Guide: Writing Equations in LaTeX on the CFD Online Forums

pete · March 15, 2009, 15:58

This is a brief introduction about how to write equations in the CFD Online discussion forums. The equation functionality is based on LaTeX, a versatile mathematical typesetting system which is often used to write scientific papers and books. With LaTeX mathematical equations are written using normal text and this makes it very suitable for a text-based forum like this. The forum will automatically generate images of the LaTeX codes it finds and display them properly. LaTeX often gives very nice looking formulas. LaTeX can be a bit difficult to get started with, but those who know it tend to like it very much. Here is a simple example to illustrate how it works:

If you in your message write: [math]a = \sqrt{\gamma R T}[/math]
The forum will display: $a = \sqrt{\gamma R T}$

A usefull feature in the forum is that the LaTeX code used to write an equation can be seen when you hoover with the pointer over it. If you click on an equation a window will be opened displaying the LaTeX code used to write it. This makes it easy to learn from other people and to copy-and-paste equations from other posts.

You can see how all equations on this page have been written either by hoovering over them with the pointer or by clicking on them!

LaTeX can be used in two ways:

Normal equations written separately away from normal text: [math]LaTeX code[/math]
Inlined equations or symbols to be used inside a text: [imath]LaTeX code[/imath]

The difference is that inlined equations are scaled to fit better in normal text whereas normal equations are scaled to look good when written separately.

There is a special LaTeX reference tool avalable in the advanced editor which helps you to find the codes needed to write symbols, relations, operators etc. in LaTeX. To open the LaTeX reference click on the $\sum$ symbol to the right just above the editor window.

Below follows a summary of the most commonly used symbols, relations, operators and functions as well as a few other frequently asked questions. To see how these symbols or equations were created just click on the one you are interested in and a window will be opened showing the code used to create it:

Symbols

Lowercase Greek letters: $\alpha$ $\beta$ $\gamma$ $\delta$ $\epsilon$ $\varepsilon$ $\zeta$ $\eta$ $\theta$ $\vartheta$ $\iota$ $\kappa$ $\lambda$ $\mu$ $\nu$ $\xi$ $\pi$ $\varpi$ $\rho$ $\varrho$ $\sigma$ $\varsigma$ $\tau$ $\upsilon$ $\phi$ $\varphi$ $\chi$ $\psi$ $\omega$

Capital Greek letters: $\Gamma$ $\Delta$ $\Theta$ $\Lambda$ $\Xi$ $\Pi$ $\Sigma$ $\Upsilon$ $\Phi$ $\Psi$ $\Omega$

Operators and relations: $\pm$ $\mp$ $\times$ $\div$ $\ast$ $\star$ $\bullet$ $\circ$ $\cdot$ $\leq$ $\ll$ $\subset$ $\geq$ $\gg$ $\equiv$ $\sim$ $\simeq$ $\approx$ $\neq$ $\propto$

Misc: $\leftarrow$ $\Leftarrow$ $\rightarrow$ $\Rightarrow$ $\leftrightarrow$ $\Leftrightarrow$ $\forall$ $\exists$ $\partial$ $\infty$

Bracketing - () {} []

You can simply write the brackets you want. To get the correct size of the brackets you sometimes have to use the \left and \right keywords in front of the bracket.
For example, just writing parentheses gives $(\frac{1}{2})^{n}$ , but with \left and \right keywords you would get $\left(\frac{1}{2}\right)^{n}$ .

Exponents and Subscripts

- [math]a_i^n[/math]

$x_{i+1}^{2^{n+1}}$ - [math]x_{i+1}^{2^{n+1}}[/math]

Functions - Fractions, Radicals, Integrals, Sums, Limits, ...

$\frac{1}{2}$ - [math]\frac{1}{2}[/math]

$\sqrt{x+y}$ - [math]\sqrt{x+y}[/math]

$\sqrt[n]{x}$ - [math]\sqrt[n]{x}[/math]

$\int^\infty_0 f(x) \, dx$ - [math]\int^\infty_0 f(x) \, dx[/math]

$\oint_\Gamma f(x) \, ds$ - [math]\oint_\Gamma f(x) \, ds[/math]

$\sum_{i=1}^{\infty}\frac{1}{i}$ - [math]\sum_{i=1}^{\infty}\frac{1}{i}[/math]

$\lim_{x\to\infty}\frac{1}{x}$ - [math]\lim_{x\to\infty}\frac{1}{x}[/math]

Trigonometric and Logarithmic Functions

Please use these instead of simply typing in "sin". That ensures that the function is typeset properly with the right font and spacing.

