From dbe8e62ba9cf0f4f5bc7cdc518b8c1de50c8b584 Mon Sep 17 00:00:00 2001
From: Philip Mueller <philip.paul.mueller@bluemain.ch>
Date: Sun, 15 Mar 2020 16:56:14 +0100
Subject: [PATCH] Read the introduction, the final conclusion and the
acknoledgment again.
I have now decided what I am doing tomorrow.
I will first finish the project.
Then after I have bring anything in a passable state, I will read the experiment section again.
I will do this until i either
- run out of time
- finish
- die out of desperation
However the first two points are very unlikely (this was sarkasm).
---
.../thesisPage__acknowledgement.tex | 2 +-
.../thesisPage__finalConclOutlook.tex | 52 ++++++++++---------
.../thesisPage__introduction.tex | 42 +++++++--------
3 files changed, 49 insertions(+), 47 deletions(-)
diff --git a/doc/report/report_philip/thesisPage__acknowledgement.tex b/doc/report/report_philip/thesisPage__acknowledgement.tex
index 92d48323..8cd80c6c 100644
--- a/doc/report/report_philip/thesisPage__acknowledgement.tex
+++ b/doc/report/report_philip/thesisPage__acknowledgement.tex
@@ -12,7 +12,7 @@ I also would like to thank Andreas Urech for introducing me to Tikz and drawing
Also I would like to thank Till Ehrengruber and Andreas Urech for correcting and commenting on various parts of this manuscript.
%
\\
-I want to thank Michal Sudwoj for providing me with an introduction of how to use the animation utilities from \texttt{matplotlib}.
+I want to thank Michal Sudwoj for providing me with an introduction to the animation utilities from \texttt{matplotlib}.
% It was a jupyter notebook, but this is the best formulation.
At the end I what to thank my family for supporting my during this project.
diff --git a/doc/report/report_philip/thesisPage__finalConclOutlook.tex b/doc/report/report_philip/thesisPage__finalConclOutlook.tex
index 51237beb..10ce3480 100644
--- a/doc/report/report_philip/thesisPage__finalConclOutlook.tex
+++ b/doc/report/report_philip/thesisPage__finalConclOutlook.tex
@@ -3,27 +3,28 @@
\chapter{Final Conclusion and Outlook}~\label{chap:finConcOutlook}
In this chapter we will draw a final conclusion about the present work.
-In the previous chapter we have already discussed the experiments, but we focused on experiment at a time.
+In the previous chapter we have already discussed the experiments, but we focused on one experiment each time.
However in this chapter we will put the results into a larger context.
%
\\
-In addition, we will also discuss new aspects for further investigations.
+In addition, we will also discuss new directions for further investigations.
\section{Final Conclusion}~\label{chap:finConcOutlook:finCinc}
Despite their simple nature, we were able to gain valuable insights from our experiments.
We will now summarize them and put them in a larger context.
+ We will also give an answer to our original question.
- In this work we have studied the patterns generated by an object pulled through a media.
+ In this work we have studied patterns generated by an object pulled through a media.
While this sounds rather simple and trivial, it has important technological applications, which makes it a good test case.
%
We learned that these patterns look similar for different flows, if they have same Reynolds number.
- Further we saw, that if the Reynolds numbers are different, the flows are different as well.
+ Further we saw, that if the Reynolds numbers are different, the flows look different as well.
%
\\
Form these experiments we also learned, that flows at low Reynolds numbers behave laminar.
- But if the Reynolds number is increased, patterns start to look chaotic and flow vortexes were formed.
+ But if the Reynolds number is increased, patterns start to look chaotic and vortexes were formed.
This is a phenomena that is known as turbulence\footnote
{
We have discussed this already in section \ref{sec:experiments:constBall:Similarities:turb} on page \pageref{sec:experiments:constBall:Similarities:turb}, but we would like to repeat ourself here again.
@@ -56,7 +57,7 @@ In addition, we will also discuss new aspects for further investigations.
But we believe that the main problems lie with the unfit surface reconstruction and grid artefacts, which perturbed the signals.
