An improved axisymmetric lattice Boltzmann flux solver for axisymmetric isothermal/thermal flows

Zhang, Liangqi; Жен, Чен; Yang, Liming; Zhang, Mengqi

doi:10.1002/fld.4738

Cited by 3 publications

(1 citation statement)

References 38 publications

(149 reference statements)

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“…In quasi-equilibrium flow regime, the distribution function can be derived by the CE expansion method. The first-order CE expansion [15,17] leads to the following distribution function that recovers Navier-Stokes (NS) flows…”

Section: The Existing Maxwellian Navier-stokes and Grad's Distributio...mentioning

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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Section: The Existing Maxwellian Navier-stokes and Grad's Distributio...mentioning

confidence: 99%

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

Yuan¹,

Chen²,

Shu³

et al. 2023

AAMM

View full text Add to dashboard Cite

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Grad's distribution functions-based gas kinetic scheme for simulation of flows beyond Navier–Stokes level

2021

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Conventional gas kinetic scheme (GKS) has been successfully utilized to obtain the accurate solution of Navier–Stokes (NS) equations. However, when it comes to flows beyond NS level, the conventional GKS is not reliable because its initial gas distribution function is approximated by the first-order Chapman–Enskog expansion, which merely recovers the NS equations. In order to make an extension for flows beyond NS level, we propose the Grad's distribution functions-based GKS in this paper. This scheme retains the advantage of conventional GKS and constructs the numerical fluxes through a time-dependent gas distribution function, which is derived from the integral solution of Boltzmann equation. In the present scheme, the initial gas distribution function in the local solution of Boltzmann equation is approximated by Grad's 13 and 26 distribution functions. Furthermore, the high-order moments in the initial Grad's distribution function are calculated by moment relationship directly, and thus, the solution of complicated partial differential equations for these high-order moments is avoided. Four benchmark numerical examples are tested to validate the performance of the present scheme, and the results demonstrate that the present scheme can not only recover NS solutions in the continuum region but also predict reasonable results for flows in the slip and transition regimes.

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An artificial compressibility method for axisymmetric swirling flows

Leloudas

Lygidakis

Delis

et al. 2021

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Purpose This study aims to feature the application of the artificial compressibility method (ACM) for the numerical prediction of two-dimensional (2D) axisymmetric swirling flows. Design/methodology/approach The respective academic numerical solver, named IGal2D, is based on the axisymmetric Reynolds-averaged Navier–Stokes (RANS) equations, arranged in a pseudo-Cartesian form, enhanced by the addition of the circumferential momentum equation. Discretization of spatial derivative terms within the governing equations is performed via unstructured 2D grid layouts, with a node-centered finite-volume scheme. For the evaluation of inviscid fluxes, the upwind Roe’s approximate Riemann solver is applied, coupled with a higher-order accurate spatial reconstruction, whereas an element-based approach is used for the calculation of gradients required for the viscous ones. Time integration is succeeded through a second-order accurate four-stage Runge-Kutta method, adopting additionally a local time-stepping technique. Further acceleration, in terms of computational time, is achieved by using an agglomeration multigrid scheme, incorporating the full approximation scheme in a V-cycle process, within an efficient edge-based data structure. Findings A detailed validation of the proposed numerical methodology is performed by encountering both inviscid and viscous (laminar and turbulent) swirling flows with axial symmetry. IGal2D is compared against the commercial software ANSYS fluent – by using appropriate metrics and characteristic flow quantities – but also against experimental measurements, confirming the proposed methodology’s potential to predict such flows in terms of accuracy. Originality/value This study provides a robust methodology for the accurate prediction of swirling flows by combining the axisymmetric RANS equations with ACM. In addition, a detailed description of the convective flux Jacobian is provided, filling a respective gap in research literature.

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An improved axisymmetric lattice Boltzmann flux solver for axisymmetric isothermal/thermal flows

Cited by 3 publications

References 38 publications

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

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

Grad's distribution functions-based gas kinetic scheme for simulation of flows beyond Navier–Stokes level

An artificial compressibility method for axisymmetric swirling flows

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