$\cos^2 x + \sin^2 x = 1$ - [math]\cos^2 x + \sin^2 x = 1[/math]

$\tanh(c)$ - [math]\tanh(c)[/math]

$\log n^2$ - [math]\log n^2[/math]

$\ln(e)$ - [math]\ln(e)[/math]

Spacing

Sometime you may want to add extra horizontal space between characters. The following codes can be used to add extra space:

a whitespace or no space at all gives a normal space ( $\alpha \beta$ )
\quad - a large space to separate equations or write conditions (i = 1, 2, 3) on the same line ( $\alpha \quad \beta$ )
\; - a thick space ( $\alpha \; \beta$ )
\: - a medium space ( $\alpha \: \beta$ )
\, - a thin space ( $\alpha \, \beta$ )
\! - a negative thin space ( $\alpha \! \beta$ )

Fluid Dynamics and CFD Related Examples

Navier-Stokes Equations using Tensor Notation:

$\frac{\partial \rho}{\partial t} + \frac{\partial}{\partial x_j}\left[ \rho u_j \right] = 0$

$\frac{\partial}{\partial t}\left( \rho u_i \right) + \frac{\partial}{\partial x_j} \left[ \rho u_i u_j + p \delta_{ij} - \tau_{ji} \right] = 0, \quad i=1,2,3$

$\frac{\partial}{\partial t}\left( \rho e_0 \right) + \frac{\partial}{\partial x_j} \left[ \rho u_j e_0 + u_j p + q_j - u_i \tau_{ij} \right] = 0$

$\bf{k - \epsilon}$ Equations:

$\frac{\partial}{\partial t} (\rho k) + \frac{\partial}{\partial x_i} (\rho k u_i) = \frac{\partial}{\partial x_j} \left[ \left(\mu + \frac{\mu_t}{\sigma_k} \right) \frac{\partial k}{\partial x_j}\right] + P_k + P_b - \rho \epsilon - Y_M + S_k$

$\frac{\partial}{\partial t} (\rho \epsilon) + \frac{\partial}{\partial x_i} (\rho \epsilon u_i) = \frac{\partial}{\partial x_j} \left[\left(\mu + \frac{\mu_t}{\sigma_{\epsilon}} \right) \frac{\partial \epsilon}{\partial x_j} \right] + C_{1 \epsilon}\frac{\epsilon}{k} \left( P_k + C_{3 \epsilon} P_b \right) - C_{2 \epsilon} \rho \frac{\epsilon^2}{k} + S_{\epsilon}$

Reynolds Averaging:

$\overline{\Phi} \equiv \frac{1}{T} \int_T \Phi(t) dt$

$\Phi' \equiv \Phi - \overline{\Phi}$

Boussinesq Eddy Viscosity Assumption:

$\tau_{ij} = 2 \, \mu_t \, S_{ij}^* - \frac{2}{3} k \delta_{ij}$ , or written more explicitly:

$-\rho \overline{u'_i u'_j} = \mu_t \, \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i} - \frac{2}{3} \frac{\partial u_k}{\partial x_k} \delta_{ij} \right) - \frac{2}{3} k \delta_{ij}$

Rhie-Chow Interpolation:

$a_p \vec v_P = \sum\limits_{neighbours} {a_l } \vec v_l - \frac{\nabla p}{V}$

$\sum\limits_{faces} \left[ {\frac{1}{a_p}\,H} \right]_{face} = \sum\limits_{faces} \left[ {\frac{1}{a_p }\,\frac{{\nabla p}}{V}} \right]_{face}$

$H = \sum\limits_{neighbours} {a_l } \vec v_l$

Realisability and Schwarz' Inequality:

