Cfd beginner I have energy equation E_t=k*dT^2/d^2x Where E_t is a time derivative of total energy w.r.t time, k thermal conductivity and T is temperature. Which explicit finite difference scheme can be used? , what about time step to satisfy CFL condition, as I know k very small then very large time step can be used? when using second order central difference scheme What about the stability when T has discontinuous initial conditions ?

Stability conditions for explicit scheme

E^n+1_i =

E^n_i + dt*k*(T^n_i+1 - 2*T^n_i + T^n_i-1)/dx^2

are: dt < dx^2/(2*k) in 1D dt < dx^2/(4*k) in 2D dt < dx^2/(6*k) in 3D

and they don't depend on initial conditions (discontinous or smooth).

Thanks for reply Alexei But I think by this scheme there an oscillation when there is discontinues T data.