Commit c25cd5dd by Lukas Riedel

### Homogenize user docs on initial conditions

* Use \mathbf to indicate vectors instead of \vec.
* Use \text instead of \mathrm for improved text rendering.
* Add formula for vertical gradient.
 ... ... @@ -31,16 +31,16 @@ They are controlled by the initial.type key and available for every model. * type = analytic An analytic function :math:f(\vec{p}) which depends on the physical position :math:\vec{p}. The function must be defined via the key An analytic function :math:f(\mathbf{p}) which depends on the physical position :math:\mathbf{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). * x: X-coordinate :math:p_1 \, [\text{m}]. * y: Y-coordinate :math:p_2 \, [\text{m}]. * z: Z-coordinate :math:p_3 \, [\text{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. ... ... @@ -50,8 +50,9 @@ They are controlled by the initial.type key and available for every model. :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}:: * Hydrostatic equilibrium: A vertical gradient of :math:\partial_h h_m = -1 and a fixed value  at height :math:h = 0 \, \text{m}: initial.equation = -h + ... ... @@ -59,7 +60,7 @@ They are controlled by the initial.type key and available for every model. .. tip:: The expression for a gaussian pulse of solute concentration centered at :math:\vec{p} = [0.5, 0.5]^T \, \mathrm{m} is:: :math:\mathbf{p} = [0.5, 0.5]^T \, \text{m} is:: initial.equation = exp(-sqrt((x-0.5)^2+(y-0.5)^2)/(4.*0.002))/(4*pi*0.002)^(2/dim). ... ... @@ -95,7 +96,7 @@ Initial condition tranformations for the Richards solver. * quantity = matricHead The input data is directly interpreted as matric head :math:f = h_m \, [\mathrm{m}]. :math:f = h_m \, [\text{m}]. .. object:: Water Content to Matric Head ... ... @@ -121,7 +122,7 @@ Initial condition tranformations for the Transport solver. * quantity = soluteConcentration The input data is directly interpreted as solute concentration, :math:f = c_w [\mathrm{kg}/\mathrm{m}^3]. :math:f = c_w [\text{kg}/\text{m}^3]. .. _H5: https://www.h5py.org/ .. _muparser: http://beltoforion.de/article.php?a=muparser&p=features