Advanced Fortran Programming : 018 : Solving Linear Advection Equation(LAE) + GNUPlot Video Lecture | Introduction to Fortran Programming (AdvancedLevel) - Database Management

hello guys my name is Aaron and welcome
to my channel this series is a series of
tutorials on advanced Fortran
programming now in this tutorial we will
be looking at how we'll be looking at a
small example on how to introduce mod
you introduce global variables inside a
program first that's the first objective
second objective will be using ginyu
plot to give us a given animation as and
when you come to data and third of all
the third and third to explain what to
extend it to explain these two concepts
simultaneously what will we do using is
that we'll be using the linear at will
is trying to solve the linear reduction
equation using the forward time
backwards backwards space finite
difference scheme okay to do all the
processes okay now it's kind of a three
big three objective kind of a job but
that's but it's not it's not that
difficult and walk you guys through over
here so order one will but what will be
going to do is that I'll be taking that
linear advection equation for those of
you guys who haven't know what linear
the convection equation is its ultimate
simplification of it's one of the
ultimate simplifications of it on
navier-stokes equation wherein you'll
have the derivative of time there is a
velocity derivative of time okay plus a
constant velocity times the derivative
velocity equals zero okay you write it
as dou u by dou T plus u dou u by dou X
equals zero okay
or sometimes you know if this yeah I
mean sometimes you know you this they
call it as one dimensional one
dimensional our linear address in
equation also okay if we were to solve
this using v our time backward scheme
okay then I mean these equations have a
lot of solutions but there is one easy
solution using numerical method and for
that I'm using a finite difference
scheme and
find a different scheme that finance key
different scheme is actually power time
backward space okay but those of you
guys who don't know I recommend you just
check this in wiki but I promise you
it's not a very difficult thing it's not
a very difficult thing what we'll be
doing is they're using the time we wish
the values of the velocities in the
previous time step okay
supposing they want to calculate the
velocity at you know the current time
step okay let's say at T equals time T
equals one second okay then what I will
be doing is that if I'd if I device the
scheme properly then I will be using the
values in the previous time step with
previous time T equals zero to get the
values velocities at velocities are this
current step and if I get the velocity
square this current stub right it right
then I can use these values to I can use
these values to find the velocity the
next time step next time step and so on
he just goes this scheme just goes on
okay
now what I have here said I'm a model
modulo callers global because because
this in this if you want to declare any
real value any numbers or arrays known
arrays you want to declare any values as
global variable then it's not possible
directly in Fortran instead you can
define a module a small model on the top
and define all the variables into it and
you can make it global to everyone using
this option say okay it's in this option
safe and to import this model type used
module in the program simple as that
when when this is done because because
of the same program okay whichever
program are subtlety in her function or
even another module
whichever module that alters you okay
you are X here they that alteration is
replicated or reflected in all the
programs I mean all the Phi all the
subroutines suppose if I were to model
change these two values and for this
program la
it'll get reflected in the subroutine
also some proteins which use this module
and even in the functions that used this
module so it so and also this makes
these variables common to all the
program subroutines which ever use this
use and use global subgroup use global
statement okay I defined two parameters
namely R max equals thousand see max
equals thousand meaning the number of
rows to be thousand and the maximum
reversibly thousand maximum number of
columns to be thousand and I'm setting
the dimension to be ranging from zero to
R max 0 to the see max so it's a
thousand and one cross thousand one
matrix U which is which I've said
everything to be zero and then I have a
thousand roam a thousand column one D
matrix whose valleys arrangement whose
index range of 0 to 2000 which is X okay
and this being done this is the other
thing comes into picture I defined a
parameter pi l is for the length of a
length of the domain c is for the
velocity with which a wave is going to
travel okay in our program in this
program what I'm going to do is it I'm
going to take a sinusoidal a sine wave
okay and I'm going to place this sine
wave in the length of thousand mean a
thousand meters okay thousand meters and
I'm going to make this wave move forward
