commit e647ffaec71a2edc3321762a5453d3f33aef6669
parent 8744d5d38e8df8e5ac914067bdc3294feb2c81c1
Author: Ivan Gankevich <i.gankevich@spbu.ru>
Date: Fri, 13 Mar 2020 19:15:33 +0300
Integral. CRLF -> LF.
Diffstat:
| main.tex | | | 543 | ++++++++++++++++++++++++++++++++++++++++--------------------------------------- |
1 file changed, 277 insertions(+), 266 deletions(-)
diff --git a/main.tex b/main.tex
@@ -1,266 +1,277 @@
-\documentclass[runningheads]{llncs}
-
-\usepackage{amsmath}
-\usepackage{booktabs}
-\usepackage{graphicx}
-\usepackage{url}
-
-\newcommand{\Length}[1]{\big|#1\big|}
-
-\begin{document}
-
-\title{TODO\thanks{Supported by Saint Petersburg State University (grants
- no.~TODO) and Council for grants of the President of the Russian
- Federation (grant no.~TODO).}}
-\author{%
- Anton Gavrikov\orcidID{0000-0003-2128-8368} \and\\
- Alexander Degtyarev\orcidID{0000-0003-0967-2949} \and\\
- Denis Egorov\orcidID{TODO-0000-0000-0000} \and\\
- Ivan Gankevich\textsuperscript{*}\orcidID{0000-0001-7067-6928} \and\\
- Artemii Grigorev\orcidID{TODO-0000-0000-0000} \and\\
- Vasily Khramushin\orcidID{0000-0002-3357-169X} \and\\
- Ivan Petriakov\inst{1}\orcidID{TODO-0000-0000-0000}
-}
-
-%\titlerunning{Abbreviated paper title}
-\authorrunning{A.\,Gavrikov et al.}
-
-\institute{Saint Petersburg State University\\
- 7-9 Universitetskaya Emb., St Petersburg 199034, Russia\\
-\email{st047437@student.spbu.ru},\\
-\email{a.degtyarev@spbu.ru},\\
-\email{TODO@student.spbu.ru},\\
-\email{i.gankevich@spbu.ru},\\
-\email{st016177@student.spbu.ru},\\
-\email{v.khramushin@spbu.ru},\\
-\email{st049350@student.spbu.ru}\\
-\url{https://spbu.ru/}}
-
-\maketitle
-
-\begin{abstract}
-The abstract should briefly summarize the contents of the paper in
-150--250 words.
-
-\keywords{%
-TODO
-\and TODO
-\and TODO.
-}
-\end{abstract}
-
-\section{Introduction}
-
-Ship motion simulation studies focus on interaction between the ship and ocean
-waves~--- a physical phenomena that gives the largest contribution to
-oscillatory motion~--- however, intelligent onboard systems require taking
-other forces into account. One of the basic functionality of such a system is
-determination of initial static ship stability parameters (roll angle, pitch
-angle and draught) from the recordings of various ship motion parameters, such
-as instantaneous roll, pitch and yaw angles, and their first and second
-instantaneous derivatives (e.g.~angular velocity and angular acceleration).
-During ship operation these initial static ship stability parameters deviate
-from the original values as a result of moving cargo between compartments,
-damaging the hull, compartment flooding etc. These effects are especially
-severe for fishing and military vessels, but can occur with any vessel
-operating in extreme conditions.
-
-Intelligent onboard system need large amount of synchronous recordings of ship
-motions parameters to operate, mainly angular displacement, velocity and
-acceleration and draught, but these parameters depend on the shape of the ship
-hull and obtaining them in model tests is complicated, let alone field tests.
-Field tests are too expensive to perform and do not allow to simulate
-particular phenomena such as compartment flooding. Model tests are too
-time-consuming for such a task and there is no reliable way to obtain all the
-derivatives for a particular parameter: sensors measure one particular
-derivative and all other derivatives have to calculated by numerical
-differentiation or integration, and integration has low accuracy for time
-series of measurements TODO. The simplest way to obtain those parameters is to
-simulate ship motion on the computer and save all the parameters in the file
-for future analysis.
