Department of Mathematics

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Subject: search.filters.subject.CCR model

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    A Viewpoint on Thermally-Induced Transport in Rarefied Gases through the Method of Fundamental Solutions
    (Taylor & Francis, 2024-04) Rana, Anirudh Singh
    Some phenomena pertaining to rarefied gases are beyond the reach of traditional fluid dynamics described, e.g., by the Euler or Navier–Stokes–Fourier equations. Therefore we adopt a recently developed model—referred to as the CCR model—to investigate thermally-induced transport in rarefied gases. To this end, the method of fundamental solutions is employed on the CCR model to investigate two problems: (i) a rarefied gas flow confined between two coaxial cylinders having different temperatures with the inner cylinder being circular while the outer being elliptical, and (ii) evaporation/condensation process in a rarefied vapor confined between two coaxial cylinders, again with the inner cylinder being circular and the outer being elliptical. Through a comprehensive analysis, the efficiency of the method of fundamental solutions is assessed. The work contributes toward a better understanding of thermally-induced confined rarefied gas flows.
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    Exploring external rarefied gas flows through the method of fundamental solutions
    (APS, 2025-01) Rana, Anirudh Singh
    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 nontrivial 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
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    Modeling of rarefied gas flows in streamwise periodic channels: Application of coupled constitutive relations and the method of fundamental solutions
    (Elsevier, 2025-03) Rana, Anirudh Singh
    Periodic structures are ubiquitous in nature and engineering, offering unique properties that inspire a range of applications. This paper explores the mathematical modeling of periodic structures in rarefied gas flows using the coupled constitutive relations (CCR) model. The method of fundamental solutions (MFS), known for its meshfree nature and computational efficiency, is utilized as a numerical tool. The streamwise periodic boundary conditions are incorporated into the MFS for modeling two-dimensional flow in periodically patterned channels. We validate the developed CCR-MFS framework with analytical solutions for force-driven Poiseuille and Couette flow. The error analysis is also performed to determine the optimal singularity location. Furthermore, we simulate the flow in channels with periodic patterns by varying the accommodation coefficient. This allows us to analyze the effects of patterning and accommodation coefficients in the Maxwell model of boundary conditions. Effects of patterning on mass flux, energy flux, and average friction coefficients are also presented for the force-driven flow in patterned channels. Our simulations demonstrate the potential of the mathematical and computational techniques to enhance the performance and functionality of a range of technological applications.