Navier in a sentence

However, the compressible case is the most general framework of Navier–Stokes equations so where not specified, Navier–Stokes equations are intended to be compressible Navier–Stokes equations.

Representations 3D Cartesian coordinates 3D Cylindrical coordinates 3D Spherical coordinates Navier–Stokes equations use in games The Navier–Stokes equations are used extensively in video games in order to model a wide variety of natural phenomena.

In the Navier boundary condition, the effect of the hydrodynamic slip is characterized by the slipping length.

An equivalent weak or variational form of the equation, proved to produce the same velocity solution as the Navier–Stokes equation, citation is given by, : for divergence-free test functions w satisfying appropriate boundary conditions.

Application to specific problems The Navier–Stokes equations, even when written explicitly for specific fluids, are rather generic in nature and their proper application to specific problems can be very diverse.

A significant feature of Cauchy equation and consequently all other continuum equations (including Euler and Navier–Stokes) is the presence of convective acceleration: the effect of time-independent acceleration of a flow with respect to space.

At very small scales or under extreme conditions, real fluids made out of discrete molecules will produce results different from the continuous fluids modeled by the Navier–Stokes equations.

Compressible flow The Navier–Stokes equations result from the following assumptions on the stress tensor: *the stress is Galileian invariant : it does not depend directly on the flow velocity, but only on spatial derivatives of the flow velocity.

Direct numerical simulation (DNS), based on the Navier–Stokes equations, makes it possible to simulate turbulent flows at moderate Reynolds numbers.

It is believed, though not known with certainty, that the Navier–Stokes equations describe turbulence properly.

Properties Nonlinearity The Navier–Stokes equations are nonlinear partial differential equations in the general case and so remain in almost every real situation.

The conservation of momentum equations for the compressible, viscous flow case are called the Navier–Stokes equations.

Time-tested formulations exist for common fluid families, but the application of the Navier–Stokes equations to less common families tends to result in very complicated formulations and often to open research problems.