Some exact solutions to the Navier–Stokes equations exist. Examples of degenerate cases — with the non-linear terms in the Navier–Stokes equations equal to zero — are Poiseuille flow, Couette flo] and the oscillatory Stokes boundary layer.
Aug 06, 2015 · However, the Navier-Stokes equations are best understood in terms of how the fluid velocity, given by in the equation above, changes over time and location within the fluid flow. Thus, is an example of a vector field as it expresses how the speed of the fluid and its direction change over a certain line (1D), area (2D) or volume (3D) and with time .
Examples of degenerate cases — with the non-linear terms in the Navier–Stokes equations equal to zero — are Poiseuille flow, Couette flow and the oscillatory Stokes boundary layer. But also more interesting examples, solutions to the full non-linear equations, exist; for example the Taylor–Green vortex . It is an example of a simple numerical method for solving the Navier-Stokes equations. It contains fundamental components, such as discretization on a staggered grid, an implicit viscosity step, a projection step, as well as the visualization of the solution over time. The main priorities of the code are 1. Solving the Equations How the fluid moves is determined by the initial and boundary conditions; the equations remain the same. Depending on the problem, some terms may be considered to be negligible or zero, and they drop out. In addition to the constraints, the continuity equation (conservation of mass) is frequently required as well.
The Navier-Stokes equations In many engineering problems, approximate solutions concerning the overall properties of a ﬂuid system can be obtained by application of the conservation equations of mass, momentum and en-ergy written in integral form, given above in (3.10), (3.35) and (3.46), for a conveniently selected control volume.