Functions

13.3 Functions

The Functions in the Expression Editor enable mathematical and logical manipulation of both Vectors and Scalars.

The functions available in Expression Editor are explained here :

Operators
- Common to Vectors and Scalars (e.g. addition and subtraction)
- Scalars only (e.g. square roots and logs)
- Vectors only (e.g. dot and cross products)
Logicals
Trigonometric and Hyperbolic
Display related functions
Other functions
Integration and Averaging
Tables

13.3.1 Operators

The operators in the Expression Editor enable mathematical manipulation of both vectors and scalars. The mathematical operations available in the Expression Editor are shown in Table 13.1. In this table: a, b, c are scalars, and U, V, W are vectors.

Expression Operators	Function	Example
Operators: Scalars and/or Vectors
+	Addition	a = b+c or V = U+W
-	Subtraction	a = b-c or V = U-W
*	Multiplication of two Scalars or a Scalar and a Vector	a = bc or V = aU (but not V = U * W)
Operator: Scalars Only
/	Division	a = b/c
exp(scalar)	Base e exponential function	a= exp(b) raises e to the power of b: a= e^b
ln(scalar)	The natural logarithm function for e	a= ln(b) returns the natural log of b
sqrt(scalar)	square root function	a = sqrt(b)
^	exponential function	a= b^c raises b to the power of c: a= b^c
Operator: Vectors Only
&	vector dot product	a = V&U (a = \|V\| \|U\| cos (angle))
^	vector cross product	V=U^W (\|V\| = \|U\| \|W\| x sin (angle) ), The right-hand-rule is applied.
len(vector)	returns the length of vector V	a = len(V)
normalize(vector)	returns a normalized unit vector V/\|V\|	V = normalize(U)
rotate(vector,angle, direction,center)	Returns a rotated vector based on the rotation angle, RHR, rotational axis and an optional rotation center. (If no center is defined, it defaults to 0,0,0)	Vrot = rotate(V,alpha,U,W) where V is the vector to be rotated, alpha is the angle in radians, and U is the axis of rotation. The right-hand-rule is applied. W is an optional center point defined as a vector.

Table 13.1 - Operators

13.3.2 Logicals

Description

The Logical functions in the Expression Editor enable the inclusion of logical statements. The following logical expressions are available in the Expression Editor:

Expression Operators	Function	Example
true	logic true
false	logic false
<	less than
>	greater than
==	Equal in logical comparison	a = (b==3) ? 1 : 2
or	logical or
and	logical and
!	logical negation	!< not less than
a = expression ? b : c	a = b if expression is true; a = c if expression is false	a = (b>3) ? 1 : 2 ==> ( If b is greater than 3, a = 1 otherwise a = 2 )

Table 13.2 - Logicals

13.3.3 Trigonometric and Hyperbolic

Description

The Trigonometric and Hyperbolic functions in the Expression Editor enable the inclusion of the corresponding functions in the mathematical statements. The following trigonometric and hyperbolic functions are available for scalars in the Expression Editor:

Transcendental Expressions	Function
Trigonometric
sin(radians)	sine function
cos(radians)	cosine function
cot(radians)	cotangent function
tan(radians)	tangent function
asin()	inverse sine function, returns value in rad
acos()	inverse cosine function, returns value in rad
acot()	inverse cotangent function, returns value in rad
atan()	inverse tangent function, returns value in rad
atan2(y,x )	two variable inverse tangent function, (-pi, pi), returns value in rad
Hyperbolic
sinh()	hyperbolic sine function
cosh()	hyperbolic cosine function
coth()	hyperbolic cotangent function
tanh()	hyperbolic tangent function
asinh()	inverse hyperbolic sine function
acosh()	inverse hyperbolic cosine function
acoth()	inverse hyperbolic cotangent function
atanh()	inverse hyperbolic tangent function

Table 13.3 - Trigonometric and Hyperbolic functions

13.3.4 Display related functions

Description

The Display related functions pertain to the Display Panel. They are used to:

Enable rotation and/or translation of the image in the Display Panel.
Enable the creation of a new variable with all the features of a Derived Variable, including the ability to display that function on selected Geometric Entities, such as Boundaries and Iso-surfaces.
Variables at Points.
Variables for XY plots.

Geometric view parameters

geom.move: (vector) translate geometry relative to Display Panel.

geom.rotate: (vector) rotate geometry relative to Display Panel. The 3 components of the vector are the same as the Z -X’-Z’’ angles defined in the View Tab in rad.

´	Note: The geom functions can be activated after running the simulations.

User defined variable for 3D display

display.varname: Defines a user variable to be used in 3D plots such as Contours / Iso Surfaces / Vectors. New variable will be added to "User Defined" under Variable in the Results Panel

#display.varname: dispname [unit]: (optional)Defines a new name with unit for a user defined display variable.

Variables at Monitoring Points

All the local cell variables at any monitor point can be accessed using the following format:

module[.subname].var@probe.name

Point coordinates:

probe.coord@probe_name

User defined variable for XY-Plot

plot.varname: Defines a user variable to be used in X-Y Plots. New variable will be added to Common section in the Plot Panel.

#plot.varname: dispname [unit]: (optional) Defines a new name with unit for a user defined variable.

