diff --git a/blflow.gif b/blflow.gif
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diff --git a/doc/blflow.lyx b/doc/blflow.lyx
index dacebd4..81ccac9 100644
--- a/doc/blflow.lyx
+++ b/doc/blflow.lyx
@@ -1,33 +1,53 @@
-#LyX 2.1 created this file. For more info see http://www.lyx.org/
-\lyxformat 474
+#LyX 2.3 created this file. For more info see http://www.lyx.org/
+\lyxformat 544
\begin_document
\begin_header
+\save_transient_properties true
+\origin unavailable
\textclass article
+\begin_preamble
+\input{tex/preamble_article.tex}
+\end_preamble
+\options twoside,final
\use_default_options true
\maintain_unincluded_children false
-\language english
-\language_package default
-\inputencoding auto
+\language american
+\language_package babel
+\inputencoding utf8
\fontencoding global
-\font_roman default
-\font_sans default
-\font_typewriter default
-\font_math auto
+\font_roman "libertine" "Linux Libertine"
+\font_sans "default" "Courier New"
+\font_typewriter "default" "default"
+\font_math "libertine-ntxm" "auto"
\font_default_family default
-\use_non_tex_fonts false
+\use_non_tex_fonts true
\font_sc false
\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures false
\graphics default
\default_output_format default
-\output_sync 0
+\output_sync 1
+\output_sync_macro "\synctex=1"
\bibtex_command default
\index_command default
-\paperfontsize default
-\use_hyperref false
-\papersize default
-\use_geometry false
+\paperfontsize 10
+\spacing single
+\use_hyperref true
+\pdf_author "Dr.ir. J.A. de Jong - ASCEE"
+\pdf_bookmarks true
+\pdf_bookmarksnumbered false
+\pdf_bookmarksopen false
+\pdf_bookmarksopenlevel 1
+\pdf_breaklinks true
+\pdf_pdfborder true
+\pdf_colorlinks true
+\pdf_backref false
+\pdf_pdfusetitle true
+\papersize a4paper
+\use_geometry true
\use_package amsmath 1
\use_package amssymb 1
\use_package cancel 1
@@ -46,16 +66,25 @@
\paperorientation portrait
\suppress_date false
\justification true
-\use_refstyle 1
+\use_refstyle 0
+\use_minted 0
\index Index
\shortcut idx
\color #008000
\end_index
+\leftmargin 3cm
+\topmargin 3cm
+\rightmargin 2.5cm
+\bottommargin 3.5cm
+\headsep 1cm
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\paragraph_indentation default
-\quotes_language english
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
\papercolumns 1
\papersides 1
\paperpagestyle default
@@ -68,79 +97,447 @@
\begin_body
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+newcommand{
+\backslash
+articletitle}{Numerical solution of the (Stokes) viscous boundary layer}
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+date{
+\backslash
+today}
+\end_layout
+
+\begin_layout Plain Layout
+
+%
+\backslash
+begin{center}
+\end_layout
+
+\begin_layout Plain Layout
+
+%
+\backslash
+includegraphics{/home/anne/bin/doctemplates/%ascee_beeldmerk_withacr.eps}
+\end_layout
+
+\begin_layout Plain Layout
+
+%
+\backslash
+end{center}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
\begin_layout Title
-Boundary layer flow
-\end_layout
-\begin_layout Standard
-\begin_inset Formula
-\begin{equation}
-\frac{\partial u}{\partial t}-\frac{1}{s^{2}}\frac{\partial^{2}u}{\partial y^{2}}=K(t)
-\end{equation}
+\series bold
+\size giant
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+articletitle
+\end_layout
\end_inset
-\end_layout
-
-\begin_layout Standard
-\begin_inset Formula $y=0:u=0$
-\end_inset
-
-,
-\begin_inset Formula $y=1,\frac{\partial u}{\partial y}=0$
+\begin_inset Newline newline
\end_inset
-\end_layout
+\size large
-\begin_layout Standard
-Discretization, FTCD:
-\end_layout
-
-\begin_layout Standard
-\begin_inset Formula
-\begin{equation}
-\frac{u_{i}^{n+1}-u_{i}^{n}}{\Delta t}-\frac{1}{s^{2}}\frac{u_{i+1}^{n}-2u_{i}^{n}-u_{i-1}^{n}}{\Delta y^{2}}=K^{n}
-\end{equation}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Rewriting:
\begin_inset Note Note
status open
\begin_layout Plain Layout
-\begin_inset Formula $u_{i}^{n+1}-u_{i}^{n}-\frac{\Delta t}{\Delta y^{2}s^{2}}\frac{u_{i+1}^{n}-2u_{i}^{n}-u_{i-1}^{n}}{}=K^{n}\Delta t$
+
+\series bold
+\size giant
+Subtitle
+\end_layout
+
\end_inset
\end_layout
-\begin_layout Plain Layout
-\begin_inset Formula $u_{i}^{n+1}=\Delta tK^{n}+u_{i}^{n}+\frac{\Delta t}{\Delta y^{2}s^{2}}\left(u_{i+1}^{n}-2u_{i}^{n}-u_{i-1}^{n}\right)$
+\begin_layout Author
+
+\series bold
+J.A.
