods for the measurement of these nonlinear ocean waves are basedupon the scattering of linear acoustic or electromagnetic radiation.The state-of-the-art in both the theory and practice of these twodisparate wave phenomena is quite different. In this proposal thePrincipal Investigator (PI) advocates the development of a unifiedapproach to the computation of these two problems with the goal ofproducing a set of reliable and accurate numerical algorithms for thedetection and simulation of ocean waves. This will involve the PIbringing together two separate threads of his research program toimplement this unified approach. Additionally, he will need to expandthe capabilities of his algorithms to account for the highlyoscillatory character of the linear waves which arise in theseapplications. The latter task will be particularly challenging and isthe current focus of a great deal of research by both civilian andmilitary agencies.

海浪播放的生成，传播和能量运输在许多技术中至关重要的作用，包括近海水导航，深海油水钻井钻机的设计以及海啸的产生和传播。 然而，用于远程检测和测量的基本技术基于线性声学磁性辐射从表面或大量流体的散射。 值得一提的是，这两个不同波浪现象的理论上，近似和数字模拟在理论上是最新的。 在该提案中，首席研究员（PI）提倡对这两个问题的统一计算方法的开发，目的是生产一组高度准确，稳定和错误控制的数值算法，以用于检测，模拟和评估WAV表面的大体内大物体表面上的波浪。 在过去的十年中，PI开发了一组稳定的高智力边界扰动（BP）算法，用于研究各个行进海浪的研究，并从不规则差异的障碍物中获得了散射回报。 这些BP算法各自涉及一个独立的扰动参数，PI提出了通过链接到eSeparameters来研究这两种不同算法的策略，从而实现了巨大的计算节省。 此外，PI提议显着扩展和改善现有的BPALGORITHM，以模拟高频主力中的线性波。 简而言之，几何光学元素解决方案指向可以用频率独立的未知数表示aslution ansatz的道路。 PI与F. Reitich合作，可以使用这种ANSATZ与经典的BP方法结合在一起，可以使用巨大的计算节省来计算来自浅滩的高频散射回报。 在此提案中，PIAD探索了这些算法的进一步发展，以结合多种反射的情况。海浪的产生和传播特性是至关重要的许多技术，包括船只导航，深入挖油钻机的设计以及Tsunamis的研究。 然而，用于测量这些非线性海浪的测量方法是基于线性声或电磁辐射的散射。这些两片膜状波现象的理论和实践中最新的现象是完全不同的。 在该提案中，原理研究者（PI）主张开发这两个问题的统一，目的是生产一组可靠，准确的数值算法，以进行海浪进行挖掘和模拟。 这将涉及这种统一方法的研究计划的两个单独的线程。 此外，他将需要扩展其算法的能力，以说明在pliceplications中出现的线性波的高度刺激特征。 后一个任务将特别具有挑战性，是平民和军事机构的大量研究重点。