Index
S-dependence
Ver: 1
 

DESCRIPTION

In the context of evolutionary tasks, material parameters or boundary condition parameters can be function of the evolution variable S.

In Polyflow version 3, any problem parameter can be defined as an algebraic function of the single evolution variable S; more than one parameter can be a function of S at the same time.

When the task setup is of the evolutionary type, the "S-dependence" menu appears after the definition of parameters which might be a function of S.

During the evolution process, the value of a specific parameter will be calculated as the product of its nominal value and the function of S selected for that particular parameter.

Implemented functions are as follows :

  OPTIONS
 
-1 
 Upper level menu
0 
 F(S) = User Defined Function
Allows the user to enter the index of his own function of S. This function will be evaluated at run-time by CLIPS interpreter. (cfr 'User Defined Functions' chapter of the User's Manual).
1 
 S-independent
This is the default setup
2 
 f(S) = S
Linear function of S.
Frequently used in non-linear problems where convergence is difficult for high values of the parameter (ex: flow rate, relaxation time).
3 
 f(S) = 1/S
Inverse function of S.
Frequently used in non-linear problems where convergence is difficult for low values of the parameter (ex: conductivity, surface tension).
Not available if Sinit = 0.0
4 
 f(S) = a + b*S + c*S**2 + d*S**3 
  Third order polynomial
5 
 f(S) = ramp function
This is a function with 4 parameters (a,b,c,d) representing the corner values of a ramp function as follows:


 
6 
 f(S) = a * cos( b*S + c ) + d + e*S
A cosine function
7 
 f(S) = a * S**b + c * S**d
Rational exponents of s
8 
 f(S) = a * exp( b*S ) + c + d*S
Exponential function (e-base)
9 
 f(S) = double ramp function
This is a function with 7 parameters (a,b,c,d,e,f,g) representing the corner values of a double ramp function as follows:


 
10 
 f(S) = trapezoidal wave
This is a function with 6 parameters (a,b,c,d,e,f) representing a 'trapezoidal wave' as follows:


 
11 
 f(S) = H step function
This is a function with 4 parameters (a,b,c,d) increasing or decreasing step by step as follows:

This last function is only available in transient schemes.
 
12 f(S) = Multi-ramp function
This is a multi-linear function : the user gives a series of n ( Si , f(Si ) ) pairs.
f(S) = f(S1)                                                                if  S < S1
f(S) = f(Si ) + ( f(Si+1) - f(Si ) ) * (S-Si )/(Si+1-Si )      if  Si < S < Si+1
f(S) = f(Sn)                                                                if  S  > Sn
13
 Modify the value of a
To enter the "a" parameter in laws (4 to 11)
 14
 Modify the value of b
To enter the "b" parameter in laws (4 to 11)
15
 Modify the value of c
To enter the "c" parameter in laws (4 to 11)
16
 Modify the value of d
To enter the "d" parameter in laws (4 to 11)
17
 Modify the value of e
To enter the "e" parameter in laws (6, 9 and 10)
18
 Modify the value of f
To enter the "f" parameter in laws (9 to 10)
19
 Modify the value of g
To enter the "g" parameter in laws (9)
EXAMPLES For an evolution problem starting at a low flow rate and ending at a flow rate of Q, enter :
Q as the flow rate; select function 2.
The calculation will start at a flow rate = Q * (Sinit)

For an evolution problem starting at a high value of the surface tension coefficient and ending at a value G for the coefficient, enter:
G as the surface tension coefficent; select function 3.
The calculation will start with a surface tension coefficient = G * 1/(Sinit)

 NOTE Options 4 to 11 are useful for assigning time-dependent boundary conditions. SEE ALSO