Note:

No space should be added before ":" when defining a new display or plot variable name and unit.
The units inside "[ ]" for both display and plot variables has to be the default unit for that type of variables. (e.g. for pressure, the unit has to be “Pa”). If the unit is properly defined, it will be displayed on the screen. In this case, user can still change the final displayed unit in GUI, and the values will also be converted. If the unit is not properly chosen, software ignores unit.

13.3.5 Other functions

Description

Expression Operators	Function	Example
abs(x)	absolute value function
max(x,y)	maximum function	a = max(b,c) ==> a= b if b >c or a=c if c>=b
min(x,y)	minimum function	a = min(b,c) ==> a= b if b <c or a=c if c<=b
mod(x,y)	modulus function,	a = mod(c,b) ==> a = the remainder of c divided by b
sgn(x)	returns a flag (-1, 0, or 1) indicating the sign	a= sgn(b) ==> a = -1 if b<0 a = 0 if b=0 a = 1 if b>0
step(x)	step function returns a 0 or 1 depending on the value relative to zero	a= step(b) ==> a = 0 if b<0 a = 1 if b>=0

Table 13.4 - Other functions

13.3.6 Integration and Averaging

13.3.7 Tables

Description

The Table functions in the Expression Editor enable the inclusion of data from external table files located in the same directory as the project file (*.spro).

The following Table functions are available in the Expression Editor:

Table Expressions	Function
table(filename,x)	Interpolates from a 1-D Table (see Tables:1-D)
table(filename, x ,y)	Interpolates from a 2-D Table (see Tables:2-D)
table(filename, vector)	3-D Mapping table format (see Tables:3-D). It can be any vector, most commonly used as coordinate vector. Considers exact point data and no interpolation from the table

Table 13.5 - Table functions

Table Format: 1-D

The 1-D Table function table(filename,x) enables access to a 1-D data table located in the same directory as the project file (*.spro).

Format of the 1-D Table for Uniform Distribution :

<?xml version="1.0" encoding="ISO-8859-1"?>

# comment - values (x is assumed to have uniform distribution with xmin and xmax as bounds and n values in between)

…

</table>

Format of the 1-D Table for Non-Uniform Distribution is :

<?xml version="1.0" encoding="ISO-8859-1"?>

# comment - values (x is assumed to have non-uniform distribution)

x1 v1

x2 v2

…

xn vn

</table>

In the table syntax, outside = “flat” or outside = "extrapolation"under the table tag dictates how to determine a value when the input x, y is out of the range. "flat" denotes that the value of the closest bound is considered, and "extrapolation" denotes that the values are extrapolated from the nearest bound values.

Note: Comments can be input by placing a hash-mark “#” in front of the text. They are not inserted before the xml line (line 1).

Table Format: 2-D

The 2-D Table function table (filename,x) enables access to a 2-D data table located in the same directory as the project file (*.spro). 2D tables are used to specify variables which depend on two other independent variables.

Format of the 2-D Table for Uniform Distribution :

<?xml version="1.0" encoding="ISO-8859-1"?>

# values (x and y assumed to have uniform distribution)

v(x1,y1) v(x2,y1) … v(xn,y1)

v(x1,y2) v(x2,y2) … v(xn,y2)

…

v(x1,ym) v(x2,ym) … v(xn,ym)

</table>

Format of the 2-D Table for Non- Uniform Distribution :

In the format outside = “flat” or outside = "extrapolation"under the table tag dictates how to determine a value when the input x, y is out of the range.

<?xml version="1.0" encoding="ISO-8859-1"?>

# x and y variable ranges

x1 x2 … xn

y1 y2 … ym

# values table

v(x1,y1) v(x2,y1) … v(xn,y1)

v(x1,y2) v(x2,y2) … v(xn,y2)

…

v(x1,ym) v(x2,ym) … v(xn,ym)

</table>

Note: Comments can be input by placing a hash-mark “#” in front of the text. They are not before the xml line (line 1).

Table Format: 3-D

The 3-D Table function table (filename,vector) enables access to a 3-D data table located in the same directory as the project file (*.spro). The 3-D tables are used to specify a variable distribution over a boundary/volume.

Format of the 3-D Table :

<?xml version="1.0" encoding="ISO-8859-1"?>

# comment - values (x is assumed to have uniform distribution with xmin and xmax as bounds and n values in between)

x1 y1 z1 v1

x2 y2 z2 v2

…

Xn yn zn vn

</table>

In the table syntax,

The table mapped size denotes the number of mapped points.
The allowed_error of ”1” maps the specified values within a tolerance of 1 m on the boundary. The distance to the closest point (can be find in the table) has to be less than this allowed error. If the distance is larger than this allowed error, then it is assumed that the point is outside.
outside_value can be “minimum” or “maximum, these dictates how to determine a value when the input is out of the range "minimum" or “maximum” denotes that the lowest\highest value in the table are considered.

# Extracting data from tables,

T_fluid = table("solid_temperature.txt", coord);

Mapping variables using tables

User can specify a variable distribution over a boundary/volume using a table. This is done using the X,Y,Z coordinates specifying the distribution of the variable in form of a table at that respective Geometric Entity, such as a Boundary or a Volume. This is primarily used for:

Specifying input on an entity from test data or external software in the form of 3D coordinates.
Mapping of boundary conditions for fluid-solid coupled simulations (eg. Heat flux/Temperature distribution on a boundary).
Specifying initial conditions for Volumes/Boundaries to start a simulation.
Specifying properties (eg. Density, Conductivity) as conditions on an entity, such as Volume.
Mapping velocity vector