Some Fluid Models
We consider a fluid flow occupying a bounded domain \(\Omega _{F} \subset \) \({\mathbb{R}}^{N}\), with N = 2 or N = 3, at the initial time t = 0 and a domain \(\Omega _{F}\)(t) at time t > 0. Let us denote by ρ \((x,t) \in {\mathbb{R}}^{+}\) the density of the fluid at time t at the point \(x\ \in \Omega _{F}\)(t) and by u(x, t) ∈ \({\mathbb{R}}^{N}\) its velocity. The fluid flow equations are derived by writing the mass conservation
and the balance of momentum
where σ is the so-called constraint tensor and frepresents a volumic force. For an isothermal fluid, there is no need to complete the system by the balance of energy....
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Raymond, JP. (2013). Control of Fluids and Fluid-Structure Interactions. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_15-1
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_15-1
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Control of Fluid Flows and Fluid-Structure Models- Published:
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_15-2
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Control of Fluids and Fluid-Structure Interactions- Published:
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_15-1