Commit 7ca455c4 by Spencer Sherwin

Merge branch 'feature/SVV-doc' into 'master'

Add SVV documentation

See merge request !816
parents bf7a4470 4a1cf354
......@@ -475,3 +475,34 @@ volume = {163},
year = {2016}
}
@article{rospjo16,
title={Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection--diffusion problems: Insights into spectral vanishing viscosity},
author={Moura, RC and Sherwin, SJ and Peir{\'o}, Joaquim},
journal={Journal of Computational Physics},
volume={307},
pages={401--422},
year={2016},
publisher={Elsevier}
}
@article{yvsiouei93,
title={Legendre pseudospectral viscosity method for nonlinear conservation laws},
author={Maday, Yvon and Kaber, Sidi M Ould and Tadmor, Eitan},
journal={SIAM Journal on Numerical Analysis},
volume={30},
number={2},
pages={321--342},
year={1993},
publisher={SIAM}
}
@article{rosh06,
title={Stabilisation of spectral/hp element methods through spectral vanishing viscosity: Application to fluid mechanics modelling},
author={Kirby, Robert M and Sherwin, Spencer J},
journal={Computer methods in applied mechanics and engineering},
volume={195},
number={23},
pages={3128--3144},
year={2006},
publisher={Elsevier}
}
\ No newline at end of file
......@@ -830,7 +830,6 @@ the advection term using the pressure inverse mass matrix. It can be used just i
<I PROPERTY="SmoothAdvection" VALUE="True"/>
\end{lstlisting}
\item \inltt{SpectralVanishingViscosity}: activates a stabilization technique
which increases the viscosity on the modes with the highest frequencies.
\begin{lstlisting}[style=XMLStyle]
......@@ -839,7 +838,34 @@ which increases the viscosity on the modes with the highest frequencies.
In a Quasi-3D simulation, this will affect both the Fourier and the spectral/hp expansions.
To activate them independently, use \inltt{SpectralVanishingViscositySpectralHP}
and \inltt{SpectralVanishingViscosityHomo1D}.
and \inltt{SpectralVanishingViscosityHomo1D}. \\
There are three spectral vanishing viscosity kernels available:
\begin{center}
\footnotesize
\begin{tabular}{lcc}
\toprule
{SVV Kernel} & {\texttt{SpectralVanishingViscosity}} \\
\midrule
Exponential Kernel & \texttt{True} \\
Power Kernel & \texttt{PowerKernel} \\
DG Kernel & \texttt{DGKernel} \\
\bottomrule
\end{tabular}
\end{center}
The Exponential kernel is based on the work of Maday et al. \cite{yvsiouei93},
its extension to 2D can be found in \cite{rosh06}. A diffusion coefficient can
be specified which defines the base magnitude of the viscosity; this parameter
is scaled by $h/p$. SVV viscosity is activated for expansion modes greater than
the product of the cut-off ratio and the expansion order. The Power kernel is a
smooth function with no cut-off frequency; it focusses on a narrower band of
higher expansion modes as the polynomial order increases. The cut-off ratio
parameter for the Power kernel corresponds to the power ratio, see Moura et al.
\cite{rospjo16}. The DG-Kernel is an attempt to match the dissipation of CG-SVV
to DG schemes of lower expansion orders. This kernel does not require any parameters
although the diffusion coefficient can still be modified.
\item \inltt{DEALIASING}: activates the 3/2 padding rule on the advection term
of a Quasi-3D simulation.
......@@ -856,7 +882,6 @@ stabilize the simulation. This method is based on the work of Kirby and Sherwin
\end{itemize}
\subsection{Parameters}
The following parameters can be specified in the \inltt{PARAMETERS} section of
the session file:
......@@ -869,7 +894,7 @@ the session file:
\item \inltt{MinSubSteps}: perform a minimum number of substeps in sub-stepping algorithm (default is 1)
\item \inltt{MaxSubSteps}: perform a maxmimum number of substeps in sub-stepping algorithm otherwise exit (default is 100)
\item \inltt{SVVCutoffRatio}: sets the ratio of Fourier frequency not affected by the SVV technique (default value = 0.75, i.e. the first 75\% of frequency are not damped)
\item \inltt{SVVDiffCoeff}: sets the SVV diffusion coefficient (default value = 0.1)
\item \inltt{SVVDiffCoeff}: sets the SVV diffusion coefficient (default value = 0.1 (Exponential and Power kernel), 1 (DG-Kernel))
\end{itemize}
\subsection{Womersley Boundary Condition}
......
......@@ -214,6 +214,7 @@ openany, % A chapter may start on either a recto or verso page.
}
\lstset{%
escapeinside={(*}{*)},%
breaklines=true,
}
\usepackage{tikz}
......
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