Dear friends, Would you please help me? Kindly tell me which scheme is best to solve advection part of NS equations for incompressible flows in LES. Also if anyone kindly send me code for universal limiter (ULTIMATE) used with QUIKCEST (leonard 1991) schemes. A student in Japan, Tanaka.

HI Tanaka,

I think the best scheme for advection term in LES is Central Differencing, as only in this the numerical diffusion is low, aiding the Subgrid scale viscosity to aid the flow, wherein the real effect of LES is felt....

As of I am working in a NS code with CD for both convection and diffusion terms...

Glen.

Hi Glen ! Thanx for the message. But I fear centeral difference (CD) is 2nd order accurate. Is it stable? Do u use explicit schemes or implicit scheme? What scheme for time derivative did u use? I also used CD but the program did not continue and stoped after giving some absurred results. What should be done, please advise..

Hello Tanaka!

Here are some recomendations:

1. try making antisymmetric directional difference of the 2nd order in a single grid cell, i.e:

double u_advection=0.0; double u_c=0.5*(u[i][j]+u[i-1][j]); if(u_c>0) u_advection=u_c*((u[i][j]-u[i-1][j])/dx); else u_advection=u_c*((u[i+1][j]-u[i][j])/dx);

2. Another part of instability: conservational and non conserv. schemes. The above is conserv., this one is not, but more stable, i.e:

double u_c_m=0.5*(u[i][j][k]+u[i-1][j][k]); double u_c_p=0.5(u[i][j]+u[i+1][j][k]); u_advection=(u_c_p*u[i+1][j][k]-u_c_m*u[i][j][k])/dx);

(here i write 2-nd order most simple aproximations)

3. CFL if you are using explicit scheme - check dt and dx,dy,dz corelations from CFL criteria.

Best regards!

But I fear centeral difference (CD) is 2nd order accurate. Is it stable?

CD is 2nd order....It is quite unstable (main reason it is used in LES,as dissipation is less), if not for special considerations it should be treated with extra care...one of the methods is as mentioned by Nick (any way it is new to me)

however....u can take care of the cell peclet number and CFL condition for the code to be stable..and one of the most popular method used by the Stanford group is Deffered correction....where in a blend of lower order (usually upwind) and higher order (central diff) is used...i would suggest u to take a luk at the codes given along with the book "computational methods for fluid mechanics" by Peric & Freziger

Do u use explicit schemes or implicit scheme?What scheme for time derivative did u use?

As such I am using a 2nd order semi-implicit Crank-Nicolson scheme...

I also used CD but the program did not continue and stoped after giving some absurred results. What should be done !!!

This is becoz CD is quite unstable...take a luk at this paper .....

"New-wall modeling for complex flows using the large eddy simulation technique in curvilinear coordinates" by Y. A. Hassan and H. R. Barsamian

International Journal of Heat and Mass Transfer Volume 44, Issue 21, Pages 4009-4026 (November 2001)

in this paper, the unstability of CD is taken care by keeping te CFL low...that is reducing the time step...and moreover there is no any external procedure mentioned to take care of the un-stability....(as per my understanding)

hope this helps, let me know if u need any more help..

Glen