Commit 4c2fa24b by Chris Cantwell

### Improvements to user guide IncNS stability section.

parent ff8b3723
Pipeline #1128 passed with stages
 ... ... @@ -1092,88 +1092,65 @@ available for this solver. \item \inltt{Reynolds stresses} (section \ref{filters:ReynoldsStresses}) \end{itemize} \section{Stability analysis Session file configuration} \section{Session file configuration: Linear stability analysis} \label{SecStabFile} The type of equation which is to be solved is specified through the \inltt {EqType} option in the session file. This can be set to any of the following: \begin{center} \footnotesize \begin{tabular}{lc} \toprule {Equation to solve} \\ \midrule $\frac{\partial\mathbf{u'}}{\partial t} +\mathcal{L}(\mathbf{U},\mathbf{u'})=-\nabla p+\nu \nabla^2 \mathbf{u'}$\\ \bottomrule \end{tabular} \end{center} \begin{center} \footnotesize \begin{tabular}{lccccc} \toprule {Equation Type} & {Dimensions} &{Projections} &{Algorithms} \\ \midrule UnsteadyNavierStokes & 2D, Quasi-3D& Continuous &VCS,DS\\ \bottomrule \end{tabular} \end{center} Stability analyses of incompressible flow involves solving the linearised Navier-Stokes equations \begin{align*} \frac{\partial\mathbf{u'}}{\partial t} +\mathcal{L}(\mathbf{U},\mathbf{u'})=-\nabla p+\nu \nabla^2 \mathbf{u'}, \end{align*} where $\mathcal{L}$ is a linear operator, its adjoint form, or both. The evolution of the linearised Navier-Stokes operator, which evolves a solution from an initial state to a future time $t$, can be written as \begin{align*} u(t) = \mathcal{A}(t)u(0). \end{align*} The adjoint evolution operator is denoted as $\mathcal{A}^*$. This section details the additional configuration options, in addition to the standard configuration options described earlier, relating to performing this task. \subsection{Solver Info} \label{SectionIncNS_SolverInfo_Stab} \begin{itemize} \item \inltt{Eqtype}: sets the type of equation to solve, according to the table above. \item \inltt{TimeIntegrationMethod}: the following types of time integration methods have been tested with each solver: \item \inltt{Eqtype}: sets the type of equation to solve. For linear stability analysis this must be set to \begin{center} \footnotesize \begin{tabular}{lccccc} \toprule {} & {Explicit} &{Diagonally Implicit} &{IMEX} & {Implicit} \\ \midrule \texttt{UnsteadyNavierStokes} & X & &X & \\ \bottomrule \end{tabular} \footnotesize \begin{tabular}{lccccc} \toprule {Equation Type} & {Dimensions} &{Projections} &{Algorithms} \\ \midrule UnsteadyNavierStokes & 2D, Quasi-3D& Continuous &VCS,DS\\ \bottomrule \end{tabular} \end{center} \item \inltt{Projection}: the Galerkin projection used may be either \item \inltt{EvolutionOperator}: sets the choice of the evolution operator: \begin{itemize} \item \inltt{Continuous}: for a C0-continuous Galerkin (CG) projection; \item \inltt{Discontinuous}: for a discontinous Galerkin (DG) projection. \end{itemize} \item \inltt{EvolutionOperator}: \begin{itemize} \item \inltt{Nonlinear} (non-linear Navier-Stokes equations). \item \inltt{Direct} (linearised Navier-Stokes equations). \item \inltt{Adjoint} (adjoint Navier-Stokes equations). \item \inltt{TransientGrowth} ((transient growth evolution operator). \item \inltt{Nonlinear} (standard non-linear Navier-Stokes equations). \item \inltt{Direct} ($\mathcal{A}$ -- linearised Navier-Stokes equations). \item \inltt{Adjoint} ($\mathcal{A}^*$ -- adjoint Navier-Stokes equations). \item \inltt{TransientGrowth} ($\mathcal{A}^*\mathcal{A}$ -- transient growth evolution operator). \end{itemize} \item \inltt{Driver}: specifies the type of problem to be solved: \begin{itemize} \item \inltt{Standard} (time integration of the equations) \item \inltt{Standard} (normal time integration of the equations) \item \inltt{ModifiedArnoldi} (computations of the leading eigenvalues and eigenmodes using modified Arnoldi method) \item \inltt{Arpack} (computations of eigenvalues/eigenmodes using Implicitly Restarted Arnoldi Method (ARPACK) ). \end{itemize} \item \inltt{ArpackProblemType}: types of eigenvalues to be computed (for Driver Arpack only) \begin{itemize} \item \inltt{LargestMag} (eigenvalues with largest magnitude). \item \inltt{SmallestMag} (eigenvalues with smallest magnitude). \item \inltt{LargestReal} (eigenvalues with largest real part). \item \inltt{SmallestReal} (eigenvalues with smallest real part). \item \inltt{LargestImag} (eigenvalues with largest imaginary part). \item \inltt{SmallestIma} (eigenvalues with smallest imaginary part ). \item \inltt{LargestMag} (eigenvalues with largest magnitude). \item \inltt{SmallestMag} (eigenvalues with smallest magnitude). \item \inltt{LargestReal} (eigenvalues with largest real part). \item \inltt{SmallestReal} (eigenvalues with smallest real part). \item \inltt{LargestImag} (eigenvalues