Using both backward timeScheme/Crank Nicholson for LES
 

Hello OpenFOAM community ;),

I'm working on LES of turbulent channel flow and I have to question about the temporal discretization.

1) I want to achive fully second order accuracy in time using the backward timeScheme for the convective term of the Navier-Stokes Equations and the Cranck Nicholson scheme for the diffusive terms.

If I select in the fvSchemes the timeScheme backward and I want to use this only for advection term while adopting the Crank Nicholson discretization for the diffusive term, then a simple advection/diffusion equation would rewrite as:

fvm::ddt(rho,U) ==
fvm:div(phi,U)+fvm:kappa*0.5*(fvm::laplacian(phi) + fvc::laplacian(phi))

is it correct in OpenFOAM ? :confused:

2) How the backward time schemes automatically take in to account at the time t=0 of the initial condition on the two levels 0 and 00 which are requested by the backward timeScheme ? :confused:

Thanks in advance

Andrea Aprovitola