-
-Arguably, the largest contribution to ship motion besides ocean waves is given
-by wind forces: air has lesser density than water, but air motion acts on the
-area of ship hull which is greater than underwater area due to ship
-superstructure. Steady wind may produce non-nought roll angle TODO, and thus
-have to be taken into account when determining initial static ship stability
-parameters.
-
-In this paper we investigate how wind velocity field can be simulated on the
-boundary and near the boundary of the ship hull. We derive a simple
-mathematical model for uniform translational motion of the air on the
-above-water boundary of the ship hull. Then we generalise this model to
-calculate wind velocity near the boundary still taking into account the shape
-of the above-water part of the ship hull. Finally, we measure the effect of
-wind velocity on the ship roll angle and carry out computational performance
-analysis of our programme.
-
-\section{Methods}
-
-\subsection{Analytic representation of wind velocity field}
-
-Air motion without turbulence can be decomposed into two components:
-translational motion~--- air particles travel in the same direction with
-constant velocity, circular motion~--- air particles travel on a circle.
-Translational motion describe sea breeze, that occures on the shore on the
-sunrise and after the sunset. Rotational motion describe storms suchs as
-typhoons and hurricane. Translational motion is a particular case of circular
-motion when the radius of the circle is infinite. Given the scale of circular
-motion relative to the scale of translational motion, and the size of a typical
-ship hull we consider only translational motion in this paper.
-
-Since there is no rotational component, air flow is described by equations for
-irrotational inviscid incompressible fluid. In this context fluid velocity
-\(\vec\upsilon\) is determined as a vector gradient \(\vec\nabla\) of scalar
-velocity potential \(\phi\) and continuity equation and equation of motion are
-written as
-\begin{equation}
- \label{eq-governing}
- \begin{aligned}
- & \Delta\phi = 0; \qquad \vec\upsilon=\vec\nabla\phi; \\
- & \rho\frac{\partial\phi}{\partial{}t} +
- \frac{1}{2}\rho\Length{\vec\nabla\phi}^2 +
- p + \rho g z = p_0.
- \end{aligned}
-\end{equation}
-Here \(p_0\) is atmospheric pressure, \(g\) is gravitational acceleration,
-\(\rho\) is air density, \(p\) is pressure. We seek solution to this system
-of equations for velocity potential \(\phi\). Continuity equation restricts
-the type of the function that can be used as the solution, and equation of
-motion gives the pressure for a particular velocity potential value.
-
-Ship hull boundary is defined by a parametric surface \(\vec{S}\) and surface
-normals \(\vec{n}\):
-\begin{equation*}
-\vec{S}=\vec{S}\left(a,b,t\right)
-\qquad
-a,b\in{}A=[0,1];
-\qquad
-\vec{n}=\frac{\partial\vec S}{\partial a} \times \frac{\partial\vec S}{\partial b}
-\end{equation*}
-The simplest parametric surface is infinite plane which has the same normal in
-each point. The computer model of a real ship hull is composed of many panels
-with different areas and different orientations that approximate continuous
-surface. On the boundary the projection of wind velocity on the surface normal
-is nought:
-\begin{equation}
- \label{eq-boundary}
- \vec\nabla\phi\cdot\vec{n} = 0;
- \qquad
- \vec{r} = \vec{S}.
-\end{equation}
-
-The solutions to the governing system of equations differ in how boundary is
-incorporated in them: in our model the boundary is taken into account by adding
-velocity of a reflected air particle in the solution. Velocity
-\(\vec\upsilon_r\) of the particle that is reflected from the surface with
-surface normal \(\vec{n}\) is given by the law of reflection
-(fig.~\ref{fig-law-of-reflection}):
-\begin{equation}
- \label{eq-reflected}
- \vec\upsilon_r = \vec\upsilon - 2\left(\vec\upsilon\cdot\vec{n}\right)\vec{n}.
-\end{equation}
-When we add velocity of incident and reflected air particles we get a vector
-that is parallel to the boundary. As we move away from the boundary its impact
-on the velocity decays quadratically with the distance. The known analytic
-solution for the potential flow around a cylinder contains similar term:
-\begin{equation*}
- \phi\left(r,\theta\right) = U r \left( 1 + \frac{R^2}{r^2} \right) \cos\theta.
