FAS multigrid method
 

Hi everyone;
I plan to apply FAS multigrid method in my code but I have some problem in understanding:

first of all, I can not understand what "relaxation" means? infact, I suspect this step used only for solving L*U=F that F and U find from restriction or prolongation steps or it is used in calculating NS equation with initial value that is obtained from these two steps?

and second, is it necessary to calculate L (coefficient matrix) in each step of relaxation? as it is known L is depends on U and V (Velocity) and with changing u and v it will change.

and finally, what should be done for pressure? is it necessary to all three step of multigrid are applied for pressure? I ask it because in convergence, only for u and v is considered.

thanks in advance

any idea about the problems?

Hi Mehdi,

Relaxation means that you do not apply the full change of a newly-calculated variable, but rather - a weighted-sum of the new and old values of it. It is a general definition, and may be used in FAS as well as in other areas.

fortunately, these problem was solved, but some other came.
first of all, I apply simpler method in collocated grid. in simpler method velocity and pressure calculated in 6 step:
1-guess initial value
2- calculate pseudo-velocity
3- solve pressure Equation
4- solve descritized momentum equation
5- solve pressure correction equation
6- correct velocity
my question is the restricted source term (the term in bracket in following equation) that is added in course grid equation should be added in which step (step 2 or 4 for velocity and step 3 or 5 for pressure)?
http://www.cfd-online.com/Forums/dat...BJRU5ErkJggg==
http://www.cfd-online.com/Forums/dat...AAAElFTkSuQmCC
thanks in advance