Highly efficient numerical solution of the Boltzmann equation for practical applications

玻尔兹曼方程的实际应用的高效数值求解

• 批准号: 1438530
• 负责人: Philip Varghese
• 金额: $ 31.64万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-07-01 至 2018-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1438530&HistoricalAwards=false
• 关键词: Highly; efficient; numerical; solution; Boltzmann

PI: Varghese, Philip L.Proposal Number: 1438530The goal of the proposed research is to develop an improved method to compute flows under conditions where the conventional continuum equations are invalid. If successful, the work would result in solution strategies for a broad range of applications where continuum equations fail. The work proposed will advance the state-of-the-art for hybrid flow simulations that are important in design and simulation of wafer fabrication machines, plasma processing equipment, and micro-sensors.The continuum approach to fluid mechanics reaches its limitations in rarefied flows and in micro- and nanoflows. A commonly used approach for computing non-continuum flows is the direct simulation Monte Carlo (DSMC) method, which can be thought of as providing a statistical representation of solutions of the Boltzmann equation by modeling the behavior of a large number of the molecules in the flow. This proposal is about a novel scheme to solve the Boltzmann equation numerically that has the potential to alleviate many of the limitations of DSMC, including feasibility for large scales. The proposed work is based on a new idea on how to compute the collisional integral, which appears in the Boltzmann equation and has been the reason for inefficient solutions and approximations to-date, using a projection into a discrete yet conservative velocity space. This approach can be viewed as a variation of DSMC that uses variable-mass fixed-velocity quasi-particles, rather than fixed-mass variable-velocity particles. Preliminary results show good agreement with theoretical predictions. The software developed during this project will be given to other academic and government laboratory users on request. The research center within the Institute for Computational Engineering and Sciences at UT Austin will be utilized for dissemination - it has established high standards for software documentation and code verification and validation. This award by the Fluid Dynamics Program of the CBET Division is co-funded by CIF 21 Software Reuse Venture Fund Program of the CISE/ACI Division.

PI：Varghese, Philip L. 提案编号：1438530 拟议研究的目标是开发一种改进的方法来计算传统连续介质方程无效的条件下的流动。如果成功的话，这项工作将为连续介质方程失效的广泛应用提供解决方案。所提出的工作将推进混合流模拟的最先进水平，这对于晶圆制造机器、等离子体处理设备和微传感器的设计和模拟非常重要。流体力学的连续介质方法在稀薄流以及微米和纳米流中达到了其局限性。计算非连续流的常用方法是直接模拟蒙特卡罗 (DSMC) 方法，可以将其视为通过对流中大量分子的行为进行建模来提供玻尔兹曼方程解的统计表示。该提案是关于一种数值求解玻尔兹曼方程的新颖方案，该方案有可能缓解 DSMC 的许多局限性，包括大规模的可行性。所提出的工作基于如何计算碰撞积分的新想法，该想法出现在玻尔兹曼方程中，并且是迄今为止解决方案和近似值低效的原因，使用投影到离散但保守的速度空间中。这种方法可以被视为 DSMC 的一种变体，它使用可变质量定速准粒子，而不是固定质量变速粒子。初步结果与理论预测吻合良好。该项目期间开发的软件将根据要求提供给其他学术和政府实验室用户。德克萨斯大学奥斯汀分校计算工程与科学研究所内的研究中心将用于传播——它为软件文档和代码验证和确认建立了高标准。该奖项由 CBET 部门流体动力学项目颁发，并由 CISE/ACI 部门 CIF 21 软件重用风险基金项目共同资助。