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.

海浪的产生、传播和能量传输在许多技术中起着至关重要的作用，包括近岸船只航行、深海石油钻井平台的设计以及海啸的产生和传播。 然而，非线性波的远程探测和测量的基本技术是基于线性声或电磁辐射从流体的表面或本体的散射。 毫不奇怪，这两种完全不同的波现象在理论、近似和数值模拟方面的最新发展是完全不同的。 在这一建议的主要研究者（PI）advocatesthe发展的统一计算方法，这两个问题的目标是产生一套高精度，稳定，误差可控的数值算法的检测，模拟和评估的波表面上的大型机构ofwater。 在过去的十年里，PI开发了一套稳定、高精度的边界扰动（BP）算法，用于研究海洋行波和不规则形状障碍物的散射回波。 这些BP算法每个都涉及一个独立的扰动参数和PI提出了一个策略，耦合这两个不同的算法通过连接theseparameters，从而实现巨大的计算节省。 此外，PI提出了显着扩展和改进现有的BP算法的线性波在高频政权的模拟。 简而言之，几何光学解决方案指出了一种解决方案，可以用与频率无关的未知数来表示。 PI与F. Reitich，已经证明了如何将这种Analog与经典BP方法相结合，可以用于计算来自浅表面的高频散射回波，并节省大量计算。 在这一建议中，PI主张进一步发展这些算法来模拟多次反射的情况。海浪的产生和传播特性在许多技术中是至关重要的，包括船舶导航，深海石油钻井平台的设计，以及海啸的研究。 然而，这些非线性海浪的测量方法都是建立在线性声波或电磁波散射的基础上的，这两种不同的海浪现象在理论和实践上都有很大的不同。 在这一建议中，主要研究者（PI）主张发展一种统一的方法来计算这两个问题，其目标是产生一套可靠和准确的数值算法，用于海浪的检测和模拟。 这将涉及PI将他的研究计划的两个独立的线程结合在一起，以实现这种统一的方法。 此外，他还需要扩展他的算法的能力，以解释在这些应用中出现的线性波的高度振荡特性。 后一项任务将特别具有挑战性，是目前民用和军事机构大量研究的重点。