From 66ceac15ae9fa10a4b9caa7666b437495aa8917d Mon Sep 17 00:00:00 2001
From: Albert de Montserrat <albert.de.montserrat@gmail.com>
Date: Thu, 8 Aug 2024 18:42:00 +0200
Subject: [PATCH] add equations symbols description

---
 docs/src/man/equations.md | 35 +++++++++++++++++++++++++++++++++--
 1 file changed, 33 insertions(+), 2 deletions(-)

diff --git a/docs/src/man/equations.md b/docs/src/man/equations.md
index b34a99ac..30b38df2 100644
--- a/docs/src/man/equations.md
+++ b/docs/src/man/equations.md
@@ -4,11 +4,11 @@ The pseudo-transient method consists in augmenting the right-hand-side of the ta
 ## Heat diffusion
 The pseudo-transient heat-diffusion equation is:
 
-$\widetilde{\rho}\frac{\partial T}{\partial \psi} + \rho C_p \frac{\partial T}{\partial t} = \nabla \cdot (K\nabla T) = -\nabla q$
+$\widetilde{\rho}\frac{\partial T}{\partial \psi} + \rho C_p \frac{\partial T}{\partial t} = \nabla \cdot (\kappa\nabla T) = -\nabla q$
 
 We use a second order pseudo-transient scheme were continuation is also done on the flux, so that:
 
-$\widetilde{\theta}\frac{\partial q}{\partial \psi} + q  = -K\nabla T$
+$\widetilde{\theta}\frac{\partial q}{\partial \psi} + q  = -\kappa\nabla T$
 
 ## Stokes equations
 
@@ -33,3 +33,34 @@ and
 $\widetilde{V} = \sqrt{ \frac{\widetilde{K} +2\widetilde{G}}{\widetilde{\rho}}}, \qquad r = \frac{\widetilde{K}}{\widetilde{G}}, \qquad Re = \frac{\widetilde{\rho}\widetilde{V}L}{\eta}$
 
 where the P-wave $\widetilde{V}=V_p$ is the characteristic velocity scale for Stokes, and $Re$ is the Reynolds number.
+
+### Physical parameters
+
+| Symbol                           | Parameter              |
+| :------------------------------- | :--------------------: |
+| $T$                              | Temperature            |
+| $q$                              | Flux                   |
+| $\boldsymbol{\tau}$              | Deviatoric stress      |
+| $\dot{\boldsymbol{\varepsilon}}$ | Deviatoric strain rate |
+| $\boldsymbol{u}$                 | Velocity               |
+| $\boldsymbol{f}$                 | External forces        |
+| $P$                              | Pressure               |
+| $\eta$                           | Viscosity              |
+| $\rho$                           | Density                |
+| $\beta$                          | Compressibility        |
+| $G$                              | Shear modulus          |
+| $\alpha$                         | Thermal expansivity    |
+| $C_p$                            | Heat capacity          |
+| $\kappa$                         | Heat conductivity      |
+
+### Pseudo-transient parameters
+
+| Symbol               | Parameter                     |
+| :------------------- | :---------------------------: |
+| $psi$                | Pseudo time step              |
+| $\widetilde{K}$      | Pseudo bulk modulus           |
+| $\widetilde{G}$      | Pseudo shear modulus          |
+| $\widetilde{V}$      | Characteristic velocity scale |
+| $\widetilde{\rho}$   | Pseudo density                |
+| $\widetilde{\theta}$ | Relaxation time               |
+| $Re$                 | Reynolds number               |