From 096baa2b6c3cb0b30c67b5083d37c4fef05942cf Mon Sep 17 00:00:00 2001 From: Loren Matilsky Date: Sat, 1 Jun 2024 14:36:34 -0700 Subject: [PATCH 1/2] Fairly certain there's a missing c_7 in ohmic heating Similar to the (formerly) missing c_5 in the viscous heating. --- doc/source/User_Guide/physics_math_overview.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/source/User_Guide/physics_math_overview.rst b/doc/source/User_Guide/physics_math_overview.rst index a641a34c..6ae56b98 100644 --- a/doc/source/User_Guide/physics_math_overview.rst +++ b/doc/source/User_Guide/physics_math_overview.rst @@ -151,7 +151,7 @@ respectively. The evolution of :math:`\Theta` is described by c_6\,\boldsymbol{\nabla}\cdot\left[\mathrm{f}_1(r)\,\mathrm{f}_4(r)\,\mathrm{f}_5(r)\,\boldsymbol{\nabla}\Theta \right] \\ +\ c_{10}\,\mathrm{f}_6(r) + c_8\,\Phi(r,\theta,\phi) - + c_9\,\mathrm{f}_7(r)|\boldsymbol{\nabla}\times\boldsymbol{B}|^2, + + c_9\,c_7\,\mathrm{f}_7(r)|\boldsymbol{\nabla}\times\boldsymbol{B}|^2, where the viscous heating :math:`\Phi` is given by From 7b1b93a0d1ec9d35db145e0bc589122f271a17d7 Mon Sep 17 00:00:00 2001 From: Loren Matilsky Date: Thu, 20 Jun 2024 18:25:08 -0600 Subject: [PATCH 2/2] Update physics_math_overview.rst Updated documentation to reflect the fact that c_9 is not actually independent of the other constants. --- doc/source/User_Guide/physics_math_overview.rst | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/doc/source/User_Guide/physics_math_overview.rst b/doc/source/User_Guide/physics_math_overview.rst index 6ae56b98..2799035d 100644 --- a/doc/source/User_Guide/physics_math_overview.rst +++ b/doc/source/User_Guide/physics_math_overview.rst @@ -151,7 +151,7 @@ respectively. The evolution of :math:`\Theta` is described by c_6\,\boldsymbol{\nabla}\cdot\left[\mathrm{f}_1(r)\,\mathrm{f}_4(r)\,\mathrm{f}_5(r)\,\boldsymbol{\nabla}\Theta \right] \\ +\ c_{10}\,\mathrm{f}_6(r) + c_8\,\Phi(r,\theta,\phi) - + c_9\,c_7\,\mathrm{f}_7(r)|\boldsymbol{\nabla}\times\boldsymbol{B}|^2, + + c_8\,c_4\,c_7\,\mathrm{f}_7(r)|\boldsymbol{\nabla}\times\boldsymbol{B}|^2, where the viscous heating :math:`\Phi` is given by @@ -161,6 +161,8 @@ where the viscous heating :math:`\Phi` is given by \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. +For historical consistency, we also define :math:`c_9\,\equiv c_8\,c_4\,c_7`. + Finally, the evolution of :math:`\boldsymbol{B}` is described by the induction equation