using this linear advection equation and
integrate this linear advection equation
with respect to time because of this non
zero velocity to - it'll be moving a 2
meter per second towards the right hand
side towards the right-hand side all
right
ok fair enough now with that being said
this integration will happen four
thousand seconds blabbin four thousand
seconds ok and there's a CFL value
there's a specific thing called a CFL
value I come I'll come to that and the
time step will be one I mean I'll be
included in degrading with for every one
second and then the space step is four
seconds meaning for four metres meaning
are the distance between two points I'm
going to take me I cannot take this
entire domain continuously so I have to
break this down into small finite points
in between so I am taking the distance
between two points to be four meters
okay and these are
some hydration variables nothing now SP
nel stands for the number of spaced
points okay
and this is equal to the total length
divided by the total length divided me
spit not spaced points space sections
whichever you can call it this is equal
to the total length divided by the
number divided by then I'm small
sections so if we have so if we have so
what what will this do this is just
calculate the number of sections would
be of sections in the length and that
will be stored here and then this line T
by Del T let's stir the number of time
sections number time gap between time
lag between two and the number of times
the steps will take from between two
number of time steps number times I'm
this other number of times CF LS the
kind of a stability criteria I mean for
this numerical stuff I on different
scheme where and if the CFL is kind of
fine one or something of more than one
the code is unstable if it is point five
something below that the code is stable
this linear regression equation code
that is I mean this you know advising
equation quoted others
okay and its defining a small farm at
here and what I'm doing instead of
setting the values of X to range from 0
to L okay the way I defined SS they were
DX here it's a such that it will just
multiply it will just increment the
value of x so in steps of 1 4 it's tough
stuff for so it will be 0 4 8 16 so 0 4
8 12 16 20 so on and so forth mm okay
here I set the corresponding sign value
corresponding sign value and I used to
PI DX by L into SS so that it the value
ranges from 0 to 0 between the men so
you'll have one big sine wave occupying
the entire thousand units letäôs and
units lengths thousand units length
let's say thousand is love domain and
then this is where I'm going to do the
linear advection scheme meaning
advection scheme here and this is the
main
since the zero the zero is actually that
the zero the time step the initial tie
initial condition and that is what I'm
sitting over here and here so around
time one one to TP okay from the first
value to the learning from the first
value to the first second to the last
second okay I'm going to have a second
to the thousand second I'm going to
integrate here I come to this point this
one later and what I'm doing is there
I'm just updating each and every space
point okay and you have to update with
every time step I have to update with
every point along the line along the
habit every point so what I'm doing is
that from the first from the second from
the second point actually from the
second point to the last last point I am
updating all the values you have impact
I mean numerically numerical image
increasing the value for my time
matching the value using this formula
over here you don't have you guys don't
have to worry about the formula just
like if you use this if you guys are
aware of power time backwards backwards
phase final different scheme and and you
can get this formula and if you guys are
unsure as to how I got it or if you
don't understand this second we keep
video or some other place you'll get the
founder nicely but it's not a difficult
one with a very very simple formula okay
a simple formula I'm just taking the
simple formula and then I'll explain you
guys this part over here what I'm doing
is that I'm taking the last well the
last point in the put in the zero the
time step the last point in the previous
time step I mean the point at the length
is thousand okay
I mean the end point of the wave in the
previous time step
I'm saving at the same time one and what
I'm doing here is that I'm setting the
for the starting point of the current
time step to be this value okay rrrh
what will happen is that when this if
this is not taken into consideration the
wave will be the way will be no integral
away will be
you will be time marching and the way
will be moving towards from left to
right left to right and when this
condition when this kind of a thing is
not put what will happen is that all
happen he said you move from left to
right and on the right left-hand side
you know filling with zeros and
ultimately after a point when the lire
wave leaves the dummy it will just full
