temperature advection-diffusion equation

[Yannick Peng]

Hello,

I’m working on solving the temperature advection-diffusion equation, but I am facing issues with the results. Below is the first approach I tried:
scalar source[];
foreach()
    source[] = (((T[1,0]-T[]) -  (T[]-T[-1,0])) / Delta / Delta
                + ((T[0,1]-T[]) -  (T[]-T[0,-1])) / Delta / Delta);
face vector uf[];
foreach_face()
    uf.x[] = (u.x[] + u.x[-1]) / 2.;
face vector flux[];
tracer_fluxes(T, uf, flux, dt, source);
foreach() {
    T[] = T[] - dt * (flux.x[1,0] - flux.x[]) / Delta
                 - dt * (flux.y[0,1] - flux.y[]) / Delta;
}
boundary({T});
  However, the results are incorrect. I then tried a different approach:
face vector uf[];
foreach_face()
    uf.x[] = (u.x[] + u.x[-1]) / 2.;  
face vector flux[];
tracer_fluxes(T, uf, flux, dt, zeroc);
scalar r[];
foreach()
    foreach_dimension()
        r[] -= (flux.x[1,0] - flux.x[]) / (Delta * cm[]);
mgstats mgd2 = diffusion(T, dt, r = r);
boundary({T});
  

Unfortunately, the results are still not correct. Could you kindly help me identify what I might be doing wrong or suggest a better approach?

Thank you in advance for your help!

[Shyam Sunder Yadav]

Dear Yannik

Please check the following example by Dr. Antoon

http://basilisk.fr/sandbox/Antoonvh/cooling2D2.c

Basically, you have to do three things

1) Declare temperature as a tracer (which will advect it with the second order accurate BCG scheme )

2) Declare a face vector for storing (and updating) thermal diffusivity kappaf

3) Diffuse the temperature using diffusion.h

    diffusion (T, dt, kappaf, theta = Cp);

Best wishes

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Dr. Shyam Sunder Yadav
Associate Professor
Mechanical Engineering
BITS Pilani
09902346342
http://www.bits-pilani.ac.in/pilani/ssyadav/Profile

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[Yannick Peng]

Thank you so much for your detailed response! I really appreciate you pointing me to Dr. Antoon's example and highlighting the key steps. I'll go ahead and implement these changes, and I’m hopeful it will resolve the issues I’ve been facing.
Thanks again for your help, and best wishes!
Kind regards,
Yannick