ULTIMATE QUICKEST

Tanaka

Dear all, I am using ULTIMATE QUICKEST (Leonard 1991) for calculation of advection part in incompressible NS equations. My problem is in the limitter.

1. After designating nodes (fi_D, fi_C, fi_U) based on the sign of advecting velocity, I calculated ABS (DEL) and ABS (CURV) where DEL = (fi_D-fi_U) and CURV =(fi_D-2*fi_C+fi_U)

2. I checked if (ABS(CURV)<=0.6*ABS(DEL), if yes, then I calculated the facevalue (flux) using unconstrained QUICKEST scheme (no limitter).

3 Otherwise if ABS(CURV)>=ABS(DEL), then the facevalue (flux) =fi_C and proceed to next face. If no, then...

4. compute the reference face value fi_Ref=fi_U+(fi_C-fi_U)/c;

5 Now SET UP SOME DESIRED HIGH ORDER FACE VALUE (fi_F). if(DEL>0, limit fi_F by Fi_C below and the smaller of fi_Ref and fi_D above. if(DEL<0), limit fi_F by Fi_C above and larger of fi_Ref and fi_D below.

My question is what is desired high order face value (No. 5). Is it different then the facevalue in step 2. (can be calculated using QUICKEST scheme). I do not understand step 5.

If any one is using ULTIMATE QUICKEST scheme,kind help me. Any kind of help will be highly appreciated. Thank you A student