-\end{equation*}
-Here \(r\) and \(\theta\) are polar coordinates, \(R\) is cylinder radius and \(U\)
-is velocity magnitude.
-
-\begin{figure}
- \centering
- %\includegraphics{}
- \caption{\label{fig-law-of-reflection}}
-\end{figure}
-
-In the following subsections we describe the solution that we obtained for the
-velocity field \emph{on} the boundary and \emph{near} the boundary.
-
-\subsection{Uniform translational motion on the static body surface}
-
-On the surface we neglect the impact of neighbouring panels on the velocity
-field on the ground that the real ship hull surface is smooth,
-i.e.~neighbouring panels have approximately the same normals. This assumption
-does not hold for aft and bow of some ships, and, as a result, velocity field
-near these features has stream lines with sharp edges. We consider this effect
-negligible for the determination of roll angle caused by the wind, since the
-area of panels that distort wind field is small compared to the area of all
-other panels.
-
-We seek solution to the governing system of equations~\eqref{eq-governing} with
-boundary condition~\eqref{eq-boundary} of the form
-\begin{equation*}
-\phi = \vec\upsilon\cdot\vec{r}
-+ C \left(\vec\upsilon_r\cdot\vec{r}\right);
-\qquad
-\vec{r}=\left(x,y,z\right),
-\end{equation*}
-Here \(\vec{r}\) is spatial coordinate, \(C\) is the coefficient, and
-\(\vec\upsilon_r\) is velocity of reflected air particle defined
-in~\eqref{eq-reflected}. This solution is independent for each panel.
-Plugging the solution into boundary condition~\eqref{eq-boundary} gives
-\begin{equation*}
-\left(\vec\upsilon + C\vec\upsilon_r\right)\cdot\vec{n} = 0,
-\end{equation*}
-hence
-\begin{equation*}
-C = -\frac{ \vec\upsilon\cdot\vec{n} }{ \vec\upsilon_r\cdot\vec{n} } = 1
-\end{equation*}
-and velocity is written simply as
-\begin{equation}
-\vec\nabla\phi = \vec\upsilon + \vec\upsilon_r.
-\end{equation}
-
-This solution satisfies continuity equation. It gives velocity only at the
-centre of each ship hull panel, but this is sufficient to calculate pressure
-and force moments acting on the ship hull.
-
-\subsection{Uniform translational motion near the static body surface}
-
-Near the surface there are no neighbouring panels, the impact of which we can
-neglect, instead we add reflected particle velocities for all the panels and
-decay the velocity quadratically with the distance to the panel. Here we can
-neglect panels surface normals of which has large angles with the wind
-direction for efficiency, but they do not blow up the solution.
-
-We seek solution of the form
-\begin{equation*}
-\phi = \vec\upsilon\cdot\vec{r}
-+ C \frac{\vec\upsilon_r\cdot\vec{r}}{1+\Length{\vec{r}-\vec{S}}^2},
-\end{equation*}
-where \(\Length{\cdot}\) is vector length. Plugging the solution into boundary
-condition gives the same coefficient \(C=1\), but velocity vector is written differently
-as
-\begin{equation*}
-\vec\nabla\phi =
-\vec\upsilon +
-\left(
- \frac{1}{s} \vec\upsilon_r
- - \frac{2}{s^2} \left(\vec\upsilon_r\cdot\vec{r}\right) \left(\vec{r}-\vec{S}\right)
-\right);
-\qquad
-s = 1+\Length{\vec{r}-\vec{S}}^2.
-\end{equation*}
-Besides the term for reflected air particle velocity that decays quadratically with
-the distance to the panel, there is a term that decays quaternary with the distance and
-that can be neglected because of this.
-
-
-\section{Results}
-\section{Discussion}
-\section{Conclusion}
-
-Future work is to include circular motion in the model.
-
-\subsubsection*{Acknowledgements.}
-Research work is supported by Saint Petersburg State University (grants
-no.~TODO) and Council for grants of the President of the Russian Federation
-(grant no.~TODO).
