Source Term#

If the problem being simulated has a source, it can be added in this section. The default parameters are:

subsection source term
  subsection fluid dynamics
    set Function expression = 0; 0; 0 #In 2D
    set Function expression = 0; 0; 0; 0 #In 3D
    set enable              = true
  end

  subsection heat transfer
    set Function expression = 0
  end

  subsection tracer
    set Function expression = 0
  end

  subsection cahn hilliard
    set Function expression = 0; 0
  end
end

Tip

Function expression, used in this subsection (but also in Initial Conditions, Analytical Solution, namely), give access to several tools:

  • define Function constants

  • use \(\pi\) variable, as pi or Pi

  • use common functions such as \(\sin\), \(\cos\)

  • use if statements

Check the Examples of Function Expression for further help.

  • subsection fluid dynamics: defines the parameters for a Navier-Stokes source term. This source term is defined by a Function expression and can depend on both space and time.

    • In 2D, the first two terms are the source terms for the \(x\), \(y\) component of the momentum equation. The third term is the mass source term.

    • In 3D, the first three terms are for the \(x\), \(y\) and \(z\) component of the momentum equation and the fourth term is for the mass source term.

    Tip

    For subsection fluid dynamics, each term can depend on both space (x, y and, if 3D, z) and time (t). See Examples of Function Expression.

    Tip

    If you are using the lethe-fluid-matrix-free application the usage of a source term significantly affects performance. If you are not using it, we advice you to disable it explicitly by setting enable = false.

  • subsection heat transfer: defines the parameters for a heat source term. This source term is defined by a Function expression and can depend on both space (x, y and, if 3D, z) and time (t). See Examples of Function Expression.

  • subsection tracer: defines the parameters for the a source term for a tracer. This source term is defined by a Function expression and can depend on both space (x, y and, if 3D, z) and time (t). See Examples of Function Expression.

  • subsection cahn hilliard: defines the parameters for a source term in the Cahn-Hilliard equations. This source term is defined by a Function expression and can depend on both space (x, y and, if 3D, z) and time (t). Both the phase order parameter (first component) and chemical potential (second component) can have source terms, hence the two components. See Examples of Function Expression.

Examples of Function Expression#

CFD source term with Function constants:

subsection fluid dynamics
  set Function constants = A=2.0
  set Function expression = A*y; -A*x; 0
end

CFD source term varying in time:

subsection fluid dynamics
    set Function expression = 0; -10*cos(2*pi*t); 0
end

Heat transfer source term with if() condition:

subsection heat transfer
  set Function expression = if(sin(x) > pi, 1, 0)
    # if ( condition , value if true , value if false )
end

Note

The first parameter in the if() function is the statement. If this statement is :

  • true, then the function expression takes the second parameter as value

  • false, the function expression takes the third parameter as value.

In this example, the heat source term will vary within the calculation domain.

CFD source term with Function constants:

subsection fluid dynamics
  set Function constants = A=2.0, B=1.0
  set Function expression = A*y; -B*x; 0
end