Chorin Artificial Compressibility Equations

[angy]

Hi! I have the following problem:

p_t + (c²u)_x + (c²v)_y = 0
u_t + (u²+p)_x + (uv)_y = α(u_xx+u_yy)
v_t + (uv)_x + (v²+p)_y = α(v_xx+v_yy)

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

Thanks

 

[Chestermiller]

Hi! I have the following problem:

p_t + (c²u)_x + (c²v)_y = 0
u_t + (u²+p)_x + (uv)_y = α(u_xx+u_yy)
v_t + (uv)_x + (v²+p)_y = α(v_xx+v_yy)

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