Eulerian-Lagrangian Runge-Kutta Discontinuous Galerkin Methods for Nonlinear Kinetics and Fluid Models

非线性动力学和流体模型的欧拉-拉格朗日龙格-库塔不连续伽辽金方法

基本信息

批准号：
2111253
负责人：
Jing-Mei Qiu
金额：
$ 30.46万
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：
2021
资助国家：
美国
起止时间：
2021-07-15 至 2025-06-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2111253&HistoricalAwards=false
关键词：
Eulerian Lagrangian Runge Kutta Discontinuous

项目摘要

The primary goal of the project is the development of new computational methodologies for a wide range of transport-dominant systems in computational fluid dynamics. Methods with large time step sizes are still underdeveloped for kinetic and fluid applications. Theoretical foundations are yet to be established for quantifying the time stepping sizes allowed for stability. There is great potential in further development of methodology for a moving mesh frame and application to moving boundaries and interfaces. This project will further state-of-art computational tools and theoretical analysis and aims to provide avenues for computational simulations that are currently intractable. The project involves training of graduate students through involvement in the research.This project will develop a class of Eulerian-Lagrangian (EL) Discontinuous Galerkin (DG) approaches for linear and nonlinear transport-dominant partial differential equation models. The EL DG method is a generalization of the (semi-Lagrangian) SL DG method for linear advection problems, based on the design of a localized adjoint problem for the test function that approximately tracks characteristics. Such features allow flexibility, especially for high dimensional and nonlinear problems, where characteristics are difficult to track. The errors occurred in approximating characteristics will be integrated in time by Runge-Kutta (RK) methods via the method-of-lines approach. This fully discrete scheme is termed "EL RK DG." When the characteristics are approximated well, the very restrictive CFL constraint in the RK DG framework can be relaxed, leading to CPU savings. The EL RK DG method can be viewed as a general framework generalizing both the classical Eulerian RK DG formulation and the SL DG formulation. Thus, existing research on positivity preserving limiters, well-balanced treatments, asymptotic preserving properties, entropy stability, and error estimates on Eulerian RK DG methods can be potentially generalized to the EL RK DG framework. A key goal is to establish large time-stepping size with nonlinear stability. The project will also explore generalization of the EL DG algorithm to a moving mesh reference frame for tracking material interfaces and moving boundaries.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.

该项目的主要目的是开发用于计算流体动力学中广泛的传输主要系统的新计算方法。对于动力学和流体应用，具有较大时间步长的方法仍然不发达。理论基础尚未建立，以量化允许稳定性的时间阶梯尺寸。进一步开发移动网格框架以及对移动边界和接口的应用有很大的潜力。该项目将进一步最先进的计算工具和理论分析，并旨在为当前棘手的计算模拟提供途径。该项目涉及通过参与研究对研究生进行培训。该项目将开发一类Eulerian-Lagrangian（EL）不连续的Galerkin（DG）方法，以实现线性和非线性运输偏差的部分差分方程模型。 EL DG方法是基于近似跟踪特征的测试功能的局部伴随问题的设计（半拉格朗日）SL DG方法，用于线性对流问题。此类功能允许灵活性，尤其是对于难以跟踪特征的高维和非线性问题。这些错误发生在近似特征中的误差将通过runge-kutta（RK）方法通过方法方法进行集成。该完全离散的方案称为“ El RK DG”。当特性良好近似时，RK DG框架中非常限制的CFL约束可以放松，从而节省CPU。 EL RK DG方法可以看作是一个通用的一般框架，可以推广经典的Eulerian RK DG公式和SL DG公式。因此，现有关于保存阳性限制器，均衡处理，渐近保留特性，熵稳定性以及对Eulerian RK DG方法的错误估计的研究可能会被推广到EL RK DG框架。一个关键目标是建立具有非线性稳定性的大型时间步长大小。该项目还将探索EL DG算法对跟踪材料界面和移动边界的移动网格参考框架的概括。该奖项反映了NSF的法定任务，并被认为是通过基金会的智力优点和更广泛影响的审查标准来评估值得通过评估来支持的。