New Finite Element Techniques for Simulating Flows and Waves

用于模拟流动和波浪的新有限元技术

• 批准号: 1912779
• 负责人: Jay Gopalakrishnan
• 金额: $ 37.44万
• 依托单位: Portland State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-09-01 至 2023-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1912779&HistoricalAwards=false
• 关键词: New; Finite; Element; Techniques; Simulating; New; Finite; Element; Techniques; Simulating

Computer simulations of various natural and technological processes require accurate and efficient numerical approximation of flows and waves. This project advances the state of the art by developing unconventional approaches that improve numerical techniques at the heart of such simulations. In addition to the anticipated mathematical inventions, the project also plans to develop a public-domain open-source software product implementing the new techniques and use the product to solve simulation problems in varied application domains including geological hazard mitigation and material science. Through inclusion of under-represented minorities, the project activities contribute to the foundation's goals to widen participation of all in science.The technical work on the project is divided into two lines of inquiry. One leads to new methods for capturing wave solutions of hyperbolic systems, methods that are expected to excel on the emerging many-core architectures. Another line of inquiry leverages a new mathematical ingredient to obtain structure-preserving numerical approximations of viscous flows. The first line of inquiry is motivated by the observation that when hyperbolic solutions can be advanced in time by varying amounts at varying spatial locations, the allocation of computational resources is optimized. When this can also be done concurrently, much faster simulations are possible. New fast methods on unstructured spacetime meshes of causal spacetime tents are the projected outcome. The advances from this project benefit simulation of various wave propagation systems as well as inviscid compressible flows. Viscous incompressible flows are targeted by the second line of inquiry. Using a Sobolev space of matrix-valued functions, novel formulations are constructed that yield optimal fluid stress approximations, exact mass conservation, and pressure robustness. Work in both lines of inquiry involve answering several technical questions, shown to be fundamental, and of potential disciplinary impact beyond the confines of this project.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

各种自然和技术过程的计算机模拟需要对流和波的准确有效的数值近似。该项目通过开发非常规的方法来提高艺术的状态，从而改善了此类模拟的核心数值技术。除了预期的数学发明外，该项目还计划开发实施新技术的公共域开源软件产品，并使用该产品来解决各种应用领域的模拟问题，包括缓解地质危害和材料科学。通过包括代表性不足的少数群体，该项目活动有助于基金会的目标扩大了所有人的参与。一种导致了捕获双曲系统波浪解决方案的新方法，这些方法有望在新兴的多核体系结构上表现出色。另一条探究线利用了一种新的数学成分来获得粘性流的结构性数值近似值。第一条询问是由观察结果激发的，即当可以通过变化的空间位置在变化的空间位置进行及时提出双曲线解决方案时，计算资源的分配得到了优化。当也可以同时完成此操作时，可以更快地模拟。预计的结果是因果时期帐篷的非结构化时空网格的新快速方法。该项目的进步有益于各种波传播系统以及不可压缩流的模拟。粘性不可压缩流是第二行查询的目标。使用基质值函数的Sobolev空间，构建了新的制剂，可产生最佳的流体应力近似，确切的质量保护和压力鲁棒性。这两种询问的工作都涉及回答几个技术问题，这些问题表明是基本的，并且在该项目的范围内涉及的潜在纪律影响。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的智力优点和更广泛影响的评估来通过评估来支持的。