Hi,all,

In my channel LES code, the set of filtered equations are integrated by a fractional step method. The discretization schemes are explicit RK for nonlinear terms and implicit CN for linear ones. You know, in the first step, the equation is written in terms of the velocity increment as follows

(1-(Lxx+Lyy))(du_i)=RHS

where du_i is the velocity increment,Lxx and Lyy are the second order derivative operators with respect to x and y. Hence an approximate factorization technique can be employed. It replaces the LHS terms by

(1-Lxx)(1-Lyy)du_i

and hence the original equation is written as

(1-Lxx)A=RHS (1)

(1-Lyy)du_i=A (2)

but I am confused by the boundary condition of the intermediate quantity A and the velocity increment du_i because my channel is NOT periodic in the any direction!

Does anyone has such an experience? Any comments and suggestions are greatly appreciated.

Linfeng

In most cases, intermediate incremental variable is set to zero at both ends of a ADI sweep, because it is usually difficult to derive a BC for an intermediate variable only due to a spliting scheme. But you can get a BC for du_i. So the rule of thumb is: alternatively use x and y direction as the the first sweep direction in ADI.

I'll try it, thanks! But I do believe there should be some kind of special tricks dealing with the intermediate variables at special boundaries such as inlet, outlet and solid wall.

Sincerely,

Linfeng