Are the Navier-Stokes equations unsolvable?
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In particular, solutions of the Navier–Stokes equations often include turbulence, which remains one of the greatest unsolved problems in physics, despite its immense importance in science and engineering. Even more basic (and seemingly intuitive) properties of the solutions to Navier–Stokes have never been proven.
Why are Navier-Stokes equations unsolvable?
The Navier-Stokes equation is difficult to solve because it is nonlinear. This word is thrown around quite a bit, but here it means something specific. You can build up a complicated solution to a linear equation by adding up many simple solutions.
The Navier–Stokes equations are useful because they describe the physics of many phenomena of scientific and engineering interest. They may be used to model the weather, ocean currents, water flow in a pipe and air flow around a wing.
What is the purpose of the Navier-Stokes equation?
The difference between them and the closely related Euler equations is that Navier–Stokes equations take viscosity into account while the Euler equations model only inviscid flow.
Is Navier Stokes equation linear?
This chapter describes the Navier-Stokes (N-S) equations. The N-S equations form a quasi-linear differential system, and such systems can be studied through linearized equations.
The Navier-Stokes equations consists of a time-dependent continuity equation for conservation of mass , three time-dependent conservation of momentum equations and a time-dependent conservation of energy equation. There are four independent variables in the problem, the x, y, and z spatial coordinates of some domain, and the time t.
How can I derive the NSE of a given volume?
The traditional approach is to derive teh NSE by applying Newton’s law to a \\fnite volume of uid.
How do Engineers solve CFD equations?
In modern computational fluid dynamics (CFD) codes the equations are solved numerically, which would be prohibitively time-consuming if done by hand. However, in some complicated practical applications even this numerical approach can be become too complicated such that engineers have to rely on statistical methods to solve the equations.