High Order Multi-Scale Numerical Methods for All-Mach Number Flows

全马赫数流的高阶多尺度数值方法

基本信息

批准号：
1818924
负责人：
Jing-Mei Qiu
金额：
$ 26.24万
依托单位：
University of Delaware
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-08-01 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1818924&HistoricalAwards=false
关键词：
Order Multi Scale Numerical Methods

项目摘要

The primary goal of this project is the design of highly accurate and multi-scale numerical methods for all-speed flow simulations. To the best of our knowledge, highly accurate multi-scale solvers for all-Mach number flows are still underdeveloped. The proposed work is expected to establish close connections on existing state-of-art computational tools for compressible flow (with shock capturing techniques) and incompressible flows (with projection and divergence cleaning techniques). Successful methodology developments for all-speed flow simulations will have a broad impact for a wide range of computational fluid dynamics (CFD)-related applications. The proposed research work in algorithm design and analysis will promote/benefit from the demands from CFD applications fields. Further impact comes from the multidisciplinary nature of the proposed research, publications, participation and organization of mini-symposium sections in conferences, as well as the training of students.High order multi-scale solvers for all-Mach number flows are proposed. The PI seeks to develop a uniform framework to build up high order solvers that could effectively capture shocks without numerical oscillations for the compressible Euler system, and would successfully approximate the incompressible solutions of the system with proper divergence cleaning steps for low Mach flows without the need in resolving acoustic waves. In particular, the main focus would be finite difference schemes with weighted essentially non-oscillatory (WENO) reconstructions coupled with proper implicit-explicit (IMEX) Runge Kutta (RK) treatments with the following properties: (1) the schemes can robustly capture shock fronts in the compressible regime when the Mach number is of order 1; (2) the schemes automatically become high order, stable and consistent solvers for the incompressible Euler system when the Mach number approaches 0; (3) the schemes are high order accurate in both space and in time both when the acoustic waves are well-resolved and are under-resolved. Along this direction, the PI develops a thorough plan in methodology development, stability and asymptotic preserving analysis, as well as extensive benchmarked tests for all-Mach number flows. Further extensions to the Navier-Stokes system with additional consideration of viscous terms and special focus on boundary conditions will be explored.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.

该项目的主要目标是设计用于全速流动模拟的高精度和多尺度数值方法。据我们所知，用于全马赫数流的高精度多尺度求解器仍然不发达。拟议的工作预计将在现有最先进的可压缩流（具有冲击捕获技术）和不可压缩流（具有投影和发散清洁技术）的计算工具上建立紧密的联系。全速流动模拟的成功方法开发将对各种计算流体动力学 (CFD) 相关应用产生广泛影响。拟议的算法设计和分析研究工作将促进/受益于 CFD 应用领域的需求。进一步的影响来自于拟议的研究、出版物、会议中小型研讨会部分的参与和组织以及学生的培训的多学科性质。提出了用于全马赫数流的高阶多尺度求解器。该 PI 寻求开发一个统一的框架来构建高阶求解器，该求解器可以有效地捕获可压缩欧拉系统的冲击而无需数值振荡，并且可以通过针对低马赫流的适当发散清理步骤成功地逼近系统的不可压缩解，而无需解决声波问题。特别是，主要关注点是具有加权基本非振荡 (WENO) 重建的有限差分方案，加上适当的隐式显式 (IMEX) 龙格库塔 (RK) 处理，具有以下属性：(1) 该方案可以稳健地捕获冲击当马赫数为 1 时，前沿处于可压缩状态； (2)当马赫数接近0时，该方案自动成为不可压缩欧拉系统的高阶、稳定、一致的求解器； (3)当声波良好分辨和欠分辨时，该方案在空间和时间上都具有高阶精度。沿着这个方向，PI 在方法开发、稳定性和渐近保持分析以及全马赫数流的广泛基准测试方面制定了全面的计划。将探索对纳维-斯托克斯系统的进一步扩展，额外考虑粘性项并特别关注边界条件。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更广泛的影响审查标准进行评估，被认为值得支持。