- Open Access
Practical Kinetic Models for Dense Fluids
Phys. Rev. Lett. 136, 104002 – Published 9 March, 2026
DOI: https://doi.org/10.1103/fd39-6hmq
Abstract
A novel approach to constructing kinetic models is proposed on the basis of the separation of local and nonlocal contributions to particle interaction. The method results in a generic kinetic equation for complex fluid systems, amenable to efficient numerical realization. The main obstruction to causality caused by a coupling between the nonuniform temperature field and the nonideal equation of state is resolved based on gauge invariance of the hydrodynamic limit. A new lattice Boltzmann model is derived for compressible nonideal fluid simulation based on the Enskog-Vlasov kinetic theory as a case of practical importance.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (45)
- U. Frisch, B. Hasslacher, and Y. Pomeau, Phys. Rev. Lett. 56, 1505 (1986).
- G. R. McNamara and G. Zanetti, Phys. Rev. Lett. 61, 2332 (1988).
- F. J. Higuera, S. Succi, and R. Benzi, Europhys. Lett. 9, 345 (1989).
- Y. Qian, D. d’Humières, and P. Lallemand, Europhys. Lett. 17, 479 (1992).
- S. Succi, The Lattice-Boltzmann Equation for Fluid Dynamics and Beyond (Oxford University Press, Oxford, 2001).
- H. Chen, S. Kandasamy, S. Orszag, R. Shock, S. Succi, and V. Yakhot, Science 301, 633 (2003).
- M. Sbragaglia, R. Benzi, L. Biferale, S. Succi, and F. Toschi, Phys. Rev. Lett. 97, 204503 (2006).
- C. Kunert and J. Harting, Phys. Rev. Lett. 99, 176001 (2007).
- J. Hyvaluoma and J. Harting, Phys. Rev. Lett. 100, 246001 (2008).
- L. Biferale, P. Perlekar, M. Sbragaglia, and F. Toschi, Phys. Rev. Lett. 108, 104502 (2012).
- R. Benzi, S. Chibbaro, and S. Succi, Phys. Rev. Lett. 102, 026002 (2009).
- M. Mendoza, B. M. Boghosian, H. J. Herrmann, and S. Succi, Phys. Rev. Lett. 105, 014502 (2010).
- M. Thiébaud, Z. Shen, J. Harting, and C. Misbah, Phys. Rev. Lett. 112, 238304 (2014).
- M. Mendoza, S. Succi, and H. J. Herrmann, Phys. Rev. Lett. 113, 096402 (2014).
- A. Mazloomi M., S. S. Chikatamarla, and I. V. Karlin, Phys. Rev. Lett. 114, 174502 (2015).
- S. A. Hosseini, B. Dorschner, and I. V. Karlin, J. Fluid Mech. 953, A4 (2022).
- S. A. Hosseini and I. V. Karlin, Phys. Rep. 1030, 1 (2023).
- N. Frapolli, S. S. Chikatamarla, and I. V. Karlin, Phys. Rev. Lett. 117, 010604 (2016).
- M. H. Saadat, S. A. Hosseini, B. Dorschner, and I. V. Karlin, Phys. Fluids 33, 046104 (2021).
- N. Sawant, B. Dorschner, and I. V. Karlin, J. Fluid Mech. 909, A1 (2021).
- S. A. Hosseini, P. Boivin, D. Thévenin, and I. Karlin, Prog. Energy Combust. Sci. 102, 101140 (2024).
- X. He and G. D. Doolen, J. Stat. Phys. 107, 309 (2002).
- E. Reyhanian, B. Dorschner, and I. V. Karlin, Phys. Rev. E 102, 020103(R) (2020).
- R. Huang, H. Wu, and N. A. Adams, Phys. Rev. Lett. 126, 244501 (2021).
- B. Shan, S. Li, G. Tang, M. Torrilhon, Y. Zhang, and Z. Guo, Acta Mech. Sin. 41, 724893 (2025).
- S. Busuioc and V. Sofonea, Phys. Fluids 37, 073384 (2025).
- W. Su, L. Gibelli, J. Li, M. K. Borg, and Y. Zhang, Phys. Rev. Fluids 8, 013401 (2023).
- B. Shan, W. Su, L. Gibelli, and Y. Zhang, J. Fluid Mech. 976, A7 (2023).
- R. Liboff, Kinetic Theory (Springer, New York, 2003).
- X. He, S. Chen, and G. Doolen, J. Comput. Phys. 146, 282 (1998).
- S. Ansumali, S. Arcidiacono, S. S. Chikatamarla, N. I. Prasianakis, A. N. Gorban, and I. V. Karlin, Eur. Phys. J. B 56, 135 (2007).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/fd39-6hmq for additional details on second order in time discretization of the kinetic model derived in the main text, the analysis of the Enskog-Vlasov kinetic model, and the Chapman-Enskog analysis of the proposed lattice Boltzmann model for compressible nonideal fluids.
- J. W. Dufty, A. Santos, and J. J. Brey, Phys. Rev. Lett. 77, 1270 (1996).
- D. Enskog, K. Sven. Vetenskapsakad. Handl. 63 (1921), https://archive.org/details/kunglsvenskavete63kung/page/n49/mode/2up.
- A. A. Vlasov, Many-Particle Theory and Its Application to Plasma (Gordon and Breach, New York, 1961).
- M. Grmela, J. Math. Phys. (N.Y.) 15, 35 (1974).
- J. Karkheck and G. Stell, J. Chem. Phys. 75, 1475 (1981).
- S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases (Cambridge University Press, Cambridge, England, 1939).
- S. A. Hosseini and I. Karlin, Data for “practical kinetic models for dense fluids”, 10.7910/DVN/XDHLDE (2026).
- I. V. Karlin, D. Sichau, and S. S. Chikatamarla, Phys. Rev. E 88, 063310 (2013).
- D. Igra and K. Takayama, Rep. Inst. Fluid Sci. Tohoku Univ. 13, 19 (2001).
- B. Dorschner, F. Bösch, and I. V. Karlin, Phys. Rev. Lett. 121, 130602 (2018).
- E. Shakhov, Fluid Dyn. 3, 95 (1968).
- H. Van Beijeren and M. H. Ernst, Physica (Amsterdam) 68, 437 (1973).
- S. A. Hosseini and I. V. Karlin, Phys. Fluids 37, 102114 (2025).