Commit 3eaf7e96 by Chris Cantwell

### Promoted solvers to chapters and restructured incns.

parent 2a8c8e67
 \section{ADRSolver} \chapter{ADRSolver} %3.4/UserGuide/Tutorial/ADRSolver %3.4/UserGuide/Examples/ADRSolver/1DAdvection %3.4/UserGuide/Examples/ADRSolver/3DAdvectionMassTransport %3.4/UserGuide/Examples/ADRSolver/Helmholtz2D \subsection{Synopsis} \section{Synopsis} The ADRSolver is designed to solve partial differential equations of the form: ... ... @@ -49,17 +49,17 @@ $\dfrac{\partial u}{\partial t} + u\nabla u = 0$ \label{t:ADR1} \end{table} \subsection{Usage} \section{Usage} ADRSolver session.xml \subsection{Session file configuration} \section{Session file configuration} The type of equation which is to be solved is specified through the EquationType SOLVERINFO option in the session file. This can be set as in table \ref{t:ADR1}. At present, the Steady non-symmetric solvers cannot be used in parallel. \\ \subsubsection{Solver Info} \subsection{Solver Info} The solver info are listed below: \begin{itemize} ... ... @@ -117,7 +117,7 @@ UnstedayInviscidBurger & \checkmark & & &\\ \end{itemize} \end{itemize} \subsubsection{Parameters} \subsection{Parameters} The following parameters can be specified in the PARAMETERS section of the session file: \begin{itemize} ... ... @@ -132,7 +132,7 @@ The following parameters can be specified in the PARAMETERS section of the sessi \textit{Default value}: 0. \end{itemize} \subsubsection{Functions} \subsection{Functions} The following functions can be specified inside the CONDITIONS section of the session file: ... ... @@ -142,6 +142,8 @@ The following functions can be specified inside the CONDITIONS section of the se \item \textbf{Forcing}: specifies the forcing function f. \end{itemize} \section{Examples} \subsection{1D Advection equation} In this example, it will be demonstrated how the Advection equation can be solved on a one-dimensional domain. ... ...
 \section{APE Solver} \chapter{APE Solver} 3.4/UserGuide/Tutorial/APESolver 3.4/UserGuide/Examples/APESolver/AeroAcousticWave
 \section{Cardiac Electrophysiology Solver} \chapter{Cardiac Electrophysiology Solver} \subsection{Synopsis} \section{Synopsis} The CardiacEPSolver is intended to model the electrophysiology of cardiac tissue, specifically using the monodomain or bidomain model. These models are ... ... @@ -9,7 +9,7 @@ cells. The system is a reaction-diffusion system, with the reaction term modeling the flow of current in and out of the cells using a separate set of ODEs. \subsubsection{Bidomain Model} \subsection{Bidomain Model} The Bidomain model is given by the following PDEs, \begin{align*} g_{ix}\frac{\partial^2 V_i}{\partial x^2} + g_{iy}\frac{\partial^2 V_i}{\partial y^2} &= \chi \left[ C_m \frac{\partial(V_i-V_e)}{\partial t} + G_m(V_i-V_e) \right] \\ ... ... @@ -23,7 +23,7 @@ of the transmembrane potential and extracellular potential, &= -g_{ix} \frac{\partial^2 V_m}{\partial x^2} - g_{iy} \frac{\partial^2 V_m}{\partial y^2} \end{align*} \subsubsection{Monodomain Model} \subsection{Monodomain Model} In the case where the intracellular and extracellular conductivities are proportional, that is $g_{ix} = kg_{ex}$ for some $k$, then the above two PDEs can be reduced to a single PDE: ... ... @@ -31,7 +31,7 @@ then the above two PDEs can be reduced to a single PDE: \chi\left[ C_m \frac{\partial V_m}{\partial t} + J_{ion} \right] &= \nabla \cdot (\sigma \nabla V_m) \end{align*} \subsubsection{Cell Models} \subsection{Cell Models} The action potential of a cardiac cell can be modelled at either a biophysical level of detail, including a number of transmembrane currents, or as a phenomenological model, to reproduce the features of the action potential, with ... ... @@ -62,14 +62,14 @@ The monodomain equation: \chi \left[ C_m \frac{\partial V_m}{\partial t} + J_{ion} \right] &= \nabla \cdot (\sigma \nabla V_m) \end{align*} \subsection{Usage} \section{Usage} \begin{lstlisting}[style=BashInputStyle] CardiacEPSolver session.xml \end{lstlisting} \subsection{Session file configuration} \subsubsection{Solver Info} \section{Session file configuration} \subsection{Solver Info} \begin{itemize} \item \inltt{Eqtype} Specifies the PDE system to solve. This should take the value \inltt{Monodomain}. ... ...
