Highly efficient numerical solution of the Boltzmann equation for practical applications

PI: Varghese, Philip l .提案号：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条件下的流动。如果成功，这项工作将为连续统方程失效的广泛应用提供解决策略。所提出的工作将推动最先进的混合流动模拟，这在晶圆制造机器、等离子体处理设备和微传感器的设计和模拟中非常重要。流体力学的连续体方法在稀薄流动和微纳米流动中达到了它的局限性。直接模拟蒙特卡罗（DSMC）方法是计算非连续介质流动的一种常用方法，它可以被认为是通过模拟流动中大量分子的行为来提供玻尔兹曼方程解的统计表示。这个提议是关于一个新的方案来解决玻尔兹曼方程的数值，有可能减轻许多限制的DSMC，包括在大尺度的可行性。提出的工作是基于如何计算碰撞积分的新思想，碰撞积分出现在玻尔兹曼方程中，并且是迄今为止低效解和近似的原因，使用投影到离散但保守的速度空间中。这种方法可以看作是DSMC的一种变体，它使用变质量固定速度准粒子，而不是固定质量可变速度粒子。初步结果与理论预测吻合较好。在此项目中开发的软件将应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的研究中心将用于传播-它已经建立了软件文档和代码验证和确认的高标准。本奖项由CBET部流体动力学项目颁发，由CISE/ACI部CIF 21软件重用风险基金项目共同资助。

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.