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Functional Underpinnings of Summation-By-Parts Finite Differences

有限差分部分求和的函数基础

基本信息

批准号：
EP/V002929/1
负责人：
Edward Brambley
金额：
$ 37.6万
依托单位：
University of Warwick
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2021
资助国家：
英国
起止时间：
2021 至无数据
项目状态：
未结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FV002929%2F1
关键词：
Functional Underpinnings Summation Parts Finite

项目摘要

Computer simulations are regularly used in engineering design, for example to predict the weight a particular design of bridge can support, or how to optimize the shape of a car to minimize drag. Computer simulations are also used throughout science, for example inferring the structure of the centre of the earth from the way seismic waves are transmitted and reflected. Most computer simulations start with a set of governing equations, and then simulate those equations using one of a few different numerical techniques. Two numerical techniques specific to this project are called finite elements and finite differences.The right technique is needed to solve each problem. Finite elements are often used to simulate solids, such as how bridges support weight. Finite differences are more commonly used to simulate waves, and in particular this project has in mind aeroacoustics simulations used to reduce noise in aircraft engines. A special class of finite differences, called Summation-By-Parts (SBP) finite differences, seem to perform particularly well at this. Interestingly, in my research I have noticed that this class of finite differences has a number of similarities to finite elements that have not been noticed before. The purpose of this project is to investigate this theoretically to see what the similarities and differences are (gaining new knowledge), and then to see how these similarities can be taken advantage of in order to produce better computer simulations (new techniques).The final part of this project aims to engage with companies who use computer simulations and who could benefit from these new techniques, to try to help them start using the new techniques.

计算机模拟经常用于工程设计，例如预测特定设计的桥梁可以支撑的重量，或者如何优化汽车的形状以最大限度地减少阻力。计算机模拟也用于整个科学领域，例如从地震波的传播和反射方式推断地球中心的结构。大多数计算机模拟从一组控制方程开始，然后使用几种不同的数值技术之一来模拟这些方程。本项目特有的两种数值技术称为有限元法和有限差分法。解决每一个问题都需要正确的技术。有限元通常用于模拟实体，例如桥梁如何支撑重量。有限差分更常用于模拟波，特别是这个项目考虑了用于减少飞机发动机噪音的航空声学模拟。一类特殊的有限差分，称为部分求和（SBP）有限差分，似乎在这方面表现得特别好。有趣的是，在我的研究中，我注意到这类有限差分与有限元有许多以前没有注意到的相似之处。这个项目的目的是从理论上对此进行调查，看看有什么相同点和不同点（获得新的知识），然后看看如何利用这些相似性，以便产生更好的计算机模拟（新技术）。该项目的最后一部分旨在与使用计算机模拟并可以从这些新技术中受益的公司进行接触，帮助他们开始使用新技术。