 \section{Compressible Flow Solver} \chapter{Compressible Flow Solver} \section{Synopsis} The CompressibleFlowSolver allows us to solve the unsteady compressible Euler and Navier-Stokes equations for 1D/2D/3D problems using a discontinuous ... ... @@ -175,14 +176,14 @@ interface fluxes just mentioned. For a more detailed description of the above the interested reader can refer to \cite{DeGMen14} and \cite{MenDeG14}. \subsection{Usage} \section{Usage} \inltt{CompressibleFlowSolver session.xml} \subsection{Session file configuration} \section{Session file configuration} In the following we describe the session file configuration. Specifically we consider the sections under the tag \inltt{} in the session (.xml) file. \subsubsection*{Parameters} \subsection*{Parameters} Under this section it is possible to set the parameters of the simulation. \begin{lstlisting}[style=XmlStyle] ... ... @@ -226,7 +227,7 @@ conditions are employed (i.e. $T_{w}$). Default value = 300.15$K$; \item \inltt{thermalConductivity} thermal conductivity (i.e. $\kappa_{\infty}$). Default value = 0.0257 $W / (K m)$; \end{itemize} \subsubsection*{Solver info} \subsection*{Solver info} Under this section it is possible to set the solver information. \begin{lstlisting}[style=XmlStyle] ... ... @@ -305,7 +306,7 @@ isentropic vortex or the Ringleb flow. \end{itemize} \end{itemize} \subsubsection*{Boundary conditions} \subsection*{Boundary conditions} In this section we can specify the boundary conditions for our problem. First we need to define the variables under the section \inltt{VARIABLES}. For a 1D problem we have: ... ... @@ -399,7 +400,7 @@ In the following some examples for a 2D problem: \end{lstlisting} \end{itemize} \subsubsection*{Initial conditions and exact solution} \subsection*{Initial conditions and exact solution} Under the two following sections it is possible to define the initial conditions and the exact solution (if existent). \begin{lstlisting}[style=XmlStyle] ... ... @@ -418,6 +419,8 @@ Under the two following sections it is possible to define the initial conditions VALUE="pInf/(Gamma-1)+0.5*rhoInf*(uInf*uInf+vInf*vInf+wInf*wInf)"/> \end{lstlisting} \section{Examples} \subsection{Shock capturing} Compressible flow is characterised by abrupt changes in density within the flow domain often referred to as shocks. These discontinuities lead to numerical instabilities (Gibbs phenomena). This problem is prevented by locally adding a diffusion term to the equations to damp the numerical fluctuations. These fluctuations in an element are identified using a sensor algorithm which quantifies the smoothness of the solution within an element. The value of the sensor in an element is defined as \label{eq:sensor} ... ...
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 \section{Pulse Wave Solver} \chapter{Pulse Wave Solver} 3.4/UserGuide/Tutorial/PulseWaveSolver 3.4/UserGuide/Examples/PulseWaveSolver/HumanVascularNetwork ... ...
 \section{Shallow Water Solver} \chapter{Shallow Water Solver} 3.4/UserGuide/Tutorial/ShallowWaterSolver 3.4/UserGuide/Examples/ShallowWaterSolver/RossbyModon
 \chapter{Solvers} \label{s:solvers} %\chapter{Solvers} %\label{s:solvers} \input{adr} \input{ape} ... ...
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