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Updated: May 27, 2025
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
8.5K
Exploring external rarefied gas flows through the method of fundamental solutions
Himanshi1, Anirudh Singh Rana2, Vinay Kumar Gupta1
1Indian Institute of Technology Indore, Department of Mathematics, Indore 453552, India.
Physical Review. E
|February 20, 2025
Summary
This study overcomes Stokes' paradox in rarefied gas dynamics using the CCR model. It provides meaningful solutions for 2D gas flows around objects, validated by the method of fundamental solutions.
Area of Science:
- Fluid Dynamics
- Rarefied Gas Dynamics
- Mathematical Physics
Background:
- Navier-Stokes-Fourier equations are inadequate for rarefied gas flows.
- Stokes equations fail for 2D flows, leading to Stokes' paradox.
- Stokes' paradox also affects rarefied gas flow problems.
Purpose of the Study:
- To present a method for meaningful 2D rarefied gas flow solutions around objects.
- To circumvent Stokes' paradox using an extended hydrodynamic model.
- To demonstrate the utility of the method of fundamental solutions for complex geometries.
Main Methods:
- Adoption of the CCR (Continuum Conservation Relations) model, an extended hydrodynamic model.
- Derivation of an analytic solution using the CCR model.
- Comparison with a numerical solution obtained via the method of fundamental solutions.
Main Results:
- Meaningful analytic and numerical solutions were obtained for 2D rarefied gas flows.
- The CCR model successfully addresses problems where Stokes' equations fail.
- The method of fundamental solutions proved effective for predicting flow past circular and semicircular cylinders.
Conclusions:
- The CCR model and method of fundamental solutions offer a viable approach to solving 2D rarefied gas flow problems.
- Stokes' paradox can be circumvented for complex geometries.
- The methodology is applicable to predicting rarefied gas flow around various objects.
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