Department of Mathematics

Permanent URI for this collectionhttp://localhost:4000/handle/123456789/1920

Browse

Filters

2011 - 201922020 - 20253

Settings

Has files: NoSubject: search.filters.subject.Rarefied gas dynamics

Search Results

Now showing 1 - 5 of 5
  • No Thumbnail Available
    Item
    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.
  • No Thumbnail Available
    Item
    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.
  • No Thumbnail Available
    Item
    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.
  • No Thumbnail Available
    Item
    Analytical and Numerical Solutions of Boundary Value Problems for the Regularized 13 Moment Equations
    (AIP Conference Proceedings, 2011-05) Rana, Anirudh
    Classical hydrodynamics—the laws of Navier-Stokes and Fourier—fails in the description of processes in rarefied gases. For not too large Knudsen numbers, extended macroscopic models offer an alternative to the solution of the Boltzmann equations. Anlytical and numerical solutions show that the regularized 13 moment equations can capture all important linear and non-linear rarefaction effects with good accuracy.
  • No Thumbnail Available
    Item
    Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory
    (MDPI, 2018-09) Rana, Anirudh
    Due to the failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as the Direct Simulation Monte Carlo method (DSMC), to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel cells, it is important to model and understand evaporation in this flow regime. Here, evaporation boundary conditions for the R13 equations, which are macroscopic transport equations with applicability in the rarefied gas regime, are derived. The new equations utilize Onsager relations, linear relations between thermodynamic fluxes and forces, with constant coefficients, that need to be determined. For this, the boundary conditions are fitted to DSMC data and compared to other R13 boundary conditions from kinetic theory and Navier–Stokes–Fourier (NSF) solutions for two one-dimensional steady-state problems. Overall, the suggested fittings of the new phenomenological boundary conditions show better agreement with DSMC than the alternative kinetic theory evaporation boundary conditions for R13. Furthermore, the new evaporation boundary conditions for R13 are implemented in a code for the numerical solution of complex, two-dimensional geometries and compared to NSF solutions. Different flow patterns between R13 and NSF for higher Knudsen numbers are observed.