-
-\bibliographystyle{splncs04}
-\bibliography{references}
-
-\end{document}
+\documentclass[runningheads]{llncs}
+
+\usepackage{amsmath}
+\usepackage{booktabs}
+\usepackage{graphicx}
+\usepackage{url}
+
+\newcommand{\Length}[1]{\big|#1\big|}
+
+\begin{document}
+
+\title{TODO\thanks{Supported by Saint Petersburg State University (grants
+ no.~TODO) and Council for grants of the President of the Russian
+ Federation (grant no.~TODO).}}
+\author{%
+ Anton Gavrikov\orcidID{0000-0003-2128-8368} \and\\
+ Alexander Degtyarev\orcidID{0000-0003-0967-2949} \and\\
+ Denis Egorov\orcidID{TODO-0000-0000-0000} \and\\
+ Ivan Gankevich\textsuperscript{*}\orcidID{0000-0001-7067-6928} \and\\
+ Artemii Grigorev\orcidID{TODO-0000-0000-0000} \and\\
+ Vasily Khramushin\orcidID{0000-0002-3357-169X} \and\\
+ Ivan Petriakov\inst{1}\orcidID{TODO-0000-0000-0000}
+}
+
+%\titlerunning{Abbreviated paper title}
+\authorrunning{A.\,Gavrikov et al.}
+
+\institute{Saint Petersburg State University\\
+ 7-9 Universitetskaya Emb., St Petersburg 199034, Russia\\
+\email{st047437@student.spbu.ru},\\
+\email{a.degtyarev@spbu.ru},\\
+\email{TODO@student.spbu.ru},\\
+\email{i.gankevich@spbu.ru},\\
+\email{st016177@student.spbu.ru},\\
+\email{v.khramushin@spbu.ru},\\
+\email{st049350@student.spbu.ru}\\
+\url{https://spbu.ru/}}
+
+\maketitle
+
+\begin{abstract}
+The abstract should briefly summarize the contents of the paper in
+150--250 words.
+
+\keywords{%
+TODO
+\and TODO
+\and TODO.
+}
+\end{abstract}
+
+\section{Introduction}
+
+Ship motion simulation studies focus on interaction between the ship and ocean
+waves~--- a physical phenomena that gives the largest contribution to
+oscillatory motion~--- however, intelligent onboard systems require taking
+other forces into account. One of the basic functionality of such a system is
+determination of initial static ship stability parameters (roll angle, pitch
+angle and draught) from the recordings of various ship motion parameters, such
+as instantaneous roll, pitch and yaw angles, and their first and second
+instantaneous derivatives (e.g.~angular velocity and angular acceleration).
+During ship operation these initial static ship stability parameters deviate
+from the original values as a result of moving cargo between compartments,
+damaging the hull, compartment flooding etc. These effects are especially
+severe for fishing and military vessels, but can occur with any vessel
+operating in extreme conditions.
+
+Intelligent onboard system need large amount of synchronous recordings of ship
+motions parameters to operate, mainly angular displacement, velocity and
+acceleration and draught, but these parameters depend on the shape of the ship
+hull and obtaining them in model tests is complicated, let alone field tests.
+Field tests are too expensive to perform and do not allow to simulate
+particular phenomena such as compartment flooding. Model tests are too
+time-consuming for such a task and there is no reliable way to obtain all the
+derivatives for a particular parameter: sensors measure one particular
+derivative and all other derivatives have to calculated by numerical
+differentiation or integration, and integration has low accuracy for time
+series of measurements TODO. The simplest way to obtain those parameters is to
+simulate ship motion on the computer and save all the parameters in the file
+for future analysis.
+
+Arguably, the largest contribution to ship motion besides ocean waves is given
+by wind forces: air has lesser density than water, but air motion acts on the
+area of ship hull which is greater than underwater area due to ship
+superstructure. Steady wind may produce non-nought roll angle TODO, and thus
+have to be taken into account when determining initial static ship stability
+parameters.
+
+In this paper we investigate how wind velocity field can be simulated on the
+boundary and near the boundary of the ship hull. We derive a simple
+mathematical model for uniform translational motion of the air on the
+above-water boundary of the ship hull. Then we generalise this model to
+calculate wind velocity near the boundary still taking into account the shape
+of the above-water part of the ship hull. Finally, we measure the effect of
+wind velocity on the ship roll angle and carry out computational performance
+analysis of our programme.
