From 2fd80ae16426b59a0ef145a7550a256f99ee8888 Mon Sep 17 00:00:00 2001 From: Mike Campbell Date: Wed, 5 Aug 2026 14:54:06 -0500 Subject: [PATCH 1/3] fix doc rendering issue --- docs/axisymmetry.md | 10 ++++------ 1 file changed, 4 insertions(+), 6 deletions(-) diff --git a/docs/axisymmetry.md b/docs/axisymmetry.md index 231e316..93e090f 100644 --- a/docs/axisymmetry.md +++ b/docs/axisymmetry.md @@ -78,16 +78,14 @@ With the Stokes hypothesis used by Theseus, the stress components needed by the meridional operator are $$ -\begin{aligned} -\tau_{zz} &= \mu\left(2\frac{\partial u_z}{\partial z} +\tau_{zz} = \mu\left(2\frac{\partial u_z}{\partial z} - \frac{2}{3}\nabla\!\cdot\mathbf{u}\right), \\ -\tau_{rr} &= \mu\left(2\frac{\partial u_r}{\partial r} +\tau_{rr} = \mu\left(2\frac{\partial u_r}{\partial r} - \frac{2}{3}\nabla\!\cdot\mathbf{u}\right), \\ -\tau_{\theta\theta} &= \mu\left(2\frac{u_r}{r} +\tau_{\theta\theta} = \mu\left(2\frac{u_r}{r} - \frac{2}{3}\nabla\!\cdot\mathbf{u}\right), \\ -\tau_{zr}=\tau_{rz} &= \mu\left( +\tau_{zr}=\tau_{rz} = \mu\left( \frac{\partial u_z}{\partial r}+\frac{\partial u_r}{\partial z}\right). -\end{aligned} $$ The radial heat flux is $q_r=-\kappa\,\partial_r T$. The Cartesian-like From 1cea456aa0c8bed8c499ff7ba1ecb151c54cbd74 Mon Sep 17 00:00:00 2001 From: Mike Campbell Date: Wed, 5 Aug 2026 14:57:14 -0500 Subject: [PATCH 2/3] Fix formatting issues in axisymmetry documentation --- docs/axisymmetry.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/docs/axisymmetry.md b/docs/axisymmetry.md index 93e090f..b8f2da2 100644 --- a/docs/axisymmetry.md +++ b/docs/axisymmetry.md @@ -68,7 +68,7 @@ For CNS, let $\mathbf{u}=(u_z,u_r)$ and use the swirl-free cylindrical velocity divergence $$ -\nabla\!\cdot\mathbf{u} +\nabla\cdot\mathbf{u} = \frac{\partial u_z}{\partial z} + \frac{\partial u_r}{\partial r} + \frac{u_r}{r}. @@ -79,11 +79,11 @@ meridional operator are $$ \tau_{zz} = \mu\left(2\frac{\partial u_z}{\partial z} -- \frac{2}{3}\nabla\!\cdot\mathbf{u}\right), \\ +- \frac{2}{3}\nabla\cdot\mathbf{u}\right), \\ \tau_{rr} = \mu\left(2\frac{\partial u_r}{\partial r} -- \frac{2}{3}\nabla\!\cdot\mathbf{u}\right), \\ +- \frac{2}{3}\nabla\cdot\mathbf{u}\right), \\ \tau_{\theta\theta} = \mu\left(2\frac{u_r}{r} -- \frac{2}{3}\nabla\!\cdot\mathbf{u}\right), \\ +- \frac{2}{3}\nabla\cdot\mathbf{u}\right), \\ \tau_{zr}=\tau_{rz} = \mu\left( \frac{\partial u_z}{\partial r}+\frac{\partial u_r}{\partial z}\right). $$ @@ -112,7 +112,7 @@ These source terms are volume terms and do not depend on a boundary normal. On an off-axis curved or oblique boundary, the numerical flux uses the actual meridional normal $\mathbf{n}=(n_z,n_r)$ through $F_n=F_z n_z+F_r n_r$; no additional source correction involving -$\hat{\mathbf r}\!\cdot\mathbf{n}$ is needed. +$\hat{\mathbf r}\cdot\mathbf{n}$ is needed. ## Axis regularity From 78b184247996242e05cb3681d863ce0361d9f5af Mon Sep 17 00:00:00 2001 From: Mike Campbell Date: Wed, 5 Aug 2026 14:59:31 -0500 Subject: [PATCH 3/3] Fix formatting of equations in axisymmetry.md --- docs/axisymmetry.md | 23 +++++++++++------------ 1 file changed, 11 insertions(+), 12 deletions(-) diff --git a/docs/axisymmetry.md b/docs/axisymmetry.md index b8f2da2..2c1a2f7 100644 --- a/docs/axisymmetry.md +++ b/docs/axisymmetry.md @@ -68,24 +68,23 @@ For CNS, let $\mathbf{u}=(u_z,u_r)$ and use the swirl-free cylindrical velocity divergence $$ -\nabla\cdot\mathbf{u} -= \frac{\partial u_z}{\partial z} -+ \frac{\partial u_r}{\partial r} -+ \frac{u_r}{r}. +\nabla\cdot\mathbf{u} = \frac{\partial u_z}{\partial z} + \frac{\partial u_r}{\partial r} + \frac{u_r}{r} $$ With the Stokes hypothesis used by Theseus, the stress components needed by the meridional operator are $$ -\tau_{zz} = \mu\left(2\frac{\partial u_z}{\partial z} -- \frac{2}{3}\nabla\cdot\mathbf{u}\right), \\ -\tau_{rr} = \mu\left(2\frac{\partial u_r}{\partial r} -- \frac{2}{3}\nabla\cdot\mathbf{u}\right), \\ -\tau_{\theta\theta} = \mu\left(2\frac{u_r}{r} -- \frac{2}{3}\nabla\cdot\mathbf{u}\right), \\ -\tau_{zr}=\tau_{rz} = \mu\left( -\frac{\partial u_z}{\partial r}+\frac{\partial u_r}{\partial z}\right). +\tau_{zz} = \mu\left(2\frac{\partial u_z}{\partial z} - \frac{2}{3}\nabla\cdot\mathbf{u}\right), +$$ +$$ +\tau_{rr} = \mu\left(2\frac{\partial u_r}{\partial r} - \frac{2}{3}\nabla\cdot\mathbf{u}\right), +$$ +$$ +\tau_{\theta\theta} = \mu\left(2\frac{u_r}{r} - \frac{2}{3}\nabla\cdot\mathbf{u}\right), +$$ +$$ +\tau_{zr}=\tau_{rz} = \mu\left(\frac{\partial u_z}{\partial r}+\frac{\partial u_r}{\partial z}\right). $$ The radial heat flux is $q_r=-\kappa\,\partial_r T$. The Cartesian-like