Entropy-Consistent Moment-Closure Approximations of Kinetic Boltzmann Equations

动力学玻尔兹曼方程的熵一致矩闭合近似

• 批准号: 2012699
• 负责人: James Rossmanith
• 金额: $ 29万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2012699&HistoricalAwards=false
• 关键词: Entropy; Consistent; Moment; Closure; Approximations

This research is concerned with the development of mathematical models and corresponding state-of-the-art computational methods for simulating and predicting the dynamics of complex fluid systems, such as those arising from multiphase flows and plasma. The ability to predict the dynamics of these complex fluid systems is of vital importance in understanding a wide range of phenomena such as particulate flow in the atmosphere, fuel sprays in combustion engines, magnetically-confined fusion reactors, laser-plasma accelerators, space weather, and astrophysical events. The underlying physics of such systems are often well-represented by kinetic models that represent the state of the fluid in terms of probability density functions. The main challenge in accurately simulating these kinetic models is that solutions live in a high-dimensional phase space and contain information over wide-ranging spatial and temporal scales. The goal of this research is to develop reduced models that simultaneously capture the important physics and can be more readily solved on modern computer architectures. As part of this research effort, graduate and undergraduate students will be trained in mathematical modeling and computational mathematics. Students from groups that are underrepresented in applied and computational mathematics will be encouraged to participate in the research efforts. The primary objective of this research is to develop accurate and efficient computational methods for solving kinetic models of both polydisperse multiphase flows and plasma flows via entropy-consistent moment closures. The purpose of moment-closure techniques is to reduce high-dimensional kinetic models to more computationally tractable approximations. However, determining a suitable moment closure is a mathematical challenge; a general approach that combines desirable mathematical features remains elusive. This research will pursue two related approaches: (1) using quasi-exponential representations of the underlying kinetic distribution functions, and (2) using delta functions in conjunction with entropy maximization. Novel moment-inversion algorithms and high-order numerical schemes will be developed. The resulting codes will be implemented on massively parallel computers. These techniques will be applied to problems in polydisperse multiphase flows and plasma flows.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.

这项研究涉及数学模型和相应的最新计算方法，用于模拟和预测复杂流体系统的动态，例如由多相流和等离子体引起的动态。预测这些复杂流体系统动力学的能力对于理解多种现象，例如大气中的颗粒流，燃烧发动机中的燃料喷雾，磁性融合融合反应器，激光 - 播出器，空间天气，天气，太空融合反应器，燃料喷雾至关重要。和天体物理事件。这种系统的潜在物理学通常由动力学模型代表了概率密度函数方面代表流体状态的动力学模型。准确模拟这些动力学模型的主要挑战是，解决方案生活在高维相空间中，并包含在广泛的空间和时间尺度上的信息。这项研究的目的是开发简化的模型，这些模型同时捕获重要的物理学，并且可以在现代计算机架构上更容易解决。作为这项研究工作的一部分，研究生和本科生将接受数学建模和计算数学的培训。将鼓励来自应用程序和计算数学代表不足的小组的学生参加研究工作。这项研究的主要目的是开发准确有效的计算方法，以通过熵一致的力矩闭合来求解多分散多相流和等离子体流的动力学模型。力矩闭合技术的目的是将高维动力学模型降低到更具计算方法的近似值。但是，确定合适的力矩闭合是数学挑战。结合理想的数学特征的一般方法仍然难以捉摸。这项研究将采用两种相关方法：（1）使用基本动力学分布函数的准指数表示，以及（2）使用Delta函数与熵最大化结合使用。新型的力矩插入算法和高阶数值方案将开发。结果代码将在大规模并行计算机上实现。这些技术将应用于多分散多相流和等离子流中的问题。该奖项反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响评估标准，被认为值得通过评估来获得支持。

项目成果

Simulating two-phase flows with thermodynamically consistent energy stable Cahn-Hilliard Navier-Stokes equations on parallel adaptive octree based meshes

• DOI: 10.1016/j.jcp.2020.109674
• 发表时间: 2019-12
• 期刊: J. Comput. Phys.
• 作者: Makrand A. Khanwale;Alec Lofquist;H. Sundar;J. Rossmanith;B. Ganapathysubramanian

Positivity-Preserving Lax–Wendroff Discontinuous Galerkin Schemes for Quadrature-Based Moment-Closure Approximations of Kinetic Models

• DOI: 10.1007/s10915-023-02117-5
• 发表时间: 2021-11
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: Erica R. Johnson;J. Rossmanith;Christine Vaughan

A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes

• DOI: 10.1016/j.jcp.2022.111874
• 发表时间: 2021-07
• 期刊: J. Comput. Phys.
• 作者: Makrand A. Khanwale;K. Saurabh;Masado Ishii;H. Sundar;J. Rossmanith;Baskar-Ganapathysubramanian

A fully-coupled framework for solving Cahn-Hilliard Navier-Stokes equations: Second-order, energy-stable numerical methods on adaptive octree based meshes

• DOI: 10.1016/j.cpc.2022.108501
• 发表时间: 2020-09
• 期刊: Comput. Phys. Commun.
• 作者: Makrand A. Khanwale;K. Saurabh;Milinda Fernando;V. Calo;J. Rossmanith;H. Sundar;B. Ganapathysubramanian