+
+\section{Methods}
+
+\subsection{Analytic representation of wind velocity field}
+
+Air motion without turbulence can be decomposed into two components:
+translational motion~--- air particles travel in the same direction with
+constant velocity, circular motion~--- air particles travel on a circle.
+Translational motion describe sea breeze, that occures on the shore on the
+sunrise and after the sunset. Rotational motion describe storms suchs as
+typhoons and hurricane. Translational motion is a particular case of circular
+motion when the radius of the circle is infinite. Given the scale of circular
+motion relative to the scale of translational motion, and the size of a typical
+ship hull we consider only translational motion in this paper.
+
+Since there is no rotational component, air flow is described by equations for
+irrotational inviscid incompressible fluid. In this context fluid velocity
+\(\vec\upsilon\) is determined as a vector gradient \(\vec\nabla\) of scalar
+velocity potential \(\phi\) and continuity equation and equation of motion are
+written as
+\begin{equation}
+ \label{eq-governing}
+ \begin{aligned}
+ & \Delta\phi = 0; \qquad \vec\upsilon=\vec\nabla\phi; \\
+ & \rho\frac{\partial\phi}{\partial{}t} +
+ \frac{1}{2}\rho\Length{\vec\nabla\phi}^2 +
+ p + \rho g z = p_0.
+ \end{aligned}
+\end{equation}
+Here \(p_0\) is atmospheric pressure, \(g\) is gravitational acceleration,
+\(\rho\) is air density, \(p\) is pressure. We seek solution to this system
+of equations for velocity potential \(\phi\). Continuity equation restricts
+the type of the function that can be used as the solution, and equation of
+motion gives the pressure for a particular velocity potential value.
+
+Ship hull boundary is defined by a parametric surface \(\vec{S}\) and surface
+normals \(\vec{n}\):
+\begin{equation*}
+\vec{S}=\vec{S}\left(a,b,t\right)
+\qquad
+a,b\in{}A=[0,1];
+\qquad
+\vec{n}=\frac{\partial\vec S}{\partial a} \times \frac{\partial\vec S}{\partial b}
+\end{equation*}
+The simplest parametric surface is infinite plane which has the same normal in
+each point. The computer model of a real ship hull is composed of many panels
+with different areas and different orientations that approximate continuous
+surface. On the boundary the projection of wind velocity on the surface normal
+is nought:
+\begin{equation}
+ \label{eq-boundary}
+ \vec\nabla\phi\cdot\vec{n} = 0;
+ \qquad
+ \vec{r} = \vec{S}.
+\end{equation}
+
+The solutions to the governing system of equations differ in how boundary is
+incorporated in them: in our model the boundary is taken into account by adding
+velocity of a reflected air particle in the solution. Velocity
+\(\vec\upsilon_r\) of the particle that is reflected from the surface with
+surface normal \(\vec{n}\) is given by the law of reflection
+(fig.~\ref{fig-law-of-reflection}):
+\begin{equation}
+ \label{eq-reflected}
+ \vec\upsilon_r = \vec\upsilon - 2\left(\vec\upsilon\cdot\vec{n}\right)\vec{n}.
+\end{equation}
+When we add velocity of incident and reflected air particles we get a vector
+that is parallel to the boundary. As we move away from the boundary its impact
+on the velocity decays quadratically with the distance. The known analytic
+solution for the potential flow around a cylinder contains similar term:
+\begin{equation*}
+ \phi\left(r,\theta\right) = U r \left( 1 + \frac{R^2}{r^2} \right) \cos\theta.
+\end{equation*}
+Here \(r\) and \(\theta\) are polar coordinates, \(R\) is cylinder radius and \(U\)
+is velocity magnitude.
+
+\begin{figure}
+ \centering
+ %\includegraphics{}
+ \caption{\label{fig-law-of-reflection}}
+\end{figure}
+
+In the following subsections we describe the solution that we obtained for the
+velocity field \emph{on} the boundary and \emph{near} the boundary.
