An incompressible flow model based on the conservation of rotational acceleration
Résumé
The discrete mechanics proposed as an alternative to the Navier-Stokes equations naturally leads to the separation of irrotational compressible flows from incompressible flows with divergence-free, whether viscous or not. The assumption of infinite fluid celerity in incompressible flows reveals the possibility of abandoning the irrotational part of the discrete law of motion to establish a version dedicated to incompressible flows. As the pressure gradient or scalar potential term is eliminated, it is replaced by the acceleration potential vector whose divergence from its dual curl is identically zero; all terms of the discrete law of motion whose variable is velocity are therefore solenoidal, and if a solution has zero divergence initially, it remains so over time.
The numerical methodology associated with this model makes it possible to simulate viscous or non-viscous unsteady flows in two and three spatial dimensions. Unlike projection methods or rotational formulations, the law of motion is not adjoined to another equation ensuring the incompressibility constraint. Elementary examples demonstrate the role of the acceleration vector potential and the implementation of the numerical method.
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