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

基本信息

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

项目摘要

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动和波浪进行准确有效的数值近似。该项目通过开发非常规方法来改进此类模拟的核心数值技术，从而推进了最先进的技术。除了预期的数学发明外，该项目还计划开发一种实施新技术的公共领域开源软件产品，并使用该产品解决包括地质灾害缓解和材料科学在内的各种应用领域的模拟问题。通过纳入代表性不足的少数群体，项目活动有助于实现基金会扩大所有人对科学的参与的目标。该项目的技术工作分为两条研究方向。其中之一导致了捕获双曲系统波解的新方法，这些方法有望在新兴的多核架构上表现出色。另一条研究路线利用一种新的数学成分来获得粘性流的结构保持数值近似。第一条探究的动机是观察到当双曲解可以在不同的空间位置及时推进不同的量时，计算资源的分配得到优化。如果这也可以同时完成，则可以实现更快的模拟。预计的结果是针对因果时空帐篷的非结构化时空网格的新快速方法。该项目的进展有利于各种波传播系统以及无粘可压缩流的模拟。第二条研究线的目标是粘性不可压缩流。使用矩阵值函数的 Sobolev 空间，构建了新颖的公式，可产生最佳的流体应力近似值、精确的质量守恒和压力鲁棒性。这两个调查领域的工作都涉及回答几个技术问题，这些问题被证明是基本的，并且具有超出该项目范围的潜在学科影响。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和技术进行评估，被认为值得支持。更广泛的影响审查标准。

项目成果

期刊论文数量（14）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

A one-dimensional field dislocation mechanics model using discontinuous Galerkin method

采用间断伽辽金法的一维场位错力学模型

DOI：
10.1016/j.commatsci.2022.111870
发表时间：
2023-01
期刊：
Computational Materials Science
影响因子：
3.3
作者：
Breeden, Ja’Nya;Drake, Dow;Gopalakrishnan, Jay;Puri, Saurabh
通讯作者：
Puri, Saurabh

Sensitivity of confinement losses in optical fibers to modeling approach

光纤中的限制损耗对建模方法的敏感性

DOI：
10.1364/oe.495467
发表时间：
2023-07
期刊：
Optics Express
影响因子：
3.8
作者：
Vandenberge, Pieter;Gopalakrishnan, Jay;Grosek, Jacob
通讯作者：
Grosek, Jacob

A Computational Framework for Time‐Dependent Deformation in Viscoelastic Magmatic Systems

粘弹性岩浆系统中随时间变形的计算框架

DOI：
10.1029/2022jb024506
发表时间：
2022-09
期刊：
Journal of Geophysical Research: Solid Earth
影响因子：
0
作者：
Rucker, Cody;Erickson, Brittany A.;Karlstrom, Leif;Lee, Brian;Gopalakrishnan, Jay
通讯作者：
Gopalakrishnan, Jay

Divergence-Conforming Velocity and Vorticity Approximations for Incompressible Fluids Obtained with Minimal Facet Coupling

通过最小面耦合获得的不可压缩流体的散度一致速度和涡度近似

DOI：
10.1007/s10915-023-02203-8
发表时间：
2023-05
期刊：
Journal of Scientific Computing
影响因子：
2.5
作者：
Gopalakrishnan, J.;Kogler, L.;Lederer, P. L.;Schöberl, J.
通讯作者：
Schöberl, J.

An explicit mapped tent pitching scheme for Maxwell equations

麦克斯韦方程的显式映射帐篷倾斜方案

DOI：
10.1007/978-3-030-39647-3_28
发表时间：
2020-01
期刊：
Spectral and High Order Methods for Partial Differential Equations
影响因子：
0
作者：
Gopalakrishnan, Jay;Hochsteger, Matthias;Schöberl, Joachim;Wintersteiger, Christoph
通讯作者：
Wintersteiger, Christoph