+ de Jong
+\begin_inset Formula $^{1}$
\end_inset
\end_layout
-\begin_layout Plain Layout
-\begin_inset Formula $u_{0}=0$
+\begin_layout Standard
+\begin_inset VSpace medskip
\end_inset
\end_layout
+\begin_layout Standard
+\align center
+\begin_inset Graphics
+ filename /home/anne/bin/doctemplates/ascee_beeldmerk_withacr.eps
+ width 45text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+
+\size small
+\begin_inset Formula $^{1}$
+\end_inset
+
+ASCEE, Máximastraat 1, 7442 NW Nijverdal, info@ascee.nl
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align left
+\begin_inset Tabular
+
+
+
+
+
+|
+\begin_inset Text
+
\begin_layout Plain Layout
-and
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
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+
+\backslash
+arrayrulecolor{asceelightblue}
\end_layout
\begin_layout Plain Layout
-\begin_inset Formula $u_{N}-u_{n-1}=0$
+
+
+\backslash
+midrule[2pt]
+\end_layout
+
+\end_inset
+
+Internal document ID:
+\end_layout
+
+\end_inset
+ |
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+\end_inset
+
+Internal document ID:
+\end_layout
+
+\end_inset
+ |
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+\end_layout
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+\end_inset
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+\end_inset
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+|
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+Document status:
+\end_layout
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+\end_inset
+ |
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+\begin_inset Text
+
+\begin_layout Plain Layout
+Draft
+\end_layout
+
+\end_inset
+ |
+
+
+|
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+
+\lang dutch
+Revisiehistorie:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+
+\lang dutch
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+today
+\end_layout
+
+\end_inset
+
+: rev.
+ 1
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+fourteendaysahead
+\end_layout
+
+\end_inset
+
+: rev.
+ 2
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+|
+\begin_inset Text
+
+\begin_layout Plain Layout
+
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+ |
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+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
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+
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+\backslash
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+\begin_layout Plain Layout
+
+
+\backslash
+bottomrule[2pt]%
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
\end_inset
@@ -152,9 +549,260 @@ and
\end_layout
\begin_layout Standard
+\begin_inset CommandInset toc
+LatexCommand tableofcontents
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+thispagestyle{empty}
+\end_layout
+
+\begin_layout Plain Layout
+
+% Optionally: set this document to confidential
+\end_layout
+
+\begin_layout Plain Layout
+
+%
+\backslash
+confidential
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Differential equation
+\end_layout
+
+\begin_layout Standard
+The Stokes layer of the velocity satisfies the following differential equation:
\begin_inset Formula
-\[
-\]
+\begin{equation}
+\frac{\partial\hat{u}}{\partial t}-\frac{\mu}{\rho_{0}}\nabla_{\mathrm{T}}^{2}\hat{u}=\hat{K}(t),\label{eq:diffeq}
+\end{equation}
+
+\end_inset
+
+where
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $t$
+\end_inset
+
+ is time,
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\nabla_{\mathrm{T}}^{2}$
+\end_inset
+
+ is the Laplacian in
+\emph on
+transverse
+\emph default
+ direction.
