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},
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))
@@ -162,13 +162,15 @@ possibly also Reynolds stresses) into single file;
\item\inltt{concatenate}: Concatenate a \nekpp binary output (.chk or .fld) field file into single file (deprecated);
\item\inltt{equispacedoutput}: Write data as equi-spaced output using simplices to represent the data for connecting points;
\item\inltt{extract}: Extract a boundary field;
\item\inltt{gradient}: Computes gradient of fields;
\item\inltt{homplane}: Extract a plane from 3DH1D expansions;
\item\inltt{homstretch}: Stretch a 3DH1D expansion by an integer factor;
\item\inltt{innerproduct}: take the inner product between one or a series of fields with another field (or series of fields).
\item\inltt{interpfield}: Interpolates one field to another, requires fromxml, fromfld to be defined;
\item\inltt{interppointdatatofld}: Interpolates given discrete data using a finite difference approximation to a fld file given an xml file;
\item\inltt{interppoints}: Interpolates a set of points to another, requires fromfld and fromxml to be defined, a line or plane of points can be defined;
\item\inltt{isocontour}: Extract an isocontour of ``fieldid'' variable and at value ``fieldvalue''. Optionally ``fieldstr'' can be specified for a string defiition or ``smooth'' for smoothing;
\item\inltt{interppoints}: Interpolates a field to a set of points. Requires fromfld, fromxml to be defined, and a topts, line, plane or box of target points;
\item\inltt{interpptstopts}: Interpolates a set of points to another. Requires a topts, line, plane or box of target points;
\item\inltt{isocontour}: Extract an isocontour of ``fieldid'' variable and at value ``fieldvalue''. Optionally ``fieldstr'' can be specified for a string definition or ``smooth'' for smoothing;
\item\inltt{jacobianenergy}: Shows high frequency energy of Jacobian;
\item\inltt{qualitymetric}: Evaluate a quality metric of the underlying mesh to show mesh quality;
\item\inltt{meanmode}: Extract mean mode (plane zero) of 3DH1D expansions;
...
...
@@ -178,6 +180,7 @@ possibly also Reynolds stresses) into single file;
With this usage, the \textit{equispacedoutput} module will be automatically
called to interpolate the field to a set of equispaced points in each element.
The result is then interpolated to a plane by the \textit{interpptstopts} module.
\begin{notebox}
This module does not work in parallel.
\end{notebox}
%
%
%
...
...
@@ -759,7 +818,8 @@ point, the first, second, and third columns contains the
$x,y,z$-coordinate and subsequent columns contain the field values, in
this case the $p$-value So in the general case of $n$-dimensional
data, the $n$ coordinates are specified in the first $n$ columns
accordingly followed by the field data.
accordingly followed by the field data. Alternatively, the \inltt{file.pts}
can be interchanged with a csv file.
The default argument is to use the equispaced (but potentially
collapsed) coordinates which can be obtained from the command.
...
...
@@ -850,6 +910,26 @@ The argument \inltt{N} and \inltt{fromfld} are compulsory arguments that respect
The input \inltt{.fld} files are the outputs of the \textit{wss} module. If they do not contain the surface normals (an optional output of the \textit{wss} modle), then the \textit{shear} module will not compute the last metric, |WSSG|.
%
%
%
\subsection{Stream function of a 2D incompressible flow: \textit{streamfunction} module}
The streamfunction module calculates the stream function of a 2D incompressible flow, by
solving the Poisson equation
\[
\nabla^2\psi=-\omega
\]
where $\omega$ is the vorticity. Note that this module applies the same boundary conditions
specified for the y-direction velocity component \inltt{v} to the stream function,
