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Add c_5 to definition of viscous heating ("Phi") #444

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Jan 31, 2023
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Add c_5 to definition of viscous heating ("Phi") #444

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4 changes: 2 additions & 2 deletions doc/source/User_Guide/physics_math_overview.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -158,8 +158,8 @@ where the viscous heating :math:`\Phi` is given by
.. math::
:label: vischeat

\Phi(r,\theta,\phi) = \mathcal{D}_{ij}e_{ij} &= 2\,\mathrm{f}_1(r)\mathrm{f}_3(r)\left[e_{ij}e_{ij} - \frac{1}{3}\left(\boldsymbol{\nabla}\cdot\boldsymbol{v}\right)^2\right] \\
&= 2\,\mathrm{f}_1(r)\mathrm{f}_3(r)\left[e_{ij} - \frac{1}{3}\left(\boldsymbol{\nabla}\cdot\boldsymbol{v}\right)\delta_{ij}\right]^2.
\Phi(r,\theta,\phi) = c_5\,\mathcal{D}_{ij}e_{ij} &= 2\,c_5\,\mathrm{f}_1(r)\mathrm{f}_3(r)\left[e_{ij}e_{ij} - \frac{1}{3}\left(\boldsymbol{\nabla}\cdot\boldsymbol{v}\right)^2\right] \\
&= 2\,c_5\,\mathrm{f}_1(r)\mathrm{f}_3(r)\left[e_{ij} - \frac{1}{3}\left(\boldsymbol{\nabla}\cdot\boldsymbol{v}\right)\delta_{ij}\right]^2.

Finally, the evolution of :math:`\boldsymbol{B}` is described by the
induction equation
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