BUG: fixed latex errors in MPPIC header documentation

This commit is contained in:
william
2013-12-18 10:46:53 +00:00
parent ccf3e1a376
commit 77d18a2c3f
6 changed files with 24 additions and 18 deletions

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@ -25,9 +25,11 @@ Class
Foam::CorrectionLimitingMethods::absolute Foam::CorrectionLimitingMethods::absolute
Description Description
Correction limiting method that limits the velocity correction to that of a Correction limiting method based on the absolute particle velocity.
rebound with a coefficient of restitution $e$. The absolute velocity of the
particle is used when calculating the magnitude of the limited correction. This method that limits the velocity correction to that of a rebound with a
coefficient of restitution \f$e\f$. The absolute velocity of the particle
is used when calculating the magnitude of the limited correction.
The direction is calculated using the relative velocity. The direction is calculated using the relative velocity.
SourceFiles SourceFiles

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@ -25,10 +25,12 @@ Class
Foam::CorrectionLimitingMethods::relative Foam::CorrectionLimitingMethods::relative
Description Description
Correction limiting method that limits the velocity correction to that of a Correction limiting method based on the relative particle velocity.
rebound with a coefficient of restitution $e$. The relative velocity of the
particle with respect to the mean value is used to calculate the direction This method limits the velocity correction to that of a rebound with a
and magnitude of the limited velocity. coefficient of restitution \f$e\f$. The relative velocity of the particle
with respect to the mean value is used to calculate the direction and
magnitude of the limited velocity.
SourceFiles SourceFiles
relative.C relative.C

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@ -39,6 +39,7 @@ Description
D Snider D Snider
Journal of Computational Physics Journal of Computational Physics
Volume 170, Issue 2, Pages 523-549, July 2001 Volume 170, Issue 2, Pages 523-549, July 2001
\endverbatim
SourceFiles SourceFiles
Explicit.C Explicit.C

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@ -29,12 +29,12 @@ Description
The stress value takes the following form: The stress value takes the following form:
\f[ \f[
\dfrac{P_s \alpha^\beta}{\max \left( \alpha_{pack} - \alpha , \epsilon \frac{P_s \alpha^\beta}{ \mathrm{max} \left( \alpha_{pack} - \alpha ,
( 1 - \alpha ) \right) } \epsilon ( 1 - \alpha ) \right) }
\f] \f]
Here, $\alpha$ is the volume fraction of the dispersed phase, and the other Here, \f$\alpha\f$ is the volume fraction of the dispersed phase, and the
values are modelling constants. A small value $\epsilon$ is used to limit other values are modelling constants. A small value \f$\epsilon\f$ is used
the denominator to ensure numerical stability. to limit the denominator to ensure numerical stability.
Reference: Reference:
\verbatim \verbatim

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@ -29,13 +29,13 @@ Description
The stress value takes the following form: The stress value takes the following form:
\f[ \f[
\left[ \alpha \rho + \alpha^2 \rho (1 + e) \frac{3}{5} \left( \alpha \rho + \alpha^2 \rho (1 + e) \frac{3}{5}
\left( \frac{\alpha_{pack}}{\alpha_{pack} - \alpha} \left( 1 - \left( \frac{\alpha}{\alpha_{pack}} \right)^\frac{1}{3}
\right)^\frac{1}{3} \right] \frac{1}{3} \sigma^2 \right) \right) \frac{1}{3} \sigma^2
\f] \f]
Here, $\alpha$ is the volume fraction of the dispersed phase, $\rho$ is the Here, \f$\alpha\f$ is the volume fraction of the dispersed phase,
density of the dispersed phase, $e$ is a coefficient of restitution, and \f$\rho\f$ is the density of the dispersed phase, \f$e\f$ is a coefficient
$\sigma$ is the RMS velocityh fluctuation. of restitution, and \f$\sigma\f$ is the RMS velocity fluctuation.
Reference: Reference:
\verbatim \verbatim

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@ -36,6 +36,7 @@ Description
P O'Rourke and D Snider P O'Rourke and D Snider
Chemical Engineering Science Chemical Engineering Science
Volume 65, Issue 22, Pages 6014-6028, November 2010 Volume 65, Issue 22, Pages 6014-6028, November 2010
\endverbatim
SourceFiles SourceFiles
nonEquilibrium.C nonEquilibrium.C