Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I have a typical 1D advection problem where a cold fluid flows over a flat plate. I did an energy balance to include conduction, convection and friction loss and I got the PDE's for the fluid and the solid. I used finite differences to solve the system as T(x, t) for both fluid and solid. After simplification, I have this kind of matrix in explicit scheme.

(see attached matrix.png)

The problem is that I want to optimise the number of nodes (time step) in my simulation to decrease time of calculation and ensure stability and convergence. I read about CFL criteria but it doesn't seem to always work in my case even if CFL < 1. Here (advection.png) is an image of the temperature distribution at a specific node for 2 different cases. By trial and error, I determined that the lowest minimum of nodes would be around 20 to get the full phenomen. However, is there a analytical way to figure out this value ?

Thank you,

Steven

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Advection equation stability for explicit scheme

Tags:

**Physics Forums | Science Articles, Homework Help, Discussion**