with largest imaginary part). \item \inltt{SmallestIma} (eigenvalues with smallest imaginary part ). \end{itemize} \item \inltt{Homogeneous}: specifies the Fourier expansion in a third direction (optional) \begin{itemize} \item \inltt{1D} (Fourier spectral method in z-direction). \end{itemize} \item \inltt{ModeType}: this specifies the type of the quasi-3D problem to be solved. \item \inltt{1D} (Fourier spectral method in z-direction). \end{itemize} \item \inltt{ModeType}: this specifies the type of the quasi-3D problem to be solved. \begin{itemize} \item \inltt{MultipleMode} (stability analysis with multiple modes, \inltt{HomModesZ} sets number of modes). \item \inltt{SingleMode} (BiGlobal Stability Analysis: full-complex mode. Overrides \inltt{HomModesZ} to 1.). ... ... @@ -1190,17 +1167,16 @@ table above. The following parameters can be specified in the \texttt{PARAMETERS} section of the session file: \begin{itemize} \item \inltt{Kinvis}: sets the kinematic viscosity $\nu$. \item \inltt{kdim}: sets the dimension of the Krylov subspace $\kappa$. Can be used in: \inltt{ModifiedArnoldi} and \inltt{Arpack}. Default value: 16. \item \inltt{evtol}: sets the tolerance of the eigenvalues. Can be used in: \item \inltt{imagShift}: provide an imaginary shift to the direct solver eigenvalue problem by the specified value. \inltt{ModifiedArnoldi} and \inltt{Arpack}. Default value: $0.0$. Works only with \inltt{Homogeneous} set to \inltt{1D} and \inltt{ModeType} set to \inltt{SingleMode}. \item \inltt{nits}: sets the maximum number of iterations. Can be used in: \inltt{ModifiedArnoldi} and \inltt{Arpack}. Default value: 500. \item \inltt{LZ}: sets the length in the spanswise direction $L_z$. Can be used in \inltt{Homogeneous} set to \inltt{1D}. Default value: 1. \item \inltt{HomModesZ}: sets the number of planes in the homogeneous directions. Can be used in \inltt{Homogeneous} set to \inltt{1D} and \inltt{ModeType} set to \inltt{MultipleModes}. \item \inltt{kdim}: sets the dimension of the Krylov subspace $\kappa$. Can be used with: \inltt{ModifiedArnoldi} and \inltt{Arpack}. Default value: 16. \item \inltt{evtol}: sets the tolerance of the iterative eigenvalue algorithm. Can be used with: \inltt{ModifiedArnoldi} and \inltt{Arpack}. Default value: $1\times10^{-6}$. \item \inltt{nvec}: sets the number of converged eigenvalues sought. Can be used with: \inltt{ModifiedArnoldi} and \inltt{Arpack}. Default value: $2$. \item \inltt{nits}: sets the maximum number of Arnoldi iterations to attempt. Can be used with: \inltt{ModifiedArnoldi} and \inltt{Arpack}. Default value: $500$. \item \inltt{realShift}: provide a real shift to the direct solver eigenvalue problem by the specified value to improve convergence. Can be used with: \inltt{Arpack} only. \item \inltt{imagShift}: provide an imaginary shift to the direct solver eigenvalue problem by the specified value to improve convergence. Can be used with: \inltt{Arpack} only. \item \inltt{LZ}: sets the length in the spanswise direction $L_z$. Can be used with \inltt{Homogeneous} set to \inltt{1D}. Default value: 1. \item \inltt{HomModesZ}: sets the number of planes in the homogeneous directions. Can be used with \inltt{Homogeneous} set to \inltt{1D} and \inltt{ModeType} set to \inltt{MultipleModes}. \item \inltt{N\_slices}: sets the number of temporal slices for Floquet stability analysis. \item \inltt{period}: sets the periodicity of the base flow. \item \inltt{realShift}: provide a real shift to the direct sovler eigenvalue problem by the specified value. \end{itemize} \subsection{Functions} ... ... @@ -1226,7 +1202,7 @@ regression test directory noting that some parameters are specified in the .tst files. \end{notebox} \section{Steady-state solver Session file configuration} \section{Session file configuration: Steady-state solver} \label{SectionSFD_XML} In this section, we detail how to use the steady-state solver (that ... ... @@ -1294,7 +1270,8 @@ IncNavierStokesSolver Session.xml.gz Session.xml \end{lstlisting} \section{Coordinate transformations Session file configuration}\label{sec:mapping} \section{Session file configuration: Coordinate transformations} \label{sec:mapping} This section describes how to include a coordinate transformation to the solution of the incompressible Navier-Stokes equations. ... ... @@ -1414,7 +1391,7 @@ Examples of the use of mappings can be found in the test directory \inlsh{KovaFlow\_3DH1D\_P8\_16modes\_Mapping-implicit.xml} and \inlsh{CylFlow\_Mov\_mapping.xml}. \end{notebox} \section{Adaptive polynomial order Session file configuration} \section{Session file configuration: Adaptive polynomial order} \label{SectionDriverAdaptive} An adaptive polynomial order procedure is available for 2D and ... ...
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