+
+\subsection{Uniform translational motion on the static body surface}
+
+On the surface we neglect the impact of neighbouring panels on the velocity
+field on the ground that the real ship hull surface is smooth,
+i.e.~neighbouring panels have approximately the same normals. This assumption
+does not hold for aft and bow of some ships, and, as a result, velocity field
+near these features has stream lines with sharp edges. We consider this effect
+negligible for the determination of roll angle caused by the wind, since the
+area of panels that distort wind field is small compared to the area of all
+other panels.
+
+We seek solution to the governing system of equations~\eqref{eq-governing} with
+boundary condition~\eqref{eq-boundary} of the form
+\begin{equation*}
+\phi = \vec\upsilon\cdot\vec{r}
++ C \left(\vec\upsilon_r\cdot\vec{r}\right);
+\qquad
+\vec{r}=\left(x,y,z\right),
+\end{equation*}
+Here \(\vec{r}\) is spatial coordinate, \(C\) is the coefficient, and
+\(\vec\upsilon_r\) is velocity of reflected air particle defined
+in~\eqref{eq-reflected}. This solution is independent for each panel.
+Plugging the solution into boundary condition~\eqref{eq-boundary} gives
+\begin{equation*}
+\left(\vec\upsilon + C\vec\upsilon_r\right)\cdot\vec{n} = 0,
+\end{equation*}
+hence
+\begin{equation*}
+C = -\frac{ \vec\upsilon\cdot\vec{n} }{ \vec\upsilon_r\cdot\vec{n} } = 1
+\end{equation*}
+and velocity is written simply as
+\begin{equation}
+\vec\nabla\phi = \vec\upsilon + \vec\upsilon_r.
+\end{equation}
+
+This solution satisfies continuity equation. It gives velocity only at the
+centre of each ship hull panel, but this is sufficient to calculate pressure
+and force moments acting on the ship hull.
+
+\subsection{Uniform translational motion near the static body surface}
+
+Near the surface there are no neighbouring panels, the impact of which we can
+neglect, instead we add reflected particle velocities for all the panels and
+decay the velocity quadratically with the distance to the panel. Here we can
+neglect panels surface normals of which has large angles with the wind
+direction for efficiency, but they do not blow up the solution.
+
+We seek solution of the form
+\begin{equation*}
+\phi = \vec\upsilon\cdot\vec{r}
++ \iint\limits_{a,b\,\in{}A}
+C \frac{\vec\upsilon_r\cdot\vec{r}}{1+\Length{\vec{r}-\vec{S}}^2}
+da\,db,
+\end{equation*}
+where \(\Length{\cdot}\) is vector length. Plugging the solution into boundary
+condition and assuming that neighbouring panels do not affect each other (this allows
+removing the integral) gives the same coefficient \(C=1\), but velocity vector is written
+differently as
+\begin{equation*}
+\vec\nabla\phi =
+\vec\upsilon +
+\iint\limits_{a,b\,\in{}A}
+\left(
+ \frac{1}{s} \vec\upsilon_r
+ - \frac{2}{s^2} \left(\vec\upsilon_r\cdot\vec{r}\right) \left(\vec{r}-\vec{S}\right)
+\right)
+da\,db;
+\qquad
+s = 1+\Length{\vec{r}-\vec{S}}^2.
+\end{equation*}
+Besides the term for reflected air particle velocity that decays quadratically with
+the distance to the panel, there is a term that decays quaternary with the distance and
+that can be neglected because of this.
+
+This solution reduces to the solution on the boundary when \(\vec{r}=\vec{S}\)
+and takes into account impact of each panel on the velocity direction which decays
+quadratically with the distance to the panel.
+
+\section{Results}
+
+\subsection{Verification of potential flow around a cylinder}
+
+\section{Discussion}
+\section{Conclusion}
+
+Future work is to include circular motion in the model.
+
+\subsubsection*{Acknowledgements.}
+Research work is supported by Saint Petersburg State University (grants
+no.~TODO) and Council for grants of the President of the Russian Federation
+(grant no.~TODO).
+
+\bibliographystyle{splncs04}
+\bibliography{references}
+
+\end{document}
