Chorin Artificial Compressibility Equations

In summary, the problem presented is a formulation of the incompressible Navier-Stokes equations with coefficients pt, ut, vt, c2, u2, v2, p, and α. The individual equations involve variables x, y, u, v, and p, and the desired solution is an exact solution. The conditions for the problem include u=v=0 and a constant density ρ.
  • #1
angy
11
0
Hi! I have the following problem:

pt + (c2u)x + (c2v)y = 0
ut + (u2+p)x + (uv)y = α(uxx+uyy)
vt + (uv)x + (v2+p)y = α(vxx+vyy)

It is a formulation of the incompressible Navier-Stokes equations.
I would like to know an exact solution.
Can anyone help me?

Thanks
 
Physics news on Phys.org
  • #2
angy said:
Hi! I have the following problem:

pt + (c2u)x + (c2v)y = 0
ut + (u2+p)x + (uv)y = α(uxx+uyy)
vt + (uv)x + (v2+p)y = α(vxx+vyy)

It is a formulation of the incompressible Navier-Stokes equations.
I would like to know an exact solution.
Can anyone help me?

Thanks
u=v=0

ρ=constant

Chet
 

Related to Chorin Artificial Compressibility Equations

1. What are Chorin artificial compressibility equations?

Chorin artificial compressibility equations are a set of equations used in computational fluid dynamics to simulate incompressible flows. They were developed by Alexandre Chorin in the 1960s and are based on the idea of approximating the incompressible Navier-Stokes equations by adding an artificial compressibility term.

2. Why are Chorin artificial compressibility equations used?

Chorin artificial compressibility equations are used because they are computationally efficient and can accurately simulate incompressible flows. They are especially useful for problems involving large time steps and high Reynolds numbers.

3. How do Chorin artificial compressibility equations work?

The Chorin artificial compressibility equations work by adding an artificial compressibility term to the incompressible Navier-Stokes equations. This term is chosen to be small enough so that it does not significantly affect the solution, but large enough to make the equations easier to solve numerically.

4. What are the limitations of Chorin artificial compressibility equations?

One limitation of Chorin artificial compressibility equations is that they are only valid for incompressible flows. They also do not account for the effects of turbulence, so they may not be accurate for highly turbulent flows. Additionally, they may not be suitable for problems with complex geometries.

5. How accurate are Chorin artificial compressibility equations?

The accuracy of Chorin artificial compressibility equations depends on the chosen artificial compressibility term and the chosen numerical method for solving the equations. In general, they can provide reasonably accurate results for incompressible flows, but may not be as accurate as other methods for more complex problems.

Similar threads

A Why are the Navier-Stokes equations inconsistent in this case?
    • Classical Physics
Replies
18
Views
1K
Navier-Stokes equation for parallel flow
    • Advanced Physics Homework Help
Replies
1
Views
2K
Compressible flow or incompressible flow equation?
    • Mechanical Engineering
Replies
14
Views
2K
I Deriving Navier-Stokes Equation
    • Classical Physics
Replies
4
Views
1K
A How to Solve Isothermal Incompressible Navier-Stokes for Compressible Fluid?
    • Classical Physics
Replies
20
Views
5K
Navier Stokes Equation - Flow of waves
    • Advanced Physics Homework Help
Replies
4
Views
2K
I Viscosity Term in Navier-Stokes Equation
    • Classical Physics
Replies
8
Views
2K
A Green's function for Stokes equation
    • Differential Equations
Replies
1
Views
2K
A Stressing Over Stress Tensor Symmetry in Navier-Stokes
    • Other Physics Topics
Replies
2
Views
1K
I Divergence of the Navier-Stokes Equation
    • Classical Physics
Replies
1
Views
4K

Hot Threads

Recent Insights

Back
Top