Variable initialisation¶
Variables in BOUT++ are not initialised automatically, but must be
explicitly given a value. For example the following code declares a
Field3D
variable then attempts to access a particular element:
Field3D f; // Declare a variable
f(0,0,0) = 1.0; // Error!
This results in an error because the data array to store values in f
has not been allocated. Allocating data can be done in several ways:
Initialise with a value:
Field3D f = 0.0; // Allocates memory, fills with zeros f(0,0,0) = 1.0; // ok
This cannot be done at a global scope, since it requires the mesh to already exist and have a defined size.
Set to a scalar value:
Field3D f; f = 0.0; // Allocates memory, fills with zeros f(0,0,0) = 1.0; // ok
Note that setting a field equal to another field has the effect of making both fields share the same underlying data. This behaviour is similar to how NumPy arrays behave in Python.
Field3D g = 0.0; // Allocates memory, fills with zeros Field3D f = g; // f now shares memory with g f(0,0,0) = 1.0; // g also modified
To ensure that a field has a unique underlying memory array call the
Field3D::allocate
method before writing to individual indices.Use
Field3D::allocate
to allocate memory:Field3D f; f.allocate(); // Allocates memory, values undefined f(0,0,0) = 1.0; // ok
In a BOUT++ simulation some variables are typically evolved in time. The initialisation of these variables is handled by the time integration solver.
Initialisation of time evolved variables¶
Each variable being evolved has its own section, with the same name as
the output data. For example, the high-\(\beta\) model has
variables “P”, “jpar”, and “U”, and so has sections [P]
, [jpar]
,
[U]
(not case sensitive).
Expressions¶
The recommended way to initialise a variable is to use the function
option for each variable:
[p]
function = 1 + gauss(x-0.5)*gauss(y)*sin(z)
This evaluates an analytic expression to initialise the \(P\)
variable. Expressions can include the usual operators
(+
,-
,*
,/
), including ^
for exponents. The
following values are also already defined:
Name |
Description |
---|---|
x |
\(x\) position between \(0\) and \(1\) |
y |
\(y\) position between \(0\) and \(2\pi\) (excluding the last point) |
z |
\(z\) position between \(0\) and \(2\pi\) (excluding the last point) |
pi π |
\(3.1415\ldots\) |
Table: Initialisation expression values
By default, \(x\) is defined as i / (nx - 2*MXG)
, where MXG
is the width of the boundary region, by default 2. Hence \(x\)
actually goes from 0 on the leftmost point to (nx-1)/(nx-4)
on the
rightmost point. This is not a particularly good definition, but for
most cases its sufficient to create some initial profiles. For some
problems like island reconnection simulations, it’s useful to define
\(x\) in a particular way which is more symmetric than the default.
To do this, set in BOUT.inp
[mesh]
symmetricGlobalX = true
This will change the definition of \(x\) to i / (nx - 1)
, so
\(x\) is then between \(0\) and \(1\) everywhere.
By default the expressions are evaluated in a field-aligned coordinate system,
i.e. if you are using the [mesh]
option paralleltransform = shifted
,
the input f
will have f = fromFieldAligned(f)
applied before being
returned. To switch off this behaviour and evaluate the input expressions in
coordinates with orthogonal x-z (i.e. toroidal \(\{\psi,\theta,\phi\}\)
coordinates when using paralleltransform = shifted
), set in BOUT.inp
[input]
transform_from_field_aligned = false
The functions in Table 1 are also available in expressions.