$\left\langle{u'_\alpha u'_\alpha}\right\rangle \geq 0$

$\frac{\left\langle{u'_\alpha u'_\beta}\right\rangle}{ \left\langle{u'_\alpha u'_\beta}\right\rangle \left\langle{u'_\alpha u'_\beta}\right\rangle} \leq 1$

lordmohit · October 30, 2009, 02:51

testing

lordmohit · October 30, 2009, 03:03

$\lim_{x\to\infty}\frac{1}{x}$

$lim_{xtoinfty}frac{1}{x-1}$

lordmohit · October 30, 2009, 03:04

$\int^\infty_0 f(x) \, dx$

lordmohit · October 30, 2009, 03:06

$\int^\frac{\Pi}{2}_5 f(x) \, dx$

ComputerGuy · December 31, 2010, 01:03

Enjoy: http://www.codecogs.com/latex/eqneditor.php

ComputerGuy

Sha Liu · November 6, 2011, 22:56

cool. i often use mathematica to write equations. then they can be transform to latex form.

stefanbj · April 14, 2013, 16:11

test test

$\frac{1}{2}$

abbott.hn · May 2, 2013, 22:15

let me have a try:
$-\frac{1}{2}\rho\overline{u'_i u'_j}+\overline{p' u'_j}=\frac{\mu_t}{\sigma_k}\frac{\partial k}{\partial x_j}$

and this " $-\frac{1}{2}\rho\overline{u'_i u'_j}+\overline{p' u'_j}=\frac{\mu_t}{\sigma_k}\frac{\partial k}{\partial x_j}$ "inline equation

