Why are the Navier Stokes equations considered difficult to solve?
Table of Contents
- 1 Why are the Navier Stokes equations considered difficult to solve?
- 2 Which assumptions have to be made for the general conservation equations to generate the Navier Stokes equations?
- 3 How many unknowns in Navier Stokes equations are there?
- 4 How many unknowns in Navier-Stokes equations are there?
- 5 What is Navier Stokes equation used for?
Navier-Stokes is on the extreme end of the spectrum. The difficulty of the mathematics of the equation is, in some sense, an exact reflection of the complexity of the turbulent flows they’re supposed to be able to describe.
What will happen if Navier-Stokes equation is solved?
You’d be able to perfectly model complex systems such as stellar gases. You’d be able to perfectly describe fluid flow through a pipe, and reduce turbulence such that you get maximum efficiency out of transport of fluids such as oil.
The Navier–Stokes equations are based on the assumption that the fluid, at the scale of interest, is a continuum, in other words is not made up of discrete particles but rather a continuous substance.
What is the Navier Stokes equation used for?
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.
1.8 Navier-Stokes equations
| Number of Equations | Number of Unknowns | |
|---|---|---|
| continuity | 1 | 1 |
| Navier-Stokes | 3 (symmetry) | 3 |
| 4 | 4 |
Why is the Navier Stokes equation important?
The Navier-Stokes equations are a family of equations that fundamentally describe how a fluid flows through its environment. Biomedical researchers use the equations to model how blood flows through the body, while petroleum engineers use them to reveal how oil is expected to flow through a well or pipeline.
What does the Navier-Stokes equation do?
Navier-Stokes equation, in fluid mechanics, a partial differential equation that describes the flow of incompressible fluids. The equation is a generalization of the equation devised by Swiss mathematician Leonhard Euler in the 18th century to describe the flow of incompressible and frictionless fluids.
What are the three forces considered in Navier Stokes equation?
There are three kinds of forces important to fluid mechanics: gravity (body force), pressure forces, and viscous forces (due to friction).