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全速流量模拟的高度准确和多尺度的数值方法。据我们所知，全程数量流的高度准确的多尺度求解器仍然不发达。预计拟议的工作将在现有的最新计算工具上建立可压缩流（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）的密切连接。全速流量模拟的成功方法发展将对广泛的计算流体动力学（CFD）相关应用产生广泛的影响。算法设计和分析的拟议研究工作将从CFD应用领域的需求中促进/受益。进一步的影响来自拟议的研究，出版物，参与和组织迷你群体中的多学科性质，以及对学生的培训。提出了全麦计量数流的高订单多规模求解器。 PI试图开发一个统一的框架来建立高阶求解器，这些框架可以有效地捕获可压缩欧拉系统的数值振荡而无需进行数值振荡的冲击，并将成功地近似于系统的不可压缩解决方案，并使用适当的差异清洁步骤，用于低头流动，而无需在解决声波方面进行差异。特别是，主要重点是具有加权基本非振荡（WENO）重建的有限差异方案，并结合适当的隐式解释（IMEX）Runge Kutta（RK）处理，并具有以下特性：（1）该方案可以在Mach Chumber cord 1 of Mach编号的情况下强有力地捕获可压缩的震动阵线的震惊阵线。（2）当马赫数接近0时，该方案会自动变为不可压缩的Euler系统的高阶，稳定且一致的求解器；（3）当声波良好且分辨不足时，方案在空间和时间上都非常准确。沿着这个方向，PI制定了方法论开发，稳定性和渐近保存分析的详尽计划，以及针对全麦数量流的广泛基准测试。将探讨Navier-Stokes系统的进一步扩展，并考虑了粘性条款，并将特别关注边界条件。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知识分子优点和更广泛影响的评估审查标准通过评估来支持的。