# max speed <--> time discretization

I'm working on a heat diffusion problem, $$\frac{\partial T}{\partial t}=\vec{\nabla}\cdot\left(\kappa T^{5/2}\,\vec{\nabla}T\right)$$

I know that, after discretization, the time step for the 1D case becomes, $$dt= \frac{\rho\,dx^2}{\kappa T_{max}^{5/2}}$$ Does this imply/mean that the maximum wave speed is $$\frac{dx}{dt} = \frac{\kappa T_{max}^{5/2}}{\rho\,dx}$$ or would I have to analyze this differently to get the wavespeed?

• What is $\rho$ here? – Geoff Oxberry Oct 23 '13 at 23:00
• Density. This is being attached to a hydro code – Kyle Kanos Oct 24 '13 at 2:14
• What do you mean by 'the time step becomes'? I suspect you interprete the CFL condition in the wrong way... – Jan Oct 24 '13 at 8:08
• @Jan: This time step was computed in Reale 1995. I admit I removed a factor of order unity, but that's the essence of $dt$ for this problem. All I am asking is if it's valid to use $dx/dt$ to get the wavespeed, or do I have to do something different. – Kyle Kanos Oct 24 '13 at 13:09
• Since $dt$ and $dx$ is your personal choice, I doubt that you can use them to get a characteristic of the actual continuous equation. – Jan Oct 24 '13 at 13:21