离散Boltzmann方程的求解:基于有限体积法  

Solution of the discrete Boltzmann equation:Based on the finite volume method

作　　者：孙佳坤 林传栋 苏咸利 谭志城 陈亚楼 明平剑 Sun Jia-Kun;Lin Chuan-Dong;Su Xian-Li;Tan Zhi-Cheng;Chen Ya-Lou;Ming Ping-Jian(Sino-French Institute of Nuclear Engineering and Technology,Sun Yat-sen University,Zhuhai 519082,China;Key Laboratory for Thermal Science and Power Engineering of Ministry of Education,Department of Energy and Power Engineering,Tsinghua University,Beijing 100084,China;Department of Mechanical Engineering,National University of Singapore,Singapore 119260,Singapore)

机构地区：[1]中山大学中法核工程与技术学院,珠海519082 [2]清华大学能源与动力工程系,热科学与动力工程教育部重点实验室,北京100084 [3]新加坡国立大学机械工程系,新加坡119260

出　　处：《物理学报》2024年第11期70-79,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:51806116);广东省基础与应用基础研究基金(批准号:2022A1515012116,2024A1515010927);国家留学基金管理委员会(批准号:202306380288)资助的课题。

摘　　要：近十年来,离散Boltzmann方法在复杂非平衡流体系统领域的应用取得了显著的进展,这种方法已逐步成为描述和预测流体系统行为的重要手段.该方法的控制方程是一套简单统一的离散Boltzmann方程,其离散格式的选取对于数值模拟的计算精度和稳定性有着直接影响.为了提高数值模拟的可靠性,本文引入有限体积法用于求解离散Boltzmann方程.有限体积法是一种常用的数值计算方法,具有守恒性强、精度高等特点,可用于有效处理高速可压缩流体的数值计算问题.本文采用MUSCL格式进行重构,并引入了通量限制器以提高数值计算的稳定性.最后,对基于有限体积的离散Boltzmann方法进行了验证,数值算例包括冲击波、Lax激波管以及声波.结果表明,该方法能够准确刻画冲击波、稀疏波、声波,以及物质界面的演化,同时确保系统的质量、动量和能量守恒,还可以准确测量流体系统的流体力学和热力学非平衡效应.Mesoscopic methods serve as a pivotal link between the macroscopic and microscopic scales,offering a potent solution to the challenge of balancing physical accuracy with computational efficiency.Over the past decade,significant progress has been made in the application of the discrete Boltzmann method(DBM),which is a mesoscopic method based on a fundamental equation of nonequilibrium statistical physics(i.e.,the Boltzmann equation),in the field of nonequilibrium fluid systems.The DBM has gradually become an important tool for describing and predicting the behavior of complex fluid systems.The governing equations comprise a set of straightforward and unified discrete Boltzmann equations,and the choice of their discrete format significantly influences the computational accuracy and stability of numerical simulations.In a bid to bolster the reliability of these simulations,this paper utilizes the finite volume method as a solution for handling the discrete Boltzmann equations.The finite volume method stands out as a widely employed numerical computation technique,known for its robust conservation properties and high level of accuracy.It excels notably in tackling numerical computations associated with high-speed compressible fluids.For the finite volume method,the value of each control volume corresponds to a specific physical quantity,which makes the physical connotation clear and the derivation process intuitive.Moreover,through the adoption of suitable numerical formats,the finite volume method can effectively minimize numerical oscillations and exhibit strong numerical stability,thus ensuring the reliability of computational results.Particularly,the MUSCL format where a flux limiter is introduced to improve the numerical robustness is adopted for the reconstruction in this paper.Ultimately,the DBM utilizing the finite volume method is rigorously validated to assess its proficiency in addressing flow issues characterized by pronounced discontinuities.The numerical experiments encompass scenarios involving shock w

关 键 词：离散Boltzmann方法 有限体积法 非平衡效应 可压缩流 

分 类 号：O17[理学—数学]