A novel solver for simulation of flows from continuum regime to rarefied regime at moderate Knudsen number

Liu, Z. J.; Chen, Shu; Chen, S. Y.; Yang, Liming; Wan, Minping; Liu, W.

doi:10.1016/j.jcp.2020.109548

Cited by 17 publications

(10 citation statements)

References 41 publications

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“…The system of the two kinetic Equations ( 4) and (5) in conjunction with the moments (6) and the boundary conditions ( 7)-( 9) is solved by applying the Discrete Velocity Method (DVM). The deterministic DVM method is nowadays considered the widely accepted numerical technique by the research community for solving kinetic equations and describing heat, mass, and momentum transfer phenomena in the whole range of gas rarefaction (e.g., [52][53][54][55][56][57][58][59][60]). The literature survey is very extensive, and for this reason, only a brief description of the method is provided here, focusing on the numerical details concerning the present flow problem.…”

Section: Complete 4d Kinetic Solutionmentioning

confidence: 99%

Numerical Study of Rarefied Gas Flow in Diverging Channels of Finite Length at Various Pressure Ratios

Tantos,

Litovoli,

Teichmann

et al. 2024

Fluids

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In the present work, the gas flows through diverging channels driven by small, moderate, and large pressure drops are studied, considering a wide range of the gas rarefaction from free molecular limit through transition flow regime up to early slip regime. The analysis is performed using the Shakhov kinetic model, and applying the deterministic DVM method. The complete 4D flow problem is considered by including the upstream and downstream reservoirs. A strong effect of the channel geometry on the flow pattern is shown, with the distributions of the macroscopic quantities differing qualitatively and quantitatively from the straight channel flows. The mass flow rate data set from the complete solution is compared with the corresponding set obtained from the approximate kinetic methodology, which is based on the fully developed mass flow rate data available in the literature. In addition, the use of the end-effect approach significantly improves the applicability range of the approximate kinetic methodology. The influence of the wall temperature on the flow characteristics is also studied and is found to be strong in less-rarefied cases, with the mass flow rate in these cases being a decreasing function of the temperature wall. Overall, the present analysis is expected to be useful in the development and optimization of technological devices in vacuum and aerospace technologies.

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Section: Complete 4d Kinetic Solutionmentioning

confidence: 99%

Numerical Study of Rarefied Gas Flow in Diverging Channels of Finite Length at Various Pressure Ratios

Tantos,

Litovoli,

Teichmann

et al. 2024

Fluids

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“…Numerical tests have been carried out on a recently developed platform called "novel solver" [21][22][23]. The key issue for this platform is how to accurately construct distribution function at the cell interface.…”

Section: Distribution Function Derived From the Third-order Truncationmentioning

confidence: 99%

Construction of Non-Equilibrium Gas Distribution Functions Through Expansions in Peculiar Velocity Space

Yuan¹,

Chen²,

Shu³

et al. 2023

AAMM

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Gas distribution function plays a crucial role in the description of gas flows at the mesoscopic scale. In the presence of non-equilibrium flow, the distribution function loses its rotational symmetricity, making the mathematical derivation difficult. From both the Chapman-Enskog expansion and the Hermite polynomial expansion (Grad's method), we observe that the non-equilibrium effect is closely related to the peculiar velocity space (C). Based on this recognition, we propose a new methodology to construct the non-equilibrium distribution function from the perspective of polynomial expansion in the peculiar velocity space of molecules. The coefficients involved in the non-equilibrium distribution function can be exactly determined by the compatibility conditions and the moment relationships. This new framework allows constructing non-equilibrium distribution functions at any order of truncation, and the ones at the third and the fourth order have been presented in this paper for illustration purposes. Numerical validations demonstrate that the new method is more accurate than the Grad's method at the same truncation error for describing non-equilibrium effects. Two-dimensional benchmark tests are performed to shed light on the applicability of the new method to practical engineering problems.

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“…However, the discrete form of VDFs greatly increases the number of variables, and the memory and computations consumed by numerical integration and algebraic operations become the major [32]. Since the Grad's distribution function expresses the VDFs as an explicit function of macroscopic variables, the moment integral could be computed in an explicit way [34].…”

Section: The Discrete and Explicit Form Of Numerical Fluxes In G13-mgksmentioning

confidence: 99%

“…Inspired by the conservation laws and finite volume method, a novel framework of Grad's distribution-based gas kinetic flux solver has been proposed recently [32]. The local solution of the Boltzmann Bhatnagar-Gross-Krook (BGK) Equation [33] is utilized to reconstruct the numerical flux with the help of the Grad's distribution function.…”

Section: Introductionmentioning

confidence: 99%

Grad's Distribution Function for 13 Moments based Moment Gas Kinetic Solver for Steady and Unsteady Rarefied flows: Discrete and Explicit Forms

Liu¹,

Liu²,

Zhang³

et al. 2022

Preprint

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Efficient modeling of rarefied flow has drawn widespread interest for practical engineering applications. In the present work, we proposed the Grad's distribution function for 13 momentsbased moment gas kinetic solver (G13-MGKS) and the macroscopic governing equations are derived based on the moment integral of discrete Boltzmann equation in the finite volume framework. Numerical fluxes at the cell interface related to the macroscopic variables, stress and heat flux can be reconstructed from the Boltzmann integration equation at surrounding points of the cell interface directly, so the complicated partial differential equations with tedious implementation of boundary conditions in the moment method can be avoided. Meanwhile, the explicit expression of numerical fluxes is proposed, which could release the present solver the from the discretization and numerical summation in molecular velocity space. To evaluate the Grad's distribution function for 13 moments in the present framework, the G13-MGKS with the discrete and explicit form of numerical fluxes are examined by several test cases covering the steady and unsteady rarefied flows. Numerical results indicate that the G13-MGKS could simulate continuum flows accurately and present reasonable prediction for rarefied flows at moderate Knudsen number. Moreover, the tests of computations and memory costs demonstrate that the present framework could preserve the highly efficient feature.

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A novel solver for simulation of flows from continuum regime to rarefied regime at moderate Knudsen number

Cited by 17 publications

References 41 publications

Numerical Study of Rarefied Gas Flow in Diverging Channels of Finite Length at Various Pressure Ratios

Numerical Study of Rarefied Gas Flow in Diverging Channels of Finite Length at Various Pressure Ratios

Construction of Non-Equilibrium Gas Distribution Functions Through Expansions in Peculiar Velocity Space

Grad's Distribution Function for 13 Moments based Moment Gas Kinetic Solver for Steady and Unsteady Rarefied flows: Discrete and Explicit Forms

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