Department of Mathematics

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Author: search.filters.author.Rana, Anirudh SinghSubject: search.filters.subject.Rarefied gas dynamics

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    A generalized fundamental solution technique for the regularized 13-moment system in rarefied gas flows
    (2025-04) Rana, Anirudh Singh
    In this work, we explore the method of fundamental solutions (MFS) for solving the regularized 13-moment (R13) equations for rarefied monatomic gases. While previous applications of the MFS in rarefied gas flows relied on problem-specific fundamental solutions, we propose a generic approach that systematically computes the fundamental solutions for any linear moment system without predefined source terms. The generalized framework is first introduced using a simple example involving the Stokes equations, and is then extended to the R13 equations. The results obtained from the generic MFS are validated against an analytical solution for the R13 equations. Following validation, the framework is applied to the case of thermally-induced flow between two non-coaxial cylinders. Since no analytical solution exists for this case, we compare the results obtained from the MFS with those obtained from the finite element method (FEM). To further assess computational efficiency, we analyze the runtimes of the FEM and MFS. The results indicate that the MFS converges faster than the FEM and serves as a promising alternative to conventional meshing-based techniques.
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    Coupled constitutive relations for two-temperature model for polyatomic gases: Linear analysis, light scattering, and shock propagation
    (AIP, 2025-07) Rana, Anirudh Singh
    This article presents a new two-temperature coupled constitutive relations (CCR) model for polyatomic gases, developed using CCR based on classical irreversible thermodynamics. The model includes nonlinear terms in entropy and heat flux to better capture non-equilibrium phenomena. It offers a significant improvement over the one-temperature CCR model recently introduced by Rana and Barve [“A second-order constitutive theory for polyatomic gases: Theory and applications,” J. Fluid Mech. 958, A23 (2023)] and simplifies the complex behavior of polyatomic gases, providing a practical alternative to the Boltzmann equation or molecular dynamics simulations. The proposed model accurately describes steady-state shocks and Rayleigh–Brillouin light scattering, showing particular advantages in rarefied flow scenarios. Additionally, the model exhibits strong stability and consistency in capturing non-equilibrium processes, making it suitable for a wide range of flow conditions.
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    Regularized Gaussian 11-moment equations for polyatomic gases: Derivation, linear analysis, and its applications
    (Springer, 2025-09) Rana, Anirudh Singh
    This article presents a macroscopic closure for rarefied polyatomic gas flows, focusing on a regularized Gaussian 11-moment (RG11) system. Our model uses a generalized Gaussian distribution-a product of Gaussian and Gamma functions-to capture both translational and internal energies of polyatomic molecules. The closure is achieved through a regularization technique, following Struchtrup & Torrilhon (Physics of Fluids, vol. 15, 2003) approach for R13 equations in monatomic gases. In addition, we use a Bhatnagar-Gross-Krook (BGK)-type relaxation model to evaluate the production terms in the moment equations. The proposed model incorporates three relaxation parameters, which can be tuned to match viscosity, bulk viscosity, and thermal conductivity accurately for the gas under consideration. By applying a Chapman-Enskog-like expansion and an order-of-magnitude analysis, we derive the RG11 equations, featuring non-zero constitutive relations for both internal and translational heat flux. This new formulation is linearly stable in one-dimensional case across all wavelengths and frequencies, aligns well with experimental data for sound wave propagation, and agrees with validated hydrodynamic theories that are known to match experimental results for Rayleigh-Brillouin scattering (RBS), outperforming the Navier-Stokes-Fourier (NSF) equations.