%
\\
- However from a visual inspection of the pressure distribution, we concluded that inertia is indeed able to generate a \emph{plausible} pressure on the body's surface.
+ However from a visual inspection of the pressure distribution, we concluded that the method is indeed able to generate a \emph{plausible} pressure on the body's surface.
On top of that, we were not able to find a similar distribution in systems that ignored inertial effects.
@@ -74,15 +75,15 @@ In addition, we will also discuss new aspects for further investigations.
But our results were not as conclusive as they were for linear movements.
%
\\
- Our the data suggests that it is very likely the method is indeed able to handle rotational movements, maybe even as well as linear ones.
- Nevertheless we suggest more investigations on such processes.
+ Our data suggests that it is very likely that the method is indeed able to handle rotational movements, maybe even as well as linear ones.
+ Nevertheless we suggest more investigations on such movements.
We started this thesis with a question about, how well a code, written for geodynamical simulations, is able to handle conditions that are radical different?
%
In this thesis we did not find a catastrophic or inherent problem in such an endeavour.
But we are hesitating to unconditionally answer it with \emph{yes}.
- Instead we conclude that the method might be suitable for it, but more research is needed to conform it.
+ Instead we conclude that the method might be suitable for it and we think that this is \emph{very} likely, but we also think that more research is needed to conform it.
% END: Final Conclusion
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -90,23 +91,23 @@ In addition, we will also discuss new aspects for further investigations.
\section{Outlook and Further Work}~\label{chap:finConcOutlook:outlook}
When we have discussed the experiments in the last chapter, we also mentioned aspects which need further investigations.
- In this section however, we would like to discuss points, which are present in all systems.
- Further we will also points towards completely new directions for investigations.
+ In this section however, we would like to discuss points, that can be observed in all systems.
+ Further we will also point towards completely new directions for investigations.
\paragraph{Rotational Effects}~\label{chap:finConcOutlook:outlook:rot}
- We mentioned it before, most of the experiments we conducted for the present work were concerned with linear movements.
+ We mentioned it before, most of the experiments we conducted for the present work, were concerned with linear movements.
However most of the problems as well as unanswered questions, are related to rotational movements.
Such movements were studied in section \ref{sec:experiments:angMom} on page \pageref{sec:experiments:angMom}.
%
\\
Most of our problems were because initially we were unable to understand our data.
- In order to obtain data, that we were able to understand and deemed consistent, we had to tune, primarily lowering the time step, some system parameters.
+ In order to obtain data, that we were able to understand and deemed consistent, we had to tune some system parameters, mostly lowering the marker displacement.
- While it is important to study if angular momentum is conserved, we suggest put it on hold, at least for the time being.
+ While it is important to study if angular momentum is conserved, we suggest to put it on hold, at least for the time being.
%
- In order to verify if the method has a \emph{fundamental} problem with rotational effects, we suggest to focus on a new experiment.
+ In order to verify if the method has a \emph{fundamental} problem with rotational effects, we suggest to focus on a new kind experiment.
%
We recommend to study a Taylor--Couette flow.
%
@@ -121,14 +122,14 @@ In addition, we will also discuss new aspects for further investigations.
Further viscous effects are no problem, but \emph{needed} to transmit the rotation to other parts of the domain.
This also lowers the influence of ghost viscosity, since we can simply ignore the ``near wall'' behaviour and just look at the undisturbed fluid.
%
- And most importantly, after some time, the system will reach a known steady state solution and maintain it\footnote
+ And most importantly, after some time, the system will reach a known steady state solution and maintain it for all time\footnote
{
Actually we have done it already, the system is mentioned as \texttt{rotTC} in the appendix, see section \ref{sec:appendix:Corello:Ini:SetUp:TYPE} on page \pageref{sec:appendix:Corello:Ini:SetUp:TYPE}.
- It is quite similar to the usual \RotDisc{} setting, but there is an outer cylinder at rest to confine some fluid.
- The inner disc is kept rotating by manipulating its intrinsic velocity, this is done by a special material model.
+ It is quite similar to the usual \RotDisc{} setting, but there is an outer cylinder to confine fluid.
