Chorin Artificial Compressibility Equations

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SUMMARY

The discussion centers on the Chorin Artificial Compressibility Equations, which are a formulation of the incompressible Navier-Stokes equations. The equations presented are: pt + (c2u)x + (c2v)y = 0, ut + (u2+p)x + (uv)y = α(uxx+uyy), and vt + (uv)x + (v2+p)y = α(vxx+vyy). The user seeks an exact solution for these equations under the conditions u=v=0 and ρ=constant. The inquiry highlights the need for precise mathematical solutions in fluid dynamics.

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  • Understanding of the incompressible Navier-Stokes equations
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  • Knowledge of partial differential equations (PDEs)
  • Basic concepts of fluid dynamics
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angy
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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
 
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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
 

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