Name |
Description |
---|---|
|
Absolute value \(|x|\) |
|
Inverse trigonometric functions |
|
|
|
Ballooning transform, using \(n\) terms (default 3) |
|
Cosine |
|
Hyperbolic cosine |
|
Exponential |
|
Hyperbolic tangent |
|
Gaussian \(\exp(-x^2/2) / \sqrt{2\pi}\) |
|
Gaussian \(\exp[-x^2/(2w^2)] / (w\sqrt{2\pi})\) |
|
Heaviside function: \(1\) if \(x > 0\) otherwise \(0\) |
|
Natural logarithm |
|
Maximum (variable arguments) |
|
Minimum (variable arguments) |
|
A mixture of Fourier modes |
|
seed determines random phase (default 0.5) |
|
Exponent \(x^y\) |
|
Sine |
|
Hyperbolic sine |
|
\(\sqrt{x}\) |
|
Tangent |
|
The error function |
|
The hat function \(\frac{1}{2}(\tanh[s (x-[c-\frac{w}{2}])]\) \(- \tanh[s (x-[c+\frac{w}{2}])] )\) |
|
The modulo operator, returns floating point remainder |
For field-aligned tokamak simulations, the Y direction is along the
field and in the core this will have a discontinuity at the twist-shift
location where field-lines are matched onto each other. To handle this,
the ballooning
function applies a truncated Ballooning
transformation to construct a smooth initial perturbation:

Fig. 3 Initial profiles in twist-shifted grid. Left: Without ballooning transform, showing discontinuity at the matching location Right: with ballooning transform¶
There is an example code test-ballooning
which compares methods of
setting initial conditions with the ballooning transform.
The mixmode(x)
function is a mixture of Fourier modes of the form:
where \(\phi\) is a random phase between \(-\pi\) and \(+\pi\), which depends on the seed. The factor in front of each term is chosen so that the 4th harmonic (\(i=4\)) has the highest amplitude. This is useful mainly for initialising turbulence simulations, where a mixture of mode numbers is desired.
Initalising variables with the FieldFactory
class¶
This class provides a way to generate a field with a specified form. For
example to create a variable var
from options we could write
FieldFactory f(mesh);
Field2D var = f.create2D("var");
This will look for an option called “var”, and use that expression to
initialise the variable var
. This could then be set in the BOUT.inp
file or on the command line.
var = gauss(x-0.5,0.2)*gauss(y)*sin(3*z)
To do this, FieldFactory
implements a recursive descent
parser to turn a string containing something like
"gauss(x-0.5,0.2)*gauss(y)*sin(3*z)"
into values in a
Field3D
or Field2D
object. Examples are
given in the test-fieldfactory
example:
FieldFactory f(mesh);
Field2D b = f.create2D("1 - x");
Field3D d = f.create3D("gauss(x-0.5,0.2)*gauss(y)*sin(z)");
This is done by creating a tree of FieldGenerator
objects
which then generate the field values:
class FieldGenerator {
public:
virtual ~FieldGenerator() { }
virtual FieldGenerator* clone(const list<FieldGenerator*> args) {return NULL;}
virtual BoutReal generate(int x, int y, int z) = 0;
};
All classes inheriting from FieldGenerator
must implement
a FieldGenerator::generate
function, which returns the
value at the given (x,y,z)
position. Classes should also implement
a FieldGenerator::clone
function, which takes a list of
arguments and creates a new instance of its class. This takes as input
a list of other FieldGenerator
objects, allowing a
variable number of arguments.
The simplest generator is a fixed numerical value, which is
represented by a FieldValue
object:
class FieldValue : public FieldGenerator {
public:
FieldValue(BoutReal val) : value(val) {}
BoutReal generate(int x, int y, int z) { return value; }
private:
BoutReal value;
};
Adding a new function¶
To add a new function to the FieldFactory, a new
FieldGenerator
class must be defined. Here we will use
the example of the sinh
function, implemented using a class
FieldSinh
. This takes a single argument as input, but
FieldPI
takes no arguments, and
FieldGaussian
takes either one or two. Study these after
reading this to see how these are handled.
First, edit src/field/fieldgenerators.hxx
and add a class
definition:
class FieldSinh : public FieldGenerator {
public:
FieldSinh(FieldGenerator* g) : gen(g) {}
~FieldSinh() {if(gen) delete gen;}
FieldGenerator* clone(const list<FieldGenerator*> args);
BoutReal generate(int x, int y, int z);
private:
FieldGenerator *gen;
};
The gen
member is used to store the input argument, and to make
sure it’s deleted properly we add some code to the destructor. The
constructor takes a single input, the FieldGenerator
argument to the sinh
function, which is stored in the member
gen
.
