Euler Equations (fluid Dynamics)
In fluid dynamics, the Euler equations are a set of equations governing inviscid flow. They are named after Leonhard Euler. The equations represent conservation of mass (continuity), momentum, and energy, corresponding to the Navier–Stokes equations with zero viscosity and heat conduction terms. Historically, only the continuity and momentum equations have been derived by Euler. However, fluid dynamics literature often refers to the full set – including the energy equation – together as "the Euler equations".
Like the Navier-Stokes equations, the Euler equations are usually written in one of two forms: the "conservation form" and the "non-conservation form". The conservation form emphasizes the physical interpretation of the equations as conservation laws through a control volume fixed in space. The non-conservation form emphasises changes to the state of a control volume as it moves with the fluid.
The Euler equations can be applied to compressible as well as to incompressible flow – using either an appropriate equation of state or assuming that the divergence of the flow velocity field is zero, respectively.
Read more about Euler Equations (fluid Dynamics): History, Conservation and Component Form, Conservation and Vector Form, Non-conservation Form With Flux Jacobians, Shock Waves, The Equations in One Spatial Dimension, Steady Flow in Streamline Coordinates