arXiv subjects

Anirudh Singh Rana

Publications and source records attributed to Anirudh Singh Rana.

8 recordsLinked to original sources

arXiv2026

Non-equilibrium modelling of polyatomic gases: generic framework and 11-moment model

In this study, we present a thermodynamically consistent framework for modelling polyatomic gases by integrating the \textit{general equation for non-equilibrium reversible-irreversible coupling} (GENERIC) with an 11-moment description. Our formulation unifies \textit{rational irreversible thermodynamics} (RIT) and \textit{extended irreversible thermodynamics} (EIT) into a single GENERIC-compatible structure that guarantees compliance with the second law of thermodynamics through the explicit construction of Poisson and friction matrices. By including translational and internal temperatures, as well as a temperature tensor, the model offers a well-structured and physically meaningful representation of non-equilibrium behavior in polyatomic gases. The entropy production is inherently non-negative, and all closure relations emerge naturally from thermodynamic principles. As a test of applicability, we compute the shock wave structure in nitrogen gas, validating the framework against Direct Simulation Monte Carlo (DSMC) simulations and experiments up to moderate Mach numbers.

math-ph↗

arXiv2025

Thermodynamically Admissible Diffuse Interface Model for Nanoscale Transport of Dense Fluids

We investigate interfacial fluid dynamics and heat transfer at nanoscales using an improved diffuse interface approach for liquid-vapor interfaces in non-equilibrium. Conventional Navier-Stokes-Korteweg (NSK) formulations often fail to accurately capture transport phenomena across extremely thin interfaces due to underestimation of interface resistances. In this work, we improve the NSK model by adding a production term in the momentum equation based on higher-order corrections. To enhance interface resistances, viscosity and thermal conductivity are made dependent on the density gradient, increasing resistance only within the interface region. The gradient-based coefficients are determined by fitting to solutions of the Enskog-Vlasov equation for Couette flow (see Struchtrup and Frezzotti, 2022). Applying these fitted equations to pure heat conduction and planar evaporation problems shows that the model accurately captures interfacial transport, making it a useful tool for studying nanoscale evaporation, thermal management, and droplet dynamics on solid surfaces.

physics.flu-dyn↗

arXiv2025

A generalized fundamental solution technique for the regularized 13-moment system in rarefied gas flows

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.

physics.flu-dyn↗

arXiv2025

Exploring external rarefied gas flows through the method of fundamental solutions

The well-known Navier--Stokes--Fourier equations of fluid dynamics are, in general, not adequate for describing rarefied gas flows. Moreover, while the Stokes equations -- a simplified version of the Navier--Stokes--Fourier equations -- are effective in modeling slow and steady liquid flow past a sphere, they fail to yield a non-trivial solution to the problem of slow and steady liquid flow past an infinitely long cylinder (a two-dimensional problem essentially); this is referred to as Stokes' paradox. The paradox also arises when studying these problems for gases. In this paper, we present a way to obtain meaningful solutions for two-dimensional flows of rarefied gases around objects by circumventing Stokes' paradox. To this end, we adopt an extended hydrodynamic model, referred to as the CCR model, consisting of the balance equations for the mass, momentum and energy and closed with the coupled constitutive relations. We determine an analytic solution of the CCR model for the problem and compare it with a numerical solution based on the method of fundamental solutions. Apart from addressing flow past a circular cylinder, we aim to showcase the capabilities of the method of fundamental solutions to predict the flow past other objects in two dimensions for which analytic solutions do not exist or are difficult to determine. For that, we investigate the problem of rarefied gas flow past an infinitely long semicircular cylinder.

physics.flu-dyn↗

arXiv2023

H-Theorem and Boundary Conditions for Two-Temperature Model: Application to Wave Propagation and Heat Transfer in Polyatomic Gases

Polyatomic gases find numerous applications across various scientific and technological fields, necessitating a quantitative understanding of their behavior in non-equilibrium conditions. In this study, we investigate the behavior of rarefied polyatomic gases, particularly focusing on heat transfer and sound propagation phenomena. By utilizing a two-temperature model, we establish constitutive equations for internal and translational heat fluxes based on the second law of thermodynamics. A novel reduced two-temperature model is proposed, which accurately describes the system's behavior while reducing computational complexity. Additionally, we develop phenomenological boundary conditions adhering to the second law, enabling the simulation of gas-surface interactions. The phenomenological coefficients in the constitutive equations and boundary conditions are determined by comparison with relevant literature. Our computational analysis includes conductive heat transfer between parallel plates, examination of sound wave behavior, and exploration of spontaneous Rayleigh-Brillouin scattering. The results provide valuable insights into the dynamics of polyatomic gases, contributing to various technological applications involving heat transfer and sound propagation.

math-ph↗

arXiv2023

Fundamental solutions of an extended hydrodynamic model in two dimensions: Derivation, theory, and applications

The inability of the Navier-Stokes-Fourier equations to capture rarefaction effects motivates us to adopt the extended hydrodynamic equations. In the present work, a hydrodynamic model, which consists of the conservation laws closed with the recently propounded coupled constitutive relations (CCR), is utilized. This model is referred to as the CCR model and is adequate for describing moderately rarefied gas flows. A numerical framework based on the method of fundamental solutions is developed to solve the CCR model for rarefied gas flow problems in quasi two dimensions. To this end, the fundamental solutions of the linearized CCR model are derived in two dimensions. The significance of deriving the two-dimensional fundamental solutions is that they cannot be deduced from their three-dimensional counterparts that do exist in literature. As applications, the developed numerical framework based on the derived fundamental solutions is used to simulate (i) a rarefied gas flow between two coaxial cylinders with evaporating walls and (ii) a temperature-driven rarefied gas flow between two non-coaxial cylinders. The results for both problems have been validated against those obtained with the other classical approaches. Through this, it is shown that the method of fundamental solutions is an efficient tool for addressing quasi two-dimensional multiphase microscale gas flow problems at a low computational cost. Moreover, the findings also show that the CCR model solved with the method of fundamental solutions is able to describe rarefaction effects, like transpiration flows and thermal stress, generally well.

physics.flu-dyn↗

arXiv2023

A second order constitutive theory for polyatomic gases: theory and applications

In the classical irreversible thermodynamics (CIT) framework, the Navier Stokes Fourier (NSF) constitutive equations are obtained so as they satisfy the entropy inequality, by and large assuming that the entropy flux is equal to the heat flux over the temperature. This article is focused on the derivation of second-order constitutive equations for polyatomic gases; it takes the basis of CIT, but most importantly, allowing up to quadratic nonlinearities in the entropy flux.

physics.flu-dyn↗

arXiv2019

Coupled constitutive relations: a second law based higher order closure for hydrodynamics

In the classical framework, the Navier-Stokes-Fourier equations are obtained through the linear uncoupled thermodynamic force-flux relations which guarantee the non-negativity of the entropy production. However, the conventional thermodynamic description is only valid when the Knudsen number is sufficiently small. Here, it is shown that the range of validity of the Navier-Stokes-Fourier equations can be extended by incorporating the nonlinear coupling among the thermodynamic forces and fluxes. The resulting system of conservation laws closed with the coupled constitutive relations is able to describe many interesting rarefaction effects, such as Knudsen paradox, transpiration flows, thermal stress, heat flux without temperature gradients, etc., which can not be predicted by the classical Navier-Stokes-Fourier equations. For this system of equations, a set of phenomenological boundary conditions, which respect the second law of thermodynamics, is also derived. Some of the benchmark problems in fluid mechanics are studied to show the applicability of the derived equations and boundary conditions.

physics.flu-dyn↗