A multiscale discrete velocity method for diatomic molecular gas

Zhang, Qingdian; Zhuo, Congshan; Mu, Junlei; Zhong, Chengwen; Liu, Sha

doi:10.1063/5.0153834

Cited by 5 publications

(1 citation statement)

References 62 publications

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“…These models distill the fundamental and mean characteristics of the original collision integral while providing physical realism [6,7]. Building upon the Boltzmann-BGK equation, numerous numerical algorithms have been devised to solve gas flow problems across all flow regimes [8][9][10][11][12][13]. These algorithms offer convenience and efficiency in simulating complex flows.…”

Section: Introductionmentioning

confidence: 99%

Unlocking the Key to Accelerating Convergence in the Discrete Velocity Method for Flows in the Near Continuous/Continuous Flow Regimes

Han,

Yang,

et al. 2023

Entropy

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How to improve the computational efficiency of flow field simulations around irregular objects in near-continuum and continuum flow regimes has always been a challenge in the aerospace re-entry process. 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 1–2 orders of magnitude acceleration. Such advancements hold promise in providing a computational approach for simulating flows around irregular objects in near-space environments.

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Section: Introductionmentioning

confidence: 99%

Unlocking the Key to Accelerating Convergence in the Discrete Velocity Method for Flows in the Near Continuous/Continuous Flow Regimes

Han,

Yang,

et al. 2023

Entropy

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Interaction between lateral jet and hypersonic rarefied flow

Zhao,

Zhong,

Liu

et al. 2024

Aerospace Science and Technology

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An implicit unified gas-kinetic wave–particle method for radiative transport process

Liu,

Li,

Wang

et al. 2023

Physics of Fluids

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The unified gas-kinetic wave–particle method (UGKWP) has been developed for the multiscale gas, plasma, and multiphase flow transport processes for the past years. In this work, we propose an implicit UGKWP (IUGKWP) method to remove the Courant–Friedrichs–Lewy time step constraint. Based on the local integral solution of the radiative transfer equation (RTE), the particle transport processes are categorized into the long-λ streaming process and the short-λ streaming process compared to a local physical characteristic time tp. In the construction of the IUGKWP method, the long-λ streaming process is tracked by the implicit Monte Carlo method; the short-λ streaming process is evolved by solving the implicit moment equations; and the photon distribution is closed by a local integral solution of RTE. In the IUGKWP method, the multiscale flux of radiation energy and the multiscale closure of photon distribution are constructed based on the local integral solution. The IUGKWP method preserves the second-order asymptotic expansion of RTE in the optically thick regime and adapts its computational complexity to the flow regime. The numerical dissipation is well controlled, and the teleportation error is significantly reduced in the optically thick regime. The computational complexity of the IUGKWP method decreases exponentially as the Knudsen number approaches zero, and the computational efficiency is remarkably improved in the optically thick regime. The IUGKWP is formulated on a generalized unstructured mesh, and multidimensional 2D and 3D algorithms are developed. Numerical tests are presented to validate the capability of IUGKWP in capturing the multiscale photon transport process. The algorithm and code will apply in the engineering applications of inertial confinement fusion.

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A multiscale discrete velocity method for diatomic molecular gas

Cited by 5 publications

References 62 publications

Unlocking the Key to Accelerating Convergence in the Discrete Velocity Method for Flows in the Near Continuous/Continuous Flow Regimes

Unlocking the Key to Accelerating Convergence in the Discrete Velocity Method for Flows in the Near Continuous/Continuous Flow Regimes

Interaction between lateral jet and hypersonic rarefied flow

An implicit unified gas-kinetic wave–particle method for radiative transport process

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