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BUG: fixed latex errors in MPPIC header documentation
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@ -25,9 +25,11 @@ Class
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Foam::CorrectionLimitingMethods::absolute
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Foam::CorrectionLimitingMethods::absolute
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Description
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Description
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Correction limiting method that limits the velocity correction to that of a
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Correction limiting method based on the absolute particle velocity.
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rebound with a coefficient of restitution $e$. The absolute velocity of the
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particle is used when calculating the magnitude of the limited correction.
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This method that limits the velocity correction to that of a rebound with a
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coefficient of restitution \f$e\f$. The absolute velocity of the particle
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is used when calculating the magnitude of the limited correction.
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The direction is calculated using the relative velocity.
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The direction is calculated using the relative velocity.
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SourceFiles
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SourceFiles
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@ -25,10 +25,12 @@ Class
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Foam::CorrectionLimitingMethods::relative
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Foam::CorrectionLimitingMethods::relative
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Description
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Description
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Correction limiting method that limits the velocity correction to that of a
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Correction limiting method based on the relative particle velocity.
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rebound with a coefficient of restitution $e$. The relative velocity of the
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particle with respect to the mean value is used to calculate the direction
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This method limits the velocity correction to that of a rebound with a
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and magnitude of the limited velocity.
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coefficient of restitution \f$e\f$. The relative velocity of the particle
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with respect to the mean value is used to calculate the direction and
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magnitude of the limited velocity.
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SourceFiles
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SourceFiles
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relative.C
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relative.C
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@ -39,6 +39,7 @@ Description
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D Snider
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D Snider
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Journal of Computational Physics
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Journal of Computational Physics
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Volume 170, Issue 2, Pages 523-549, July 2001
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Volume 170, Issue 2, Pages 523-549, July 2001
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\endverbatim
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SourceFiles
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SourceFiles
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Explicit.C
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Explicit.C
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@ -29,12 +29,12 @@ Description
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The stress value takes the following form:
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The stress value takes the following form:
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\f[
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\f[
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\dfrac{P_s \alpha^\beta}{\max \left( \alpha_{pack} - \alpha , \epsilon
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\frac{P_s \alpha^\beta}{ \mathrm{max} \left( \alpha_{pack} - \alpha ,
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( 1 - \alpha ) \right) }
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\epsilon ( 1 - \alpha ) \right) }
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\f]
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\f]
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Here, $\alpha$ is the volume fraction of the dispersed phase, and the other
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Here, \f$\alpha\f$ is the volume fraction of the dispersed phase, and the
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values are modelling constants. A small value $\epsilon$ is used to limit
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other values are modelling constants. A small value \f$\epsilon\f$ is used
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the denominator to ensure numerical stability.
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to limit the denominator to ensure numerical stability.
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Reference:
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Reference:
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\verbatim
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\verbatim
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@ -29,13 +29,13 @@ Description
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The stress value takes the following form:
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The stress value takes the following form:
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\f[
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\f[
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\left[ \alpha \rho + \alpha^2 \rho (1 + e) \frac{3}{5}
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\left( \alpha \rho + \alpha^2 \rho (1 + e) \frac{3}{5}
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\left( \frac{\alpha_{pack}}{\alpha_{pack} - \alpha}
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\left( 1 - \left( \frac{\alpha}{\alpha_{pack}} \right)^\frac{1}{3}
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\right)^\frac{1}{3} \right] \frac{1}{3} \sigma^2
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\right) \right) \frac{1}{3} \sigma^2
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\f]
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\f]
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Here, $\alpha$ is the volume fraction of the dispersed phase, $\rho$ is the
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Here, \f$\alpha\f$ is the volume fraction of the dispersed phase,
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density of the dispersed phase, $e$ is a coefficient of restitution, and
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\f$\rho\f$ is the density of the dispersed phase, \f$e\f$ is a coefficient
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$\sigma$ is the RMS velocityh fluctuation.
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of restitution, and \f$\sigma\f$ is the RMS velocity fluctuation.
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Reference:
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Reference:
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\verbatim
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\verbatim
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@ -36,6 +36,7 @@ Description
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P O'Rourke and D Snider
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P O'Rourke and D Snider
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Chemical Engineering Science
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Chemical Engineering Science
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Volume 65, Issue 22, Pages 6014-6028, November 2010
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Volume 65, Issue 22, Pages 6014-6028, November 2010
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\endverbatim
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SourceFiles
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SourceFiles
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nonEquilibrium.C
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nonEquilibrium.C
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