Yadav, U and Jonnalagadda, A and Agrawal, A (2023) Third-order accurate 13-moment equations for non-continuum transport phenomenon. In: AIP Advances, 13 (4).
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Abstract
The derivation of analytical equations of non-continuum macroscopic transport phenomena is underpinned by approximate descriptions of the particle distribution function and is required due to the inability of the Navier-Stokes equations to describe flows at high Knudsen number (Kn ∼1). In this paper, we present a compact representation of the second-order correction to the Maxwellian distribution function and 13-moment transport equations that contain fewer terms compared to available moment-based representations. The intrinsic inviscid and isentropic assumptions of the second-order accurate distribution function are then relaxed to present a third-order accurate representation of the distribution function, using which corresponding third-order accurate moment transport equations are derived. Validation studies performed for Grad's second problem and the force-driven plane Poiseuille flow problem at non-zero Knudsen numbers for Maxwell molecules highlight an improvement over results obtained by using the Navier-Stokes equations and Grad's 13-moment (G13) equations. To establish the ability of the proposed equations to accurately capture the bulk behavior of the fluid, the results of Grad's second problem have been validated against the analytical solution of the Boltzmann equation. For the planar Poiseuille flow problem, validations against the direct simulation Monte Carlo method data reveal that, in contrast to G13 equations, the proposed equations are capable of accurately capturing the Knudsen boundary layer.
| Item Type: | Journal Article |
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| Publication: | AIP Advances |
| Publisher: | American Institute of Physics Inc. |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Boltzmann equation; Boundary layers; Maxwell equations; Monte Carlo methods; Navier Stokes equations; Transport properties; Viscous flow, Analytical equations; Distribution-functions; Flow problems; Knudsen; Macroscopic transport; Moment equations; Navier-Stokes equation; Third order; Transport equation; Transport phenomenon, Distribution functions |
| Department/Centre: | Division of Interdisciplinary Sciences > Computational and Data Sciences |
| Date Deposited: | 22 May 2023 10:49 |
| Last Modified: | 22 May 2023 10:49 |
| URI: | https://eprints.iisc.ac.in/id/eprint/81555 |
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