I'm working on a 3D stationary simulation of brachiocefalic artery; i'm using laminar flow physics with a known velocity in inlet and a normal stress in outlet. The model geometry is a simple cylinder.

For the normal stress i'm using this formula:

S=Q*C+po (where S= normal stress; Q= flow rate; po= outlet pressure (in this case venous pressure; C= resistance coefficient)

All the data are known, except the coeffcient C that is the parameter which i want to find: so i'm using the OPTIMIZATION module.

My objective is to find the C value for which the average pressure (p) in the domain is near to a reference pressure (called Pref), so i used these settings:

INTEGRAL OBJECTIVE (applied to domain):

Objective expression: abs(p-Pref)

CONTROL VARIABLE FIELD (applied to outlet boundary) :

Control variable name: C

Initial value: 0

All other are default settings.

The problem is that the solver returns always the initial value as optimal value, even if the resultant pressure is very far from the reference one.

I tried to change mesh, initial value for variable C, i used also probe objective instead of integral objective, but the problem persists: optimization solver terminate WITHOUT errors, returning back whatever initial value used for C as the optimal value.

EXAMPLE:

Pref=15000Pa (so p should be near to this value)

C initial value = 1000

Log of simulation:

Optimization Solver 1 in Solver 1 started at 28-apr-2012 19:02:53.

Optimization solver (SNOPT)

Itns Major Minor Step nPDE Error Objective

0 0 0 - 1 2.48e-011 0.3085

Number of optimization variables: 75.

Number of objective function evaluations: 3.

Number of Jacobian evaluations: 2.

Final objective function value: 0.3085111759.

Optimality conditions satisfied.

Optimization Solver 1 in Solver 1: Solution time: 110 s. (1 minute, 50 seconds)

p average on the domain= 1460 Pa ( instead of 15000!)

What's the problem?

P.S.Tell me if you need more informations or data;