Abstract
After reading this chapter, you will have a working understanding of the equations of fluid mechanics, which describe a fluid’s behaviour through its conservation of mass and momentum. You will understand the basics of the kinetic theory on which the lattice Boltzmann method is founded. Additionally, you will have learned about how different descriptions of a fluid, such as the continuum fluid description and the mesoscopic kinetic description, are related.
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Notes
- 1.
A fifth conservation equation for energy can also be derived, though we will only briefly address it later in Sect. 1.3.5 since it is less important both in fluid mechanics and in the LBM.
- 2.
The ideal gas law is expressed in many forms throughout science, often with quantities given in moles. Equation (1.21) is expressed using the state variables employed in fluid mechanics, the cost being that the specific gas constant R varies between different gases. Here, R = k B∕m, where k B is Boltzmann’s constant and m is the mass of the a gas molecule.
- 3.
While p 0 is relevant to the energy equation that we will see later in Sect. 1.3.5, this equation is usually not taken into account in LB simulations.
- 4.
However, the thermal velocity v T is of the order of the speed of sound c s [2].
- 5.
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Krüger, T., Kusumaatmaja, H., Kuzmin, A., Shardt, O., Silva, G., Viggen, E.M. (2017). Basics of Hydrodynamics and Kinetic Theory. In: The Lattice Boltzmann Method. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-44649-3_1
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