norm

Overview

The norm function object normalises an input field with a chosen norm, and writes a new normalised field.

Usage

Example of function object specification:

norm1
{
    // Mandatory entries
    type            norm;
    libs            (fieldFunctionObjects);
    field           <word>;
    norm            <word>;

    // Conditional entries

        // When norm = Lp
        p               <scalar>;

        // When norm = composite
        divisor         <Function1<scalar>>;

        // When norm = divisorField
        divisorField    <word>;

    // Inherited entries
    ...
}

where the entries mean:

Property	Description	Type	Required	Default
type	Type name: norm	word	yes	-
libs	Library name: fieldFunctionObjects	word	yes	-
field	Name of the operand field	word	yes	-
norm	Name of normalisation operation	word	yes	-
p	Norm exponent for the p-norm	scalar	conditional	-
divisor	Norm divisor for the composite norm	Function1<scalar>	conditional	-
divisorField	Divisor scalar field for the field norm	word	conditional	-

Options for the norm entry:

Property	Description	Expression
L1	L1/Taxicab norm	$\vec{y} = \frac{\vec{x}}{\Sigma_{i=1}^n \vert x_i \vert}$
L2	L2/Euclidean norm	$\vec{y} = \frac{\vec{x}}{\sqrt{x_1^2 + ... + x_n^2}}$
Lp	p norm	$\vec{y} = \frac{\vec{x}}{(\Sigma_{i=1}^n \vert x_i \vert^p)^{1/p}}$
max	Maximum norm	$\vec{y} = \frac{\vec{x}}{\max\vert x_i \vert}$
composite	Composite norm with Function1 divisor	$\vec{y} = \frac{\vec{x}}{f(t)}$
divisorField	Normalise by field	$\vec{y} = \frac{\vec{x}}{\vec{z}}$

The inherited entries are elaborated in:

• functionObject
• fieldExpression
• Function1

Divisor quantity is perturbed by SMALL value to prevent any divisions by zero irrespective of whether the quantity is close to zero or not.

Operands

Operand	Type	Location
Input	{vol,surface,polySurface}<Type>Field	<case>/<time>/
Output file	-	-
Output field	{vol,surface,polySurface}<Type>Field	<case>/<time>/

where <Type>={Scalar,Vector,SphericalTensor,SymmTensor,Tensor}.

Further information

Tutorial:

• cavity

Source code:

• norm

API:

• Foam::functionObjects::norm

History: Introduced in version v2206