Merge pull request idaholab#25443 from GiudGiud/PR_catch_all

Second catch all PR for the tutorial

tutorials/darcy_thermo_mech/doc/content/workshop/intro/moose_multiphysics.md

@@ -6,7 +6,7 @@
 - Scientists are adept at creating applications in their domain
 - What about collaborating across research groups and/or disciplines?
 
-  - Head in the sand?
+  - Iterating between design teams?
   - Development of "coupling" codes?
   - Is there something better?
 

tutorials/darcy_thermo_mech/doc/content/workshop/numerical/fem_overview.md

@@ -229,31 +229,31 @@ Write in inner product notation. Each term of the equation will inherit from an
 !style! fontsize=60%
 
 !row!
-!col! width=20%
+!col! width=15%
 !listing test/tests/kernels/2d_diffusion/2d_diffusion_neumannbc_test.i block=Kernels remove=Kernels/active
 !col-end!
 
 !col! width=1%
 $\quad$
 !col-end!
 
-!col! width=20%
+!col! width=15%
 !listing test/tests/kernels/2d_diffusion/2d_diffusion_neumannbc_test.i block=BCs remove=BCs/active BCs/left
 !col-end!
 
 !col! width=1%
 $\quad$
 !col-end!
 
-!col! width=20%
+!col! width=15%
 !listing test/tests/dgkernels/1d_advection_dg/1d_advection_dg.i block=Kernels remove=Kernels/time_u
 !col-end!
 
 !col! width=1%
 $\quad$
 !col-end!
 
-!col! width=20%
+!col! width=15%
 !listing test/tests/bcs/nodal_normals/circle_tris.i block=Kernels remove=Kernels/diff
 !col-end!
 

tutorials/darcy_thermo_mech/doc/content/workshop/numerical/fem_shape.md

@@ -107,17 +107,17 @@ $\psi_8$ is associated to the "center" node, it is symmetric and $\geq 0$ on the
 
 !row!
 !col! width=33%
-!media darcy_thermo_mech/fem_quad9_phi0.png style=width:100% caption=    $\psi_0$ prefix=''
+!media darcy_thermo_mech/fem_quad9_phi0.png style=width:100% caption=    $\psi_0$ prefix='            '
 !col-end!
 
 !col! width=33%
 !col width=33%
-!media darcy_thermo_mech/fem_quad9_phi4.png style=width:100%; caption=    $\psi_4$ prefix=''
+!media darcy_thermo_mech/fem_quad9_phi4.png style=width:100%; caption=    $\psi_4$ prefix='           '
 !col-end!
 
 !col! width=33%
 !col width=33%
-!media darcy_thermo_mech/fem_quad9_phi8.png style=width:100%; caption=    $\psi_8$ prefix=''
+!media darcy_thermo_mech/fem_quad9_phi8.png style=width:100%; caption=    $\psi_8$ prefix='           '
 !col-end!
 
 !row-end!

tutorials/darcy_thermo_mech/doc/content/workshop/numerical/fem_solve.md

@@ -42,7 +42,7 @@ Gaussian Quadrature can exactly integrate polynomials of order $2n-1$ with $n$ q
 
 !---
 
-Quadrature applied to [ref_elems] yields an equation that can be analyzed numerically:
+Applying the quadrature to [ref_elems] we can simply compute:
 
 !equation
 \sum_e \int_{\hat{\Omega}_e} f(\vec{\xi}) \left|\mathcal{J}_e\right| \;\text{d}\vec{\xi} \approx
@@ -208,9 +208,9 @@ Some examples:
 
 - LU : form the actual Jacobian inverse, useful for small to medium problems but does not scale well
 - Hypre BoomerAMG : algebraic multi-grid, works well for diffusive problems
-- jacobi : preconditions with the diagonal of Jacobian
+- Jacobi : preconditions with the diagonal, row sum, or row max of Jacobian
 
-Can also combine pre-conditioners using sub-preconditioning with option `-sub_pc_type`.
+For parallel preconditioners, the sub-block (on-process) preconditioners can be controlled with the PETSc option `-sub_pc_type`. E.g. for a parallel block Jacobi preconditioner (-pc_type bjacobi) the sub-block preconditioner could be set to ILU or LU etc. with `-sub_pc_type ilu`, `-sub_pc_type lu`, etc.
 
 !---
 
@@ -227,7 +227,7 @@ Integrals are computed numerically using quadrature.
 
 Newton's method provides a mechanism for solving a system of nonlinear equations.
 
-The Preconditioned Jacobian Free Newton Krylov (JFNK) method allows us to avoid explicitly forming
+The Preconditioned Jacobian Free Newton Krylov (PJFNK) method allows us to avoid explicitly forming
 the Jacobian matrix while still computing its action.
 
 !---
@@ -286,6 +286,12 @@ Thus, the $i^{th}$ component of the residual vector is:
 
 !---
 
+!equation
+\begin{aligned}
+\vec{R}_i(u_h) = \left(\nabla\psi_i, k\nabla u_h \right) - \langle\psi_i, k\nabla u_h\cdot \hat{n} \rangle +
+\left(\psi_i, \vec{\beta} \cdot \nabla u_h\right) - \left(\psi_i, f\right)
+\end{aligned}
+
 Using the previously-defined rules in [diff_u] and [grad_u] for $\frac{\partial u_h}{\partial u_j}$
 and $\frac{\partial \left(\nabla u_h\right)}{\partial u_j}$, the $(i,j)$ entry of the Jacobian is
 then:

tutorials/darcy_thermo_mech/doc/content/workshop/problem/step01.md

@@ -21,8 +21,8 @@ where $\psi_i$ are the test functions and $u_h$ is the finite element solution.
 
 ## Input File(s)
 
-All capabilities of MOOSE, modules, and your application are compiled into a single executable.
-An input file is used to define which capabilities are used to perform a simulation.
+An input file is used to represent the problem in MOOSE. It follows a very standardized
+syntax.
 
 MOOSE uses the "hierarchical input text" (hit) format.
 
@@ -37,7 +37,7 @@ A basic MOOSE input file requires six parts, each of which will be covered in gr
 - `[Kernels]`: Define the equation(s) to solve
 - `[BCs]`: Define the boundary condition(s) of the problem
 - `[Executioner]`: Define how the problem will be solved
-- `[Outputs]`: Define how the solution will be written
+- `[Outputs]`: Define how the solution will be returned
 
 !---
 
@@ -49,6 +49,9 @@ A basic MOOSE input file requires six parts, each of which will be covered in gr
 
 ## Step 1: Run
 
+An executable is produced by compiling an application or a MOOSE module. It can be used
+to run input files.
+
 ```bash
 cd ~/projects/moose/tutorials/darcy-thermo_mech/step01_diffusion
 make -j 12 # use number of processors for your system