of zeroes so instead what I'm doing is
that I'm just connecting the last point
to the first point there way what
happens it'll just kind there the
continuous flow of sine waves from one
end to the other
okay and that's about this that's about
this scheme and I had written a separate
do loop I could have written this both
in one shot but anyway I thought I
wanted to grow the first part also so I
think more nothing nothing important of
that what I'm doing is third in this do
loop the stay in the beginning it starts
from zero to TP this time I'm including
even the Rhenish first value of the
matrix you okay I'm starting a file okay
with ID unit ID one and the file name is
data dot txt okay and I'm writing each
and every okay and this and writing each
and every data point each and every data
point space from x equals zero to x
equals thousand okay and the
corresponding velocity values well as
velocity values correspond to that
particular time step in each and every
line and I'm proceeding with it for each
and every point okay and then when the
entire thing has written and close this
do loop or gets over and it prints all
the 250 points in of 250 points and then
the close command plug close command
closes the file and then I'm calling and
I'm using a system module there's a
system module and for transit from which
through which you can you can use this
to call shell functions the shell script
or a shell found shell commands in the
shell okay
a bash okay will you are using this
system command to call the call as
already written file called as green you
plot plot underscore space plot
underscore lae you're using a new plot
to plot this file okay and then I cannot
comment on this but if this we're using
this you can delete
expensive if there are any and then I'm
closing the file okay and now let's go
to this plot underscore a later GNU it's
nothing just a simple plot there's a
simple one-line keno plot script okay so
guys don't know what keno plotters I
recommend you go and check my previous
tutorial I mean not peruse to tell the
tutorial my basic series our basic
series of Fortran I would have mentioned
about the Sugino part slightly it's a
kind of plotting soft plotting software
made plotting program made for you know
made for Linux and run the G from the
Ginn from genome family and we get give
me a family so it's it's quite nice and
useful and it kind of works very nicely
per shift from the terminal so it's
governor to look at so I'm using that
over here I'm using that then that
script this this kind of syntax tells
you to plot the first first color in the
data to be grow and takes a second
column to be Carl take a second column
to be the y-axis call the first letter
to be the x-axis and the second data to
be the second column value to be the
y-axis and it just plots a script I mean
this plot gives a plot and a cinnamon is
plot this closest of so what do you get
here you will get a flicker you'll just
get a flicker of the function okay when
that being done okay
I just wrote a small shell script to
delete all the object files font files
execute of files index text files and
then I'm compiling the Fortran file in
this line execute a building in the
Fortran file in this line to produce an
executable and then I'm running
executable here okay and this file is
already made already given were already
given permissions to execute so the
shell script so what I'm going to do is
I'm going to run this okay simple f5
watch if you guys can see if you guys
can see that the sine function is
actually being plotted over here is it I
bought it for the flicker that's the
simple way I can make this work is if
you guys notice this
there this function will be moving from
left to right in a more or less in a
nice nice space and it will be plotting
for a thousand time steps and sometimes
it may not come but he can definitely
see that the entire sine wave is moving
from left to right okay this is that's
three that's the speciality of linear
advection equation it does nothing it
just transports whatever condition you
have to from one end to the other and
okay and this way if you see the sine
wave is kind of getting preserved and
it's going towards right and nasan when
the valleys go towards right that value
is being at taken to the left and then
the wave continues on this is because of
that adjustment we did in the last thing
I just when we did to the last thing now
this working it is printing nicely
hopefully I let me see if I can push
this on the side okay probably not okay
probably not this will be working like
this this will be working like this and
going on and this will just go on for
another two minute a minute or two but I
don't want to bore you guys but this is
kind of an example of how to use key
gnuplot
how to use game how to use gimmick plot
in in collaboration with in assistance
with Fortran to get some nice little
fancy plots okay that's all I have for
you guys in this tutorial hope you guys
like this tutorial thank you guys for
watching and I'll see you guys next
tutor
see ya bye