Commit 84c235f3 by Lukas Riedel

### Update user docs for initial conditions

parent 63255b37
 ... ... @@ -25,35 +25,39 @@ They are controlled by the initial.type key and available for every model. * type = analytic This type of initial condition defines an analytic function :math:f(x,y,z) by the keyword initial.equation. .. math:: f(x,y,z) Possible variables * x * y * z (Only in 3D) * pi * dim Possible operations * The mos common ones. Check out the complete list in muParser_. .. _muParser: http://beltoforion.de/article.php?a=muparser&p=features Richards For instance, for Richards simulations it is useful to set a gravity flow regime with the equation -y (or -z) for 2 (or 3) dimensions. Transport Another example is to set a pulse in the middle of the domain for the solute concentration in the transport model, in such case, the a possible equation may be exp(-sqrt((x-0.5)^2+(y-0.5)^2)/(4.*0.002))/(4*pi*0.002)^(2/dim). An analytic function :math:f(\vec{p}) which depends on the physical position :math:\vec{p}. The function must be defined via the key initial.equation. For parsing the input expression, we use muparser_ which supports a set of common mathematical functions. Additionally, the following variables can be used: Available variables: * x: X-coordinate :math:p_1 \, [\mathrm{m}]. * y: Y-coordinate :math:p_2 \, [\mathrm{m}]. * z: Z-coordinate :math:p_3 \, [\mathrm{m}] (only in 3D). * h: Height above origin. Synonymous to y in 2D and z in 3D. * pi: Mathematical constant :math:\pi. * dim: Number of physical dimensions. .. tip:: Assuming the target quantity is the matric head (see :ref:initial-transformation), typical initial conditions for a Richards simulation are * Hydrostatic equilibrium: A vertical gradient of :math:-1 and a fixed value  at height :math:h = 0 \, \mathrm{m}:: initial.equation = -h + * Gravity flow: Constant value. .. tip:: The expression for a gaussian pulse of solute concentration centered at :math:\vec{p} = [0.5, 0.5]^T \, \mathrm{m} is:: initial.equation = exp(-sqrt((x-0.5)^2+(y-0.5)^2)/(4.*0.002))/(4*pi*0.002)^(2/dim). .. _initial-transformation: Transformation Types -------------------- ... ... @@ -68,8 +72,8 @@ Initial condition tranformations for the Richards solver. * quantity = matricHead The input data is directly interpreted as matric head :math:h_m [\mathrm{m}]. The input data is directly interpreted as matric head, :math:f = h_m [\mathrm{m}]. Transport ^^^^^^^^ ... ... @@ -79,5 +83,8 @@ Initial condition tranformations for the Transport solver. * quantity = soluteConcentration The input data is directly interpreted as solute concentration :math:c_w. The input data is directly interpreted as solute concentration, :math:f = c_w. .. _muparser: http://beltoforion.de/article.php?a=muparser&p=features
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!