A High Order Discontinuous Galerkin Multi-Scale Approach for Kinetic-Hydrodynamic Simulations

运动流体动力学模拟的高阶间断伽辽金多尺度方法

• 批准号: 1834686
• 负责人: Jing-Mei Qiu
• 金额: $ 13.76万
• 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: 2018-01-16 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1834686&HistoricalAwards=false
• 关键词: Order; Discontinuous; Galerkin; Multi; Scale

This research project will develop novel numerical methods for simulation of the dynamics of rarefied gas. Compared with the widely used Monte Carlo approach, the algorithm under development will be able to more accurately capture complicated solution structures in long-time simulations. Moreover, physically conserved quantities such as mass, momentum, and energy can be exactly preserved at the discrete level. The new algorithm also has the potential to be extended to a broader class of applications such as plasma physics, astrophysics, and semi-conductor device simulation. Students will be trained through involvement in the research project.This project aims to develop a very high order mesh-based multi-scale numerical approach to modeling rarified gas dynamics between the kinetic and hydrodynamic regimes. The approach is based on the so-called micro-macro formulation of the kinetic equation, which involves a natural decomposition of the problem into equilibrium and non-equilibrium parts. The high order spatial accuracy is achieved by a nodal discontinuous Galerkin (DG) finite element approach, and the high order temporal accuracy is achieved by globally stiffly accurate implicit-explicit Runge-Kutta methods. Due to deliberate design and considerations of the hydrodynamic asymptotics, the scheme under development becomes a DG method with explicit RK time discretizations for the Euler system in the zero limit of the Knudsen number, and a local DG discretization of the Navier-Stokes equations for a simplified BGK collision operator in a formal asymptotic analysis. Such a local DG method is similar in spirit to classical approaches based on a mixed formulation of the equations. The new scheme will be tested on problems at kinetic-hydrodynamic scales and compared with the results from the simplified BGK model, its ellipsoidal statistical (ES-BGK) extension, as well as with results from the macroscopic hydrodynamic models. The project will also study numerically the boundary layer for kinetic simulations when a diffusive hydrodynamic limit is considered.

该研究项目将开发新的数值方法，以模拟稀有气体的动力学。 与广泛使用的蒙特卡洛方法相比，开发的算法将能够在长期模拟中更准确地捕获复杂的解决方案结构。此外，可以在离散水平上精确保留物理保守的量，例如质量，动量和能量。新算法也有可能扩展到更广泛的应用程序，例如等离子体物理学，天体物理学和半导体设备模拟。 将通过参与研究项目对学生进行培训。该项目旨在开发一种非常高级网格的多尺度数值方法来建模动力学和流体动力学制度之间的稀有气体动态。该方法基于动力学方程的所谓微型麦克罗公式，该制定涉及将问题自然分解为平衡和非平衡部分。高阶空间精度是通过鼻子不连续的Galerkin（DG）有限元方法实现的，并且通过全球僵硬准确的隐式解释runge-kutta方法，高阶时间精度是实现的。 由于故意设计和对流体动力学渐近学的考虑，正在开发的方案成为一种DG方法，具有欧拉尔系统零极限的显式RK时间离散化，而Navier-Stokes方程的局部DG离散化在形式的渐近分析中，简化的BGK碰撞操作员。这种局部DG方法在精神上与基于方程式混合表述的经典方法相似。新方案将在动力学量表的问题上进行测试，并将其与简化的BGK模型，其椭圆形统计（ES-BGK）扩展以及宏观流体动力学模型的结果进行了比较。当考虑扩散流体动力学极限时，该项目还将在数值上研究动力学模拟的边界层。