*Sauro Succi*

- Published in print:
- 2018
- Published Online:
- June 2018
- ISBN:
- 9780199592357
- eISBN:
- 9780191847967
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199592357.003.0027
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

This chapter deals with the extension of the LB methodology to the case of non-ideal fluids, i.e., fluids in which potential energy can no longer be neglected as compared to kinetic energy. The ...
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This chapter deals with the extension of the LB methodology to the case of non-ideal fluids, i.e., fluids in which potential energy can no longer be neglected as compared to kinetic energy. The macroscopic consequences are major, primarily phase-transitions and attendant interface formation, which lie at the heart of the physics of multiphase and multicomponent flows, a branch of the physics of fluids with numerous applications in modern science and engineering.Less

This chapter deals with the extension of the LB methodology to the case of non-ideal fluids, i.e., fluids in which potential energy can no longer be neglected as compared to kinetic energy. The macroscopic consequences are major, primarily phase-transitions and attendant interface formation, which lie at the heart of the physics of multiphase and multicomponent flows, a branch of the physics of fluids with numerous applications in modern science and engineering.

*Sauro Succi*

- Published in print:
- 2018
- Published Online:
- June 2018
- ISBN:
- 9780199592357
- eISBN:
- 9780191847967
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199592357.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

This chapter presents the basic elements of the kinetic theory of non-ideal fluids, to which both kinetic and potential energy contribute on comparable footing. Non-ideal fluids lie at the heart of ...
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This chapter presents the basic elements of the kinetic theory of non-ideal fluids, to which both kinetic and potential energy contribute on comparable footing. Non-ideal fluids lie at the heart of many complex fluid-dynamic applications, such as those involving multiphase and multicomponent flows. This chapter features a degree of abstraction which may not come by handy to the reader with limited interest to the formal theory of classical many-body systems. The interested readers can safely skip the math and retain the basic bottomline. They may just skip this chapter altogether, but in this author’s opinion, this is likely to come with a toll on the full appreciation of Lattice Boltzmann theory for non-ideal fluids, in fact one of the most successful offsprings of Lattice Boltzmann theory.Less

This chapter presents the basic elements of the kinetic theory of non-ideal fluids, to which both kinetic and potential energy contribute on comparable footing. Non-ideal fluids lie at the heart of many complex fluid-dynamic applications, such as those involving multiphase and multicomponent flows. This chapter features a degree of abstraction which may not come by handy to the reader with limited interest to the formal theory of classical many-body systems. The interested readers can safely skip the math and retain the basic bottomline. They may just skip this chapter altogether, but in this author’s opinion, this is likely to come with a toll on the full appreciation of Lattice Boltzmann theory for non-ideal fluids, in fact one of the most successful offsprings of Lattice Boltzmann theory.

*S. G. Rajeev*

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198805021
- eISBN:
- 9780191843136
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805021.003.0002
- Subject:
- Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Euler derived the fundamental equations of an ideal fluid, that is, in the absence of friction (viscosity). They describe the conservation of momentum. We can derive from it the equation for the ...
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Euler derived the fundamental equations of an ideal fluid, that is, in the absence of friction (viscosity). They describe the conservation of momentum. We can derive from it the equation for the evolution of vorticity (Helmholtz equation). Euler’s equations have to be supplemented by the conservation of mass and by an equation of state (which relates density to pressure). Of special interest is the case of incompressible flow; when the fluid velocity is small compared to the speed of sound, the density may be treated as a constant. In this limit, Euler’s equations have scale invariance in addition to rotation and translation invariance. d’Alembert’s paradox points out the limitation of Euler’s equation: friction cannot be ignored near the boundary, nomatter how small the viscosity.Less

Euler derived the fundamental equations of an ideal fluid, that is, in the absence of friction (viscosity). They describe the conservation of momentum. We can derive from it the equation for the evolution of vorticity (Helmholtz equation). Euler’s equations have to be supplemented by the conservation of mass and by an equation of state (which relates density to pressure). Of special interest is the case of incompressible flow; when the fluid velocity is small compared to the speed of sound, the density may be treated as a constant. In this limit, Euler’s equations have scale invariance in addition to rotation and translation invariance. d’Alembert’s paradox points out the limitation of Euler’s equation: friction cannot be ignored near the boundary, nomatter how small the viscosity.