March 15, 2009, 15:58	Guide: Writing Equations in LaTeX on the CFD Online Forums	#1
pete Administrator Peter Jones Join Date: Jan 2009 Posts: 399 Rep Power: 10	This is a brief introduction about how to write equations in the CFD Online discussion forums. The equation functionality is based on LaTeX, a versatile mathematical typesetting system which is often used to write scientific papers and books. With LaTeX mathematical equations are written using normal text and this makes it very suitable for a text-based forum like this. The forum will automatically generate images of the LaTeX codes it finds and display them properly. LaTeX often gives very nice looking formulas. LaTeX can be a bit difficult to get started with, but those who know it tend to like it very much. Here is a simple example to illustrate how it works: If you in your message write: [math]a = \sqrt{\gamma R T}[/math] The forum will display: $a = \sqrt{\gamma R T}$ A usefull feature in the forum is that the LaTeX code used to write an equation can be seen when you hoover with the pointer over it. If you click on an equation a window will be opened displaying the LaTeX code used to write it. This makes it easy to learn from other people and to copy-and-paste equations from other posts. You can see how all equations on this page have been written either by hoovering over them with the pointer or by clicking on them! LaTeX can be used in two ways: Normal equations written separately away from normal text: [math]LaTeX code[/math] Inlined equations or symbols to be used inside a text: [imath]LaTeX code[/imath] The difference is that inlined equations are scaled to fit better in normal text whereas normal equations are scaled to look good when written separately. There is a special LaTeX reference tool avalable in the advanced editor which helps you to find the codes needed to write symbols, relations, operators etc. in LaTeX. To open the LaTeX reference click on the $\sum$ symbol to the right just above the editor window. Below follows a summary of the most commonly used symbols, relations, operators and functions as well as a few other frequently asked questions. To see how these symbols or equations were created just click on the one you are interested in and a window will be opened showing the code used to create it: Symbols Lowercase Greek letters: $\alpha$ $\beta$ $\gamma$ $\delta$ $\epsilon$ $\varepsilon$ $\zeta$ $\eta$ $\theta$ $\vartheta$ $\iota$ $\kappa$ $\lambda$ $\mu$ $\nu$ $\xi$ $\pi$ $\varpi$ $\rho$ $\varrho$ $\sigma$ $\varsigma$ $\tau$ $\upsilon$ $\phi$ $\varphi$ $\chi$ $\psi$ $\omega$ Capital Greek letters: $\Gamma$ $\Delta$ $\Theta$ $\Lambda$ $\Xi$ $\Pi$ $\Sigma$ $\Upsilon$ $\Phi$ $\Psi$ $\Omega$ Operators and relations: $\pm$ $\mp$ $\times$ $\div$ $\ast$ $\star$ $\bullet$ $\circ$ $\cdot$ $\leq$ $\ll$ $\subset$ $\geq$ $\gg$ $\equiv$ $\sim$ $\simeq$ $\approx$ $\neq$ $\propto$ Misc: $\leftarrow$ $\Leftarrow$ $\rightarrow$ $\Rightarrow$ $\leftrightarrow$ $\Leftrightarrow$ $\forall$ $\exists$ $\partial$ $\infty$ Bracketing - () {} [] You can simply write the brackets you want. To get the correct size of the brackets you sometimes have to use the \left and \right keywords in front of the bracket. For example, just writing parentheses gives $(\frac{1}{2})^{n}$ , but with \left and \right keywords you would get $\left(\frac{1}{2}\right)^{n}$ . Exponents and Subscripts - [math]a_i^n[/math] $x_{i+1}^{2^{n+1}}$ - [math]x_{i+1}^{2^{n+1}}[/math] Functions - Fractions, Radicals, Integrals, Sums, Limits, ... $\frac{1}{2}$ - [math]\frac{1}{2}[/math] $\sqrt{x+y}$ - [math]\sqrt{x+y}[/math] $\sqrt[n]{x}$ - [math]\sqrt[n]{x}[/math] $\int^\infty_0 f(x) \, dx$ - [math]\int^\infty_0 f(x) \, dx[/math] $\oint_\Gamma f(x) \, ds$ - [math]\oint_\Gamma f(x) \, ds[/math] $\sum_{i=1}^{\infty}\frac{1}{i}$ - [math]\sum_{i=1}^{\infty}\frac{1}{i}[/math] $\lim_{x\to\infty}\frac{1}{x}$ - [math]\lim_{x\to\infty}\frac{1}{x}[/math] Trigonometric and Logarithmic Functions Please use these instead of simply typing in "sin". That ensures that the function is typeset properly with the right font and spacing. $\cos^2 x + \sin^2 x = 1$ - [math]\cos^2 x + \sin^2 x = 1[/math] $\tanh(c)$ - [math]\tanh(c)[/math] $\log n^2$ - [math]\log n^2[/math] $\ln(e)$ - [math]\ln(e)[/math] Spacing Sometime you may want to add extra horizontal space between characters. The following codes can be used to add extra space: a whitespace or no space at all gives a normal space ( $\alpha \beta$ ) \quad - a large space to separate equations or write conditions (i = 1, 2, 3) on the same line ( $\alpha \quad \beta$ ) \; - a thick space ( $\alpha \; \beta$ ) \: - a medium space ( $\alpha \: \beta$ ) \, - a thin space ( $\alpha \, \beta$ ) \! - a negative thin space ( $\alpha \! \beta$ ) Fluid Dynamics and CFD Related Examples Navier-Stokes Equations using Tensor Notation: $\frac{\partial \rho}{\partial t} + \frac{\partial}{\partial x_j}\left[ \rho u_j \right] = 0$ $\frac{\partial}{\partial t}\left( \rho u_i \right) + \frac{\partial}{\partial x_j} \left[ \rho u_i u_j + p \delta_{ij} - \tau_{ji} \right] = 0, \quad i=1,2,3$ $\frac{\partial}{\partial t}\left( \rho e_0 \right) + \frac{\partial}{\partial x_j} \left[ \rho u_j e_0 + u_j p + q_j - u_i \tau_{ij} \right] = 0$ $\bf{k - \epsilon}$ Equations: $\frac{\partial}{\partial t} (\rho k) + \frac{\partial}{\partial x_i} (\rho k u_i) = \frac{\partial}{\partial x_j} \left[ \left(\mu + \frac{\mu_t}{\sigma_k} \right) \frac{\partial k}{\partial x_j}\right] + P_k + P_b - \rho \epsilon - Y_M + S_k$ $\frac{\partial}{\partial t} (\rho \epsilon) + \frac{\partial}{\partial x_i} (\rho \epsilon u_i) = \frac{\partial}{\partial x_j} \left[\left(\mu + \frac{\mu_t}{\sigma_{\epsilon}} \right) \frac{\partial \epsilon}{\partial x_j} \right] + C_{1 \epsilon}\frac{\epsilon}{k} \left( P_k + C_{3 \epsilon} P_b \right) - C_{2 \epsilon} \rho \frac{\epsilon^2}{k} + S_{\epsilon}$ Reynolds Averaging: $\overline{\Phi} \equiv \frac{1}{T} \int_T \Phi(t) dt$ $\Phi' \equiv \Phi - \overline{\Phi}$ Boussinesq Eddy Viscosity Assumption: $\tau_{ij} = 2 \, \mu_t \, S_{ij}^* - \frac{2}{3} k \delta_{ij}$ , or written more explicitly: $-\rho \overline{u'_i u'_j} = \mu_t \, \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i} - \frac{2}{3} \frac{\partial u_k}{\partial x_k} \delta_{ij} \right) - \frac{2}{3} k \delta_{ij}$ Rhie-Chow Interpolation: $a_p \vec v_P = \sum\limits_{neighbours} {a_l } \vec v_l - \frac{\nabla p}{V}$ $\sum\limits_{faces} \left[ {\frac{1}{a_p}\,H} \right]_{face} = \sum\limits_{faces} \left[ {\frac{1}{a_p }\,\frac{{\nabla p}}{V}} \right]_{face}$ $H = \sum\limits_{neighbours} {a_l } \vec v_l$ Realisability and Schwarz' Inequality: $\left\langle{u'_\alpha u'_\alpha}\right\rangle \geq 0$ $\frac{\left\langle{u'_\alpha u'_\beta}\right\rangle}{ \left\langle{u'_\alpha u'_\beta}\right\rangle \left\langle{u'_\alpha u'_\beta}\right\rangle} \leq 1$ chegdan and abbott.hn like this.

