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The discrete velocity method (DVM) is a commonly used algorithm for the discretized solutions of the Boltzmann-BGK model equation. However, the discretization of both physical and molecular velocity spaces in DVM can result in significant computational costs. This paper focuses on unlocking the key to accelerate the convergence in DVM calculations, thereby reducing the computational burden. Three versions of DVM are investigated: the semi-implicit DVM (DVM-I), fully implicit DVM (DVM-II), and fully implicit DVM with an inner iteration of the macroscopic governing equation (DVM-III). In order to achieve full implicit discretization of the collision term in the Boltzmann-BGK equation, it is necessary to solve the corresponding macroscopic governing equation in DVM-II and DVM-III. In DVM-III, an inner iterative process of the macroscopic governing equation is employed between two adjacent DVM steps, enabling a more accurate prediction of the equilibrium state for the full implicit discretization of the collision term. Fortunately, the computational cost of solving the macroscopic governing equation is significantly lower than that of the Boltzmann-BGK equation. This is primarily due to the smaller number of conservative variables in the macroscopic governing equation compared to the discrete velocity distribution functions in the Boltzmann-BGK equation. Our findings demonstrate that the fully implicit discretization of the collision term in the Boltzmann-BGK equation can accelerate DVM calculations by one order of magnitude in continuum and near-continuum flow regimes. Furthermore, the introduction of the inner iteration of the macroscopic governing equation provides an additional 1\u20132 orders of magnitude acceleration. Such advancements hold promise in providing a computational approach for simulating flows around irregular objects in near-space environments.<\/jats:p>","DOI":"10.3390\/e25121609","type":"journal-article","created":{"date-parts":[[2023,11,30]],"date-time":"2023-11-30T07:44:42Z","timestamp":1701330282000},"page":"1609","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Unlocking the Key to Accelerating Convergence in the Discrete Velocity Method for Flows in the Near Continuous\/Continuous Flow Regimes"],"prefix":"10.3390","volume":"25","author":[{"given":"Linchang","family":"Han","sequence":"first","affiliation":[{"name":"Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7961-4854","authenticated-orcid":false,"given":"Liming","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"},{"name":"State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"},{"name":"Key Laboratory of Unsteady Aerodynamics and Flow Control, Ministry of Industry and Information Technology, Nanjing 210016, China"}]},{"given":"Zhihui","family":"Li","sequence":"additional","affiliation":[{"name":"National Laboratory for Computational Fluid Dynamics, China Aerodynamics Research and Development Center, Beijing 100191, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6963-0244","authenticated-orcid":false,"given":"Jie","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}]},{"given":"Yinjie","family":"Du","sequence":"additional","affiliation":[{"name":"Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}]},{"given":"Xiang","family":"Shen","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Construction Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, UK"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,30]]},"reference":[{"key":"ref_1","unstructured":"Chapman, S., and Cowling, T.G. 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