diff --git a/2025R2/system-coupling-2025-r2/articles/user-guide/multiregion.md b/2025R2/system-coupling-2025-r2/articles/user-guide/multiregion.md index e7203cd32f..a4efc506f5 100644 --- a/2025R2/system-coupling-2025-r2/articles/user-guide/multiregion.md +++ b/2025R2/system-coupling-2025-r2/articles/user-guide/multiregion.md @@ -94,9 +94,9 @@ To get the average temperature on these two regions, the sum of temperature nodal values is divided by the number of unique nodes. In this example, the average temperature is -\f$\f$ +$$ (500 + 300 + 800 + 600 + 500 + 300) / 6 = 500 [K] -\f$\f$. +$$. ![Figure 6: Nodal intensive variable (temperature) values for the multi-region case with shared nodes](../images/MultiregionFigure6.png) *Figure 6: Nodal intensive variable (temperature) values for the multi-region case with shared nodes* diff --git a/2025R2/system-coupling-2025-r2/articles/user-guide/pipe-mapping-tutorial.md b/2025R2/system-coupling-2025-r2/articles/user-guide/pipe-mapping-tutorial.md index ef71c3e5af..7eb6d40dc4 100644 --- a/2025R2/system-coupling-2025-r2/articles/user-guide/pipe-mapping-tutorial.md +++ b/2025R2/system-coupling-2025-r2/articles/user-guide/pipe-mapping-tutorial.md @@ -35,7 +35,7 @@ elements. The meshes with default settings are shown in _Figure 1_. _Figure 1: Default pipe meshes_ On each side, we initialize the nodal -solution data with a simple linear profile \f$f(x,y,z) = 1x + 2y + 3z + 4\f$. On the **quad** region, we initialize +solution data with a simple linear profile $f(x,y,z) = 1x + 2y + 3z + 4$. On the **quad** region, we initialize **linear1** variable, and on the **tri** region, we initialize the **linear2** variable. We then use the mapping capabilities within the Participant Library to transfer diff --git a/2025R2/system-coupling-2025-r2/articles/user-guide/plate-damping-tutorial.md b/2025R2/system-coupling-2025-r2/articles/user-guide/plate-damping-tutorial.md index 2f0a46f45c..9fffde1008 100644 --- a/2025R2/system-coupling-2025-r2/articles/user-guide/plate-damping-tutorial.md +++ b/2025R2/system-coupling-2025-r2/articles/user-guide/plate-damping-tutorial.md @@ -42,14 +42,14 @@ _Figure 1: Structural solver geometry_ Since the purpose of this example is to demonstrate the use of Participant Library APIs for a transient analysis, a simple damping force solver will be used to couple with Mechanical via System Coupling. This solver receives nodal -displacements \f$\vec{X}\f$ from Mechanical and calculates the damping force -\f$\vec{F}\f$ using the following formula: +displacements $\vec{X}$ from Mechanical and calculates the damping force +$\vec{F}$ using the following formula: -\f$\f$ +$$ \vec{F} = - c \frac{d\vec{X}}{dt} -\f$\f$ +$$ -where \f$c\f$ is the damping coefficient and \f$\frac{d\vec{X}}{dt}\f$ is the rate of change +where $c$ is the damping coefficient and $\frac{d\vec{X}}{dt}$ is the rate of change of nodal positions with respect to time (nodal velocities). The damping solver will then provide the calculated forces to Mechanical via System Coupling, and these damping forces will cause the