物理学报2024，Vol.73Issue(11)：34-43,10.DOI:10.7498/aps.73.20231984
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
摘要
Abstract
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 waves,Lax shock tubes,and acoustic waves.The results demonstrate the method's precise depiction of shock wave evolution,rarefaction waves,acoustic phenomena,and material interfaces.Furthermore,it ensures the conservation of mass,momentum,and energy within the system,as well as accurately measures the hydrodynamic and thermodynamic nonequilibrium effects of the fluid system.Compared with the finite difference method,the finite volume method is also more convenient and flexible in dealing with boundary conditions of different geometries,and can be adapted to a variety of systems with complex boundary conditions.Consequently,the finite volume method further broadens the scope of DBM in practical applications.关键词
离散Boltzmann方法/有限体积法/非平衡效应/可压缩流Key words
discrete Boltzmann method/finite volume method/nonequilibrium effect/compressible flow引用本文复制引用
孙佳坤,林传栋,苏咸利,谭志城,陈亚楼,明平剑..离散Boltzmann方程的求解:基于有限体积法[J].物理学报,2024,73(11):34-43,10.基金项目
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)和国家留学基金管理委员会(批准号:202306380288)资助的课题. Project supported by the National Natural Science Foundation of China(Grant No.51806116),the Guangdong Basic and Applied Basic Research Foundation,China(Grant Nos.2022A1515012116,2024A1515010927),and the China Scholarship Council(Grant No.202306380288). （批准号:51806116）