Next edit src/field/fieldgenerators.cxx
and add the implementation
of the clone
and generate
functions:
FieldGenerator* FieldSinh::clone(const list<FieldGenerator*> args) {
if(args.size() != 1) {
throw ParseException("Incorrect number of arguments to sinh function. Expecting 1, got %d", args.size());
}
return new FieldSinh(args.front());
}
BoutReal FieldSinh::generate(double x, double y, double z, double t) {
return sinh(gen->generate(x,y,z,t));
}
The clone
function first checks the number of arguments using
args.size()
. This is used in FieldGaussian
to handle
different numbers of input, but in this case we throw a
ParseException
if the number of inputs isn’t
one. clone
then creates a new FieldSinh
object,
passing the first argument ( args.front()
) to the constructor
(which then gets stored in the gen
member variable).
The generate
function for sinh
just gets the value of the input
by calling gen->generate(x,y,z)
, calculates sinh
of it and
returns the result.
The clone
function means that the parsing code can make copies of
any FieldGenerator
class if it’s given a single instance
to start with. The final step is therefore to give the
FieldFactory
class an instance of this new
generator. Edit the FieldFactory
constructor
FieldFactory::FieldFactory
in
src/field/field_factory.cxx
and add the line:
addGenerator("sinh", new FieldSinh(NULL));
That’s it! This line associates the string "sinh"
with a
FieldGenerator
. Even though FieldFactory
doesn’t know what type of FieldGenerator
it is, it can
make more copies by calling the clone
member function. This is a
useful technique for polymorphic objects in C++ called the “Virtual
Constructor” idiom.
Parser internals¶
When a FieldGenerator
is added using the addGenerator
function, it is entered into a std::map
which maps strings to
FieldGenerator
objects (include/field_factory.hxx
):
map<string, FieldGenerator*> gen;
Parsing a string into a tree of FieldGenerator
objects is
done by first splitting the string up into separate tokens like
operators like ’*’, brackets ’(’, names like ’sinh’ and so on, then
recognising patterns in the stream of tokens. Recognising tokens is
done in src/field/field_factory.cxx
:
char FieldFactory::nextToken() {
...
This returns the next token, and setting the variable char curtok
to
the same value. This can be one of:
-1 if the next token is a number. The variable
BoutReal curval
is set to the value of the token-2 for a string (e.g. “sinh”, “x” or “pi”). This includes anything which starts with a letter, and contains only letters, numbers, and underscores. The string is stored in the variable
string curident
.0 to mean end of input
The character if none of the above. Since letters and numbers are taken care of (see above), this includes brackets and operators like ’+’ and ’-’.
The parsing stage turns these tokens into a tree of
FieldGenerator
objects, starting with the parse()
function:
FieldGenerator* FieldFactory::parse(const string &input) {
...
which puts the input string into a stream so that nextToken()
can
use it, then calls the parseExpression()
function to do the actual
parsing:
FieldGenerator* FieldFactory::parseExpression() {
...
This breaks down expressions in stages, starting with writing every expression as:
expression := primary [ op primary ]
i.e. a primary expression, and optionally an operator and another
primary expression. Primary expressions are handled by the
parsePrimary()
function, so first parsePrimary()
is called, and
then parseBinOpRHS
which checks if there is an operator, and if so
calls parsePrimary()
to parse it. This code also takes care of
operator precedence by keeping track of the precedence of the current
operator. Primary expressions are then further broken down and can
consist of either a number, a name (identifier), a minus sign and a
primary expression, or brackets around an expression:
primary := number
:= identifier
:= '-' primary
:= '(' expression ')'
:= '[' expression ']'
The minus sign case is needed to handle the unary minus e.g. "-x"
.
Identifiers are handled in parseIdentifierExpr()
which handles
either variable names, or functions
identifier := name
:= name '(' expression [ ',' expression [ ',' ... ] ] ')'
i.e. a name, optionally followed by brackets containing one or more
expressions separated by commas. names without brackets are treated the
same as those with empty brackets, so "x"
is the same as "x()"
.
A list of inputs (list<FieldGenerator*> args;
) is created, the
gen
map is searched to find the FieldGenerator
object
corresponding to the name, and the list of inputs is passed to the
object’s clone
function.