+ The inner disc is kept rotating by manipulating its intrinsic velocity, this is done by a special material model and the other disc is at rest.
%
\\
- Due to time constrains we were not able to fully review the data we have gathered on it nor to include it into this report.
+ Due to time constrains we were not able to fully review the data, we have gathered on it nor to include it into this report.
However our primarily analysis suggests, that the simulations indeed reach and maintain the analytical steady state.
%
We measured the radial velocity profiles and found that the curves look very similar to the expected one.
@@ -166,7 +167,7 @@ In addition, we will also discuss new aspects for further investigations.
\paragraph{Combined Effects}~\label{chap:finConcOutlook:outlook:magnus}
- We have tested linear and angular momentum separately, we have not combined them.
+ We have tested linear and angular momentum separately, we have not combined them in a single system.
Such as a disc that moves and rotates at the same time.
%
\\
@@ -180,7 +181,7 @@ In addition, we will also discuss new aspects for further investigations.
\paragraph{Marker Occupation}~\label{chap:finConcOutlook:outlook:markerOcc}
The velocity field of an incompressible flow has zero divergence, thus markers should not cluster or form voids.
- However this is a known problem, and different schemes were invented to solve the issues, \cite{Pusok2015}.
+ However this is a known problem, and different schemes were invented to solve the issues, see \cite{Pusok2015} for a discussion about it.
%
\\
Due to time constraints we were not able to investigate this point further.
@@ -195,17 +196,17 @@ In addition, we will also discuss new aspects for further investigations.
In some cases we also looked at the behaviour if the discretization was changed.
But in these experiments were primarily used to evaluate the influence of the ghost viscosity.
%
- We have not performed a systematic investigation on the influence on the spatial or temporal discretization.
+ We have not performed a systematic investigation on the influence of the spatial or temporal discretization.
% END: Dependency on discretization
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{Fluid-Fluid}~\label{chap:finConcOutlook:outlook:FluidFluid}
- The systems we have studied in this work, can be summarized as ``rigid body moves through a fluid.''
+ The systems we have studied in this work, can be described as ``rigid body moves through a fluid.''
While this is fine on its own, we should also start considering systems involving two fluids instead.
%
- For example such problems are covered in \cite{LeVeque}.
+ Such problems are covered in \cite{LeVeque}.
% END: Fluid-Fluid
%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -218,7 +219,8 @@ In addition, we will also discuss new aspects for further investigations.
}.
We did this because it offered us a particular simple geometry.
%
- However we suggest to simulate other objects including objects without symmetries, such that forces are not cancelled by it.
+ However we suggest to simulate other geometries as well.
+ We especially recommend to chose objects without symmetries, such that forces are not cancelling each other.
% END: Different geomtery
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
diff --git a/doc/report/report_philip/thesisPage__introduction.tex b/doc/report/report_philip/thesisPage__introduction.tex
index 227985f8..ebc1d471 100644
--- a/doc/report/report_philip/thesisPage__introduction.tex
+++ b/doc/report/report_philip/thesisPage__introduction.tex
@@ -19,7 +19,7 @@ When such large scales are considered, a single rock becomes irrelevant, it is j
The branch of physics studying such systems is known as \emph{continuum mechanics}.
%
-From the balance equations, formulated within its framework, the \emph{Navier--Stokes} equations can be derived.
+From the balance laws, formulated within its framework, the \emph{Navier--Stokes} equations can be derived.
They describe the flow in \emph{any} viscous continuum, which involve fluids \emph{but} solids as well.
% I know the Boltzmann equations are even more general, but earth is no rarified gas.
@@ -35,23 +35,22 @@ This simplification transforms the Navier--Stokes equations into the so called \
% Now we come to the meat
%
While the long term evolution, is indeed governed by the Stokes regime, other processes have a great influence on its course.
-We can characterize such processes by.
+We can attribute certain traits to them.
%
\begin{itemize}
- \item Most of them are rare.
+ \item Most of them are rare events.
- \item They affect the system on large spatial scales and can be seen as a \emph{cataclysm}.
+ \item They can be seen as some form of a \emph{cataclysm} and affects the system on large scales.
\item They only last for a short amount of time.
