diff --git a/man/mkdocs/mkdocs.yml b/man/mkdocs/mkdocs.yml index 8b715ad8f20..ccce264ae95 100644 --- a/man/mkdocs/mkdocs.yml +++ b/man/mkdocs/mkdocs.yml @@ -78,6 +78,11 @@ hooks: extra_css: - grassdocs.css +# MathJax configuration +extra_javascript: + - https://polyfill.io/v3/polyfill.min.js?features=es6 + - https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js + # Plugins plugins: - search @@ -115,6 +120,8 @@ markdown_extensions: format: !!python/name:pymdownx.superfences.fence_code_format - pymdownx.tabbed: alternate_style: true + - pymdownx.arithmatex: + generic: true # Navigation nav: diff --git a/raster/r.gwflow/r.gwflow.md b/raster/r.gwflow/r.gwflow.md index 4df37b0f202..ca796feb1ce 100644 --- a/raster/r.gwflow/r.gwflow.md +++ b/raster/r.gwflow/r.gwflow.md @@ -30,24 +30,28 @@ indicator of the quality of the numerical result. The groundwater flow calculation is based on Darcy's law and a numerical implicit finite volume discretization. The discretization results in a -symmetric and positive definite linear equation system in form of *Ax = -b*, which must be solved. The groundwater flow partial differential +symmetric and positive definite linear equation system in form of $Ax = +b$, which must be solved. The groundwater flow partial differential equation is of the following form: -(dh/dt)\*S = div (K grad h) + q +$$ +\frac{dh}{dt} \cdot S = \text{div}(K \nabla h) + q +$$ In detail for 2 dimensions: -(dh/dt)\*S = Kxx \* (d^2h/dx^2) + Kyy \* (d^2h/dy^2) + q +$$ +\frac{dh}{dt} \cdot S = K_{xx} \frac{\partial^2 h}{\partial x^2} + K_{yy} \frac{\partial^2 h}{\partial y^2} + q +$$ -- h -- the piezometric head im \[m\] -- dt -- the time step for transient calculation in \[s\] -- S -- the specific storage \[1/m\] -- Kxx -- the hydraulic conductivity tensor part in x direction in - \[m/s\] -- Kyy -- the hydraulic conductivity tensor part in y direction in - \[m/s\] -- q - inner source/sink in meter per second \[1/s\] +- $h$ -- the piezometric head in [m] +- $dt$ -- the time step for transient calculation in [s] +- $S$ -- the specific storage [1/m] +- $K_{xx}$ -- the hydraulic conductivity tensor part in x direction in + [m/s] +- $K_{yy}$ -- the hydraulic conductivity tensor part in y direction in + [m/s] +- $q$ -- inner source/sink in meter per second [1/s] Confined and unconfined groundwater flow is supported. Be aware that the storativity input parameter is handled differently in case of unconfined @@ -75,7 +79,7 @@ Additionally the linear equation system will be allocated, so the memory consumption of this module rapidely grow with the size of the input maps. -The resulting linear equation system *Ax = b* can be solved with several +The resulting linear equation system $Ax = b$ can be solved with several solvers. An iterative solvers with sparse and quadratic matrices support is implemented. The conjugate gradients method with (pcg) and without (cg) precondition. Additionally a direct Cholesky solver is available.