Commit 3d0c585c authored by Michael Turner's avatar Michael Turner

Merge branch 'ticket/65-Userguide-IncNS-WrongSign' into 'master'

Fix sign of the viscous term in the velocity correction scheme equations in the user guide

Closes #65

See merge request !856
parents 8c9438e2 30d6c839
......@@ -65,6 +65,10 @@ v4.4.2
- Fix missing periodic boundary meshing and boundary layer mesh adjustment
configurations in 2D (!859)
**Documentation**:
- Fix sign of the viscous term in the velocity correction scheme equations in
the user guide (!856)
v4.4.1
------
**Library**
......
......@@ -66,7 +66,7 @@ zero. If we now integrate the 1st, 2nd and last term in equation
(\ref{eqn.weakp}) by parts we can obtain the weak pressure equation
\begin{align}
\int_{\Omega} \nabla q \cdot \nabla p^{n+1} &= \int_{\Omega} q\, \nabla \cdot \left ( \frac{\partial \mathbf{u}}{\partial t}^{n+1} + \mathbf{N}(\mathbf{u})^{n+1} \right ) \nonumber \\
&- \int_{\partial \Omega} q \left ( \frac{\partial \mathbf{u}}{\partial t}^{n+1} + \mathbf{N}(\mathbf{u})^{n+1} - \nu \nabla \times \nabla \times \mathbf{u}^{n+1} \right ) \cdot \mathbf{n}
&- \int_{\partial \Omega} q \left ( \frac{\partial \mathbf{u}}{\partial t}^{n+1} + \mathbf{N}(\mathbf{u})^{n+1} + \nu \nabla \times \nabla \times \mathbf{u}^{n+1} \right ) \cdot \mathbf{n}
\label{eqn.weakp1}
\end{align}
where $\partial \Omega$ is the boundary of the domain and we have used
......@@ -98,7 +98,7 @@ which to decouple the system we impose that $\nabla \cdot
\int_{\Omega} \nabla q \cdot \nabla p^{n+1} &=
\int_{\Omega} q \, \nabla \cdot \left (-\frac{\hat{\mathbf{u}}}{\Delta t}
+ \mathbf{N}(\mathbf{u})^{*,n+1} \right ) \nonumber \\
&- \int_{\partial \Omega} q \left ( \frac{\partial \mathbf{u}}{\partial t}^{n+1} + \mathbf{N}(\mathbf{u})^{*.n+1} - \nu (\nabla \times \nabla \times \mathbf{u})^{*,n+1} \right ) \cdot \mathbf{n}
&- \int_{\partial \Omega} q \left ( \frac{\partial \mathbf{u}}{\partial t}^{n+1} + \mathbf{N}(\mathbf{u})^{*.n+1} + \nu (\nabla \times \nabla \times \mathbf{u})^{*,n+1} \right ) \cdot \mathbf{n}
\label{eqn.weakpfinal}
\end{align}
We note this can be recast into an equivalent strong form of the
......@@ -109,7 +109,7 @@ which to decouple the system we impose that $\nabla \cdot
\end{equation}
with consistent Neumann boundary conditions prescribed as
\begin{equation}
\frac{\partial p}{\partial n}^{n+1}= - \Bigl[ \frac{\partial \mathbf{u}}{\partial t}^{n+1} - \nu (\nabla \times \nabla \times \mathbf{u})^{*,n+1} + \mathbf{N}^{*,n+1}\Bigr]\cdot \mathbf{n}
\frac{\partial p}{\partial n}^{n+1}= - \Bigl[ \frac{\partial \mathbf{u}}{\partial t}^{n+1} + \nu (\nabla \times \nabla \times \mathbf{u})^{*,n+1} + \mathbf{N}^{*,n+1}\Bigr]\cdot \mathbf{n}
\label{eqn.pressurebcs}
\end{equation}
......
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