\end{itemize}
%
-Since they happen on extremely large scales, they have large scale influence on the further evolution of the system, and are able to change its course.
+Since they happen on extremely large scales, they will have large scale influence on the further evolution of the system.
%
-\\
-While they act on large \emph{spatial} scales, they happens over a very short amount of time, which means that the Stokes regime is not applicable to them.
-Thus we can no longer neglect inertia and have to consider the full Navier--Stokes equations again.
+However while they act on large \emph{spatial} scales, they happens over a very short amount of time, which means that the Stokes regime is not applicable to them.
+Thus we can no longer neglect inertial effects and have to consider the full Navier--Stokes equations again.
% How to simulate
@@ -60,28 +59,29 @@ Since they have great influence on the long term evolution it is important to ac
\\
A na\"ive solution for this problem would be to use \emph{two} programs.
One for simulating the cataclysm (program A) and one for the long term evolution (program B).
-Each time an ``event'' happens, program B is stopped and its state is stored to disc.
+Each time an ``event'' happens, program B is stopped and its state is written to disc.
Program A, will then load the state and simulate the cataclysm.
-After the system settled down, program A is stopped and its state is stored to disc.
-Program B would load the state and resume the long term evolution.
+After the system settled down, program A stops and write its state to disc.
+Program B would then load that state and resume the long term evolution.
%
There are several problems with this approach.
-The most severe one is, that we have to translate the internal format, every time, we switch between the programs.
+The most severe is, that we have to translate the internal format, every time, we switch between the programs.
%
\\
-A better, if not the best, approach would be to have a method that, with only a few changes, could handle both regimes.
+A better, if not the best, approach would be to have a method can handle both regimes.
%
% Main goal
%
-In this thesis, we have implemented a code suited for simulating geodynamical processes, that are governed by the Stokes regime.
+For this thesis, we have implemented a code suited for simulating geodynamical processes, that are governed by the Stokes regime.
We have applied a simple extension to it, such that it is able to solve the Navier--Stokes equations and thus handling inertial processes as well.
However no further adaptions to the code were made.
%
\\
-Our main question was, if a method, that was designed to simulate geodynamical processes, is also able to handle processes governed by radical different regimes?
-
+Our main question was, if a method, that was designed to simulate geodynamical processes, is also able to handle processes governed by radical different regimes, after some basic modifications were applied to it?
+%
+\\ % for below
Chapter \ref{chap:GoverningEq} is dedicated to the theoretical foundations.
In \ref{sec:GoverningEq:TheNSEQ} we will present an heuristic derivation of the Navier--Stokes equations.
@@ -90,16 +90,16 @@ We will also discuss how the classical method, can be extended such that the Nav
%
\\
We will continue our discussion about the MIC method in chapter \ref{chap:discretization}.
-While similar to \ref{sec:GoverningEq:UsedScheme}, it will contain much more details.
-Before, we have described what each step has to do, but we did not explain \emph{how} this is done.
-In this chapter we will present a particular choice for them.
+While similar to \ref{sec:GoverningEq:UsedScheme}, it will contain much more detailed description of the method.
+Before, we have described what each step has to do, but we did not explain \emph{how} this should be done.
+A \emph{particular} choice for the different tasks will be presented here.
%
\\
In chapter \ref{chap:experiments}, we will present and discuss the results of several experiments that we have conducted.
%
\\
-In chapter \ref{chap:finConcOutlook} will present a final conclusion about the project.
+In chapter \ref{chap:finConcOutlook} will then present a final conclusion about the project.
As well as several points, that needs further research.
-A technical documentation for the programs, that we wrote to perform the simulations, as well as the analysis software, that was developed for analysing the data, can be found in the appendixes \ref{chap:appendix:EGD}, \ref{chap:appendix:Corello} and \ref{chap:appendix:sibyl}.
+A technical documentation for the programs, that we wrote to perform the simulations, as well as the analysis software, that was developed, can be found in the appendixes \ref{chap:appendix:EGD}, \ref{chap:appendix:Corello} and \ref{chap:appendix:sibyl}, starting at page \pageref{chap:appendix:EGD}.
--
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