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Old   July 23, 1998, 11:15
Default Mathematica
  #1
Ravi Venkatesan
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Hi, I would be very grateful if someone could either provide me with, or lead me to, a Mathematica Notebook (preferably Mathematica V 2.2) which solves:____________________________ 1. The advection equation: u_t + a*u_x=0, "a" is constant 2. The equations of hydrodynamics in any dimension, and in either Eulerian or Lagrangian form.

Thanks Regards

Ravi
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Old   July 23, 1998, 22:00
Default Re: Mathematica
  #2
Igor Antropov
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1) Surely I can provide you with a Mathematica notebook to solve u_t + a*u_x=0, "a" is constant.

Beginning of Mathematica notebook, cut here ---------------------------------------------

u=f[x-a t]

---------------------------------------------

End of Mathematica notebook, cut here

Hint: any function of the form f(x-at) is a solution of the equation. If you find another solution, please let me know ;-)

2) Viscous incompressible fluid, Eulerian, x1,x2,x3 are Cartesian coordinates, t is time, u1,u2,u3 are velocity components, P is specific excess pressure, ro is density, nu is kinematic viscosity:

u1_t+u1*(u1_x1)+u2*(u1_x2)+u3*(u1_x3)= -(1/ro)P_x1+nu(u1_x1x1+u1_x2x2+u1_x3x3)

u2_t+u1*(u2_x1)+u2*(u2_x2)+u3*(u2_x3)= -(1/ro)P_x2+nu(u2_x1x1+u2_x2x2+u2_x3x3)

u3_t+u1*(u3_x1)+u2*(u3_x2)+u3*(u3_x3)= -(1/ro)P_x3+nu(u3_x1x1+u3_x2x2+u3_x3x3)

u1_x1+u2_x2+u3_x3=0

There is a shorter way to write it, but I had impresiion that you would prefer the long way.

Good luck.

Igor
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