October 30, 2009, 02:51	test	#2
lordmohit New Member Mohit Madan Join Date: Oct 2009 Posts: 4 Rep Power: 5	testing

December 31, 2010, 01:03	Useful website for generating LaTeX equations	#6
ComputerGuy Senior Member Real Name :) Join Date: Jan 2010 Location: United States Posts: 177 Rep Power: 5	Enjoy: http://www.codecogs.com/latex/eqneditor.php ComputerGuy Amir likes this.

Thread Tools
Show Printable Version Email this Page
Display Modes
Linear Mode Switch to Hybrid Mode Switch to Threaded Mode

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Guide: Getting Started with the CFD Online Discussion Forums	pete	Site Help, Feedback & Discussions	2	March 19, 2009 11:28
Writting equations on cfd-online.com	Guillermo Marraco	CFD-Wiki	2	September 11, 2006 18:12
latex and dvi	Hong	Main CFD Forum	1	March 31, 2000 09:27
Latex	chaker	Main CFD Forum	3	October 27, 1999 09:19

October 30, 2009, 03:03		#3
lordmohit New Member Mohit Madan Join Date: Oct 2009 Posts: 4 Rep Power: 5	$\lim_{x\to\infty}\frac{1}{x}$ $lim_{xtoinfty}frac{1}{x-1}$

October 30, 2009, 03:04		#4
lordmohit New Member Mohit Madan Join Date: Oct 2009 Posts: 4 Rep Power: 5	$\int^\infty_0 f(x) \, dx$

October 30, 2009, 03:06		#5
lordmohit New Member Mohit Madan Join Date: Oct 2009 Posts: 4 Rep Power: 5	$\int^\frac{\Pi}{2}_5 f(x) \, dx$

November 6, 2011, 22:56		#7
Sha Liu New Member Sha Liu Join Date: Nov 2011 Posts: 1 Rep Power: 0	cool. i often use mathematica to write equations. then they can be transform to latex form.

April 14, 2013, 16:11		#8
stefanbj New Member Stefan Bjornsson Join Date: Apr 2013 Posts: 7 Rep Power: 2	test test $\frac{1}{2}$

May 2, 2013, 22:15		#9
abbott.hn New Member zdong Join Date: Aug 2011 Posts: 10 Rep Power: 3	let me have a try: $-\frac{1}{2}\rho\overline{u'_i u'_j}+\overline{p' u'_j}=\frac{\mu_t}{\sigma_k}\frac{\partial k}{\partial x_j}$ and this " $-\frac{1}{2}\rho\overline{u'_i u'_j}+\overline{p' u'_j}=\frac{\mu_t}{\sigma_k}\frac{\partial k}{\partial x_j}$ "inline equation