Midterm Project for HPC 2019
This code is designed to take an initial input, and evolve the state by the means of the Korteweg-de Vries equation of state, and 4th order Runge-Kutta.
NOTE: Currently, the code does not behave in the manner expected, despite being stable. The KdV equation is meant to simulate a wave cresting, with some independent waves with differing phase velocities passing through eachother. The current code keeps a stable wave, and corrects the wave from cresting too far. This is a bug that was not able to be corrected.
The code consists of two main parts: generating the initial conditions and evolving those conditions.
There are four current functions that can be created for a domain of length $L$:
In the file 'init_func_gen.cpp', you can define 'size' for the number of points in the simulation (the resolution), the starting point and ending point (end-start=L), and the choose the function you want to create.
When this is compiled and ran (which we will do below along the the evolution), you will get a data fle "KdVInitData.dat". This file will be read into program to evolve.
To actually run the simulation, two parameters need to be chosen in main.cpp. The first is 'numIter', which is the number of timesteps. Since we generally have a small space step, we will need a much smaller timestep, so many timesteps are usually required to see anything. $10^6$ is a good starting point.
The second value is 'save_every_nth_iter', which determines how often data will be exported. With such small timesteps, there is often very little change between steps, so it is often helpful to only save every nth step for plotting. We have found that having this value about three orders of magnitude lower than 'numIter'. For example if numIter=$10^6$, then save_every_nth_iter=$10^3$ is a good ballpark to start in.
First, clone the repo from Github. Then in the HPC2019-Project1-KdV directory (which I will call the master directory from now on), create a build/ directory, to keep the master directory clean. Change the parameters in init_func_gen.cpp and main.cpp to match what you want. Change directory to build/ and execute the following commands:
cmake ..
make
./init_data
./kdv KdVInitData.datDepending on your parameters, this last step could take a long time, or could go quickly. It will output a datafile called 'EvolvedData.dat', which has been organized to be plotted with gnuplot. Each timestep is organized by column, so to plot a particular timestep (say 300), you would just use
gnuplot -e "plot 'EvolvedData.dat' using 300"To make a video, gnuplot can be utilized with ffmpeg. Assuming numIter=$10^5$ and save_every_nth_iter=$10^2$, then numIter/save_every = $10^3$, and 50 frames a second, we can do
for i in $(seq 1 1000)
do echo $i
gnuplot -e "set term png size 800,600; set output 'plot_$i.png'; plot 'EvolvedData.dat' using $i"
done
ffmpeg -y -r 50 image2 -s 1920x1080 -i plot_%d.png -vcodec libx264 -crf 25 plot.mp4
rm plot_*That last line may be omitted if you want to keep all of the timestep plots.
An example of the video output is shown https://youtu.be/3xA9Cb5XLVM
Despite code around the for loops in the rk4.cpp file, there is no parallelization, as time tests show:
Cores: 1
File read in: 0.000143051
Calc time in: 2.70381
File written: 2.79171
Cores: 2
File read in: 0.000200987
Calc time in: 2.66961
File written: 2.75758
Cores: 3
File read in: 0.000150919
Calc time in: 2.68494
File written: 2.77323
Cores: 4
File read in: 0.000212908
Calc time in: 2.67505
File written: 2.76322
Cores: 5
File read in: 0.000210047
Calc time in: 2.69984
File written: 2.78853
Cores: 6
File read in: 0.000218153
Calc time in: 2.67993
File written: 2.76789
Cores: 7
File read in: 0.000221968
Calc time in: 2.68864
File written: 2.77655
Cores: 8
File read in: 0.000174999
Calc time in: 2.68136
File written: 2.76973