by default the comparison is made with the $p-1$ solution, but this can be changed by setting the parameter \inltt{SensorOffset}.
An artificial diffusion term is introduced locally to the Euler equations to deal with flow discontinuity and the consequential numerical oscillations. Two models are implemented, a non-smooth and a smooth artificial viscosity model.
For the non-smooth artificial viscosity model the added artificial viscosity is constant in each element and discontinuous between the elements. The Euler system is augmented by an added laplacian term on right hand side of equation \ref{eq:euler}. The diffusivity of the system is controlled by a variable viscosity coefficient $\epsilon$. The value of $\epsilon$ is dependent on $\epsilon_0$, which is the maximum viscosity that is dependent on the polynomial order ($p$), the mesh size ($h$) and the maximum wave speed and the local sensor value. Based on pre-defined sensor threshold values, the variable viscosity is set accordingly
...
...
@@ -450,6 +449,24 @@ For the non-smooth artificial viscosity model the added artificial viscosity is
\end{array}
\right.
\end{equation}
To enable the non-smooth viscosity model, the following line has to be added to the \inltt{SOLVERINFO} section:
@@ -512,54 +530,52 @@ The polynomial order in each element can be adjusted based on the sensor value t
\right.
\end{equation}
For now, the threshold values $s_e$, $s_{ds}$, $s_{sm}$ and $s_{fl}$ are determined empirically by looking at the sensor distribution in the domain. Once these values are set, two .txt files are outputted, one that has the composites called VariablePComposites.txt and one with the expansions called VariablePExpansions.txt. These values have to copied into a new .xml file to create the adapted mesh.
\subsection{De-Aliasing Techniques}
Aliasing effects, arising as a consequence of the nonlinearity of the
underlying problem, need to be address to stabilise the simulations. Aliasing
appears when nonlinear quantities are calculated at an insufficient number of
quadrature points. We can identify two types of nonlinearities:
\begin{itemize}
\item PDE nonlinearities, related to the nonlinear and quasi-linear fluxes.
\item Geometrical nonlinearities, related to the deformed/curves meshes.
\end{itemize}
We consider two de-aliasing strategies based on the concept of consistent integration:
\subsection{Quasi-1D nozzle flow}
A quasi-1D inviscid flow (flow with area variation) can be obtained using the
\inltt{Quasi1D} forcing in a 1D solution of the Euler equations:
\begin{lstlisting}[style=XMLStyle]
<FORCING>
<FORCE TYPE="Quasi1D">
<AREAFCN> Area </AREAFCN>
</FORCE>
</FORCING>
\end{lstlisting}
in this case a function named \inltt{Area} must be specified in the \inltt{CONDITIONS} section of the session file.
\begin{itemize}
\item Local dealiasing: It only targets the PDE-aliasing sources, applying a consistent integration of them locally.
\item Global dealiasing: It targets both the PDE and the geometrical-aliasing sources. It requires a richer quadrature order to consistently integrate the nonlinear fluxes, the geometric factors, the mass matrix and the boundary term.
\end{itemize}
In this case, it is possible to prescribe the inflow conditions in terms of stagnation properties (density and pressure)
