Why is it hard to solve Navier Stokes equation?
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The Navier Stokes equation is so hard to solve because it is non-linear. If the inertial terms were not present (either because of the geometry or because the inertial terms are negligible0, it would (and can) be much easier to solve.
What is the purpose of the Navier Stokes equation?
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.
Famous Fluid Equations Are Incomplete For one thing, that the Navier-Stokes equations will always behave nicely. That is, given any initial state of the fluid, mathematicians want to be able to prove that the equations will never lead to a nonsensical result.
Is Navier-Stokes proven?
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.
The Navier–Stokes problem in two dimensions was solved by the 1960s: there exist smooth and globally defined solutions. Terence Tao in 2016 published a finite time blowup result for an averaged version of the 3-dimensional Navier–Stokes equation.
Are there any solutions to the Navier Stokes equations?
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 properties of the solutions to Navier–Stokes have never been proven.
Even though the Navier-Stokes equations have only a limited number of known analytical solutions, they are amenable to fine-gridded computer modeling. The main tool available for their analysis is CFD analysis.
Why is it so hard to solve N-s equations numerically?
For numerical simulations, the tiny errors introduced by the finite grid can have the same cascading effect. And that is what makes it so hard to solve the N-S equations numerically. An alternative way to solve a fluid flow problem is the Lattice Boltzmann method.
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.