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\hat{u}$
+\end_inset
+
+ is the
+\emph on
+axial
+\emph default
+ velocity,
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\hat{K}(t)$
+\end_inset
+
+ is the forcing function as a function of time, which in acoustics equals
+ minus the gradient of the pressure,
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\mu$
+\end_inset
+
+ is the dynamic viscosity,
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\rho_{0}$
+\end_inset
+
+ the density.
+\end_layout
+
+\begin_layout Section
+Harmonic solution
+\end_layout
+
+\begin_layout Standard
+If we assume harmonic motion, we may write
+\begin_inset Formula
+\begin{equation}
+\hat{u}=\Re\left(ue^{i\omega t}\right)\quad;\quad K=\Re\left(\hat{K}e^{i\omega t}\right)\quad\mathrm{etc}
+\end{equation}
+
+\end_inset
+
+where
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\Re$
+\end_inset
+
+ is the operator taking the real part of its argument,
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $i=\sqrt{-1}$
+\end_inset
+
+,
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\omega$
+\end_inset
+
+ is the frequency in rad/s.
+\end_layout
+
+\begin_layout Standard
+For flow close to a plate and unbounded in the
+\begin_inset Formula $+y$
+\end_inset
+
+-direction, the solution for
+\begin_inset Formula $u$
+\end_inset
+
+ yields:
+\begin_inset Formula
+\begin{equation}
+u=\frac{1}{i\omega\rho_{0}}K\left(1-\exp\left(-\left(1+i\right)y/\delta_{\nu}\right)\right),
+\end{equation}
+
+\end_inset
+
+where
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\delta_{\nu}=\sqrt{\frac{2\mu}{\rho_{0}\omega}}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For oscillating flow between two parallel plates, separated at distances
+
+\begin_inset Formula $2y_{0}$
+\end_inset
+
+, and
+\begin_inset Formula $y=0$
+\end_inset
+
+ at the center between the two plates:
+\begin_inset Formula
+\begin{equation}
+u=\frac{1}{i\omega\rho_{0}}\frac{1-h_{\nu}}{1-f_{\nu}}K,
+\end{equation}
+
+\end_inset
+
+where
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $h_{\nu}=\frac{\cosh\left(\left(1+i\right)y/\delta_{\nu}\right)}{\cosh\left(\left(1+i\right)y_{0}/\delta_{\nu}\right)},$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $f_{\nu}=\frac{\tanh\left(\left(1+i\right)y_{0}/\delta_{\nu}\right)}{\left(1+i\right)y_{0}/\delta_{\nu}}$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Forward Euler time, central in space
+\end_layout
+
+\begin_layout Standard
+For
+\begin_inset Formula $\nabla_{\mathrm{T}}^{2}\equiv\frac{\partial^{2}}{\partial y^{2}}$
+\end_inset
+
+, the forward Euler time, central in space (uniform grid) formulation of
+ Eq.
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:diffeq"
+
+\end_inset
+
+ is
+\begin_inset Formula
+\begin{equation}
+\frac{u_{i}^{n+1}-u_{i}^{n}}{\Delta t}-\frac{\mu}{\rho_{0}}\frac{u_{i+1}^{n}-2u_{i}^{n}-u_{i-1}^{n}}{\Delta y^{2}}=K^{n},
+\end{equation}
+
+\end_inset
+
+where upper index
+\begin_inset Formula $n$
+\end_inset
+
+ denotes a discrete time instance and lower index
+\begin_inset Formula $i$
+\end_inset
+
+ denotes a discrete position index.
+ This is an explicit form for the velocity at the next time index
+\begin_inset Formula $n+1$
+\end_inset
+
+.
+ Solving for
+\begin_inset Formula $u_{i}^{n+1}$
+\end_inset
+
+ yields:
+\begin_inset Formula
+\begin{equation}
+u_{i}^{n+1}=u_{i}^{n}+\Delta tK^{n}+\frac{\mu\Delta t}{\rho_{0}\Delta y^{2}}\left(u_{i+1}^{n}-2u_{i}^{n}-u_{i-1}^{n}\right)
+\end{equation}
\end_inset
diff --git a/doc/blflow.pdf b/doc/blflow.pdf
new file mode 100644
index 0000000..c0c5486
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