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Multispecies Bhatnagar-Gross-Krook models and the Onsager reciprocal relations
1Department of Mathematics and Statistics, <a href="https://ror.org/00a0n9e72">University of Limerick</a>, Limerick V94 T9PX, Ireland.
Physical Review. E
|October 19, 2024
Summary
Most Bhatnagar-Gross-Krook models fail Onsager relations due to velocity-independent coefficients. This complicates matching model transport properties to real fluids.
Area of Science:
- Fluid dynamics
- Kinetic theory
- Statistical mechanics
Background:
- The Bhatnagar-Gross-Krook (BGK) model is a widely used kinetic model in fluid dynamics.
- Accurate modeling of transport properties is crucial for simulating fluid behavior.
- Onsager relations are fundamental principles governing transport phenomena in thermodynamic systems.
Purpose of the Study:
- To investigate the validity of existing Bhatnagar-Gross-Krook models concerning Onsager relations.
- To identify the limitations of current BGK models in accurately representing fluid transport properties.
Main Methods:
- Analysis of Bhatnagar-Gross-Krook model formulations.
- Examination of the conditions under which the Onsager relations are satisfied.
Main Results:
- Most existing Bhatnagar-Gross-Krook models, with velocity-independent coefficients, do not satisfy the Onsager relations.
- This violation poses a significant challenge for the calibration of these models.
Conclusions:
- The velocity-independent coefficient assumption in standard BGK models leads to a fundamental inconsistency with Onsager relations.
- Revisions to the Bhatnagar-Gross-Krook model are necessary to ensure accurate prediction of transport properties and thermodynamic consistency.
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