Highly efficient numerical solution of the Boltzmann equation for practical applications

PI：Varghese，Philip L.Proposal Number：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，这项工作将为连续体方程失效的广泛应用提供解决策略。所提出的工作将促进混合流动模拟的最新发展，而混合流动模拟在晶片制造设备、等离子体处理设备和微传感器的设计和模拟中非常重要。流体力学的连续介质方法在稀薄流动以及微纳流动方面达到了其局限性。计算非连续流的一种常用方法是直接模拟蒙特卡罗方法，它可以被认为是通过模拟流动中大量分子的行为来提供Boltzmann方程解的统计表示。这一建议是关于一种数值求解Boltzmann方程的新方案，该方案有可能缓解DSMMC的许多局限性，包括在大范围内的可行性。所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Boltzmann方程中，并且到目前为止一直是低效解和近似的原因，使用到离散但保守的速度空间的投影。这种方法可以看作是变质量的定速准粒子而不是固定质量的变速粒子的DSMMC的变种。初步计算结果与理论预测吻合较好。在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。得克萨斯大学奥斯汀分校计算工程和科学研究所内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验证的高标准。该奖项由CBET部门的流体动力学项目获得，由CEISE/ACI部门的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.