THE SIMULATION OF NAVIER STOKES EQUATION

This is a simulation of Navier Stokes Equation. I still keep on modifying these files to opimize, make it faster, greater. Let me know when you find something wrong or could be better.

SIMULATION MODEL

I adopted "The Arakawa C-types Staggared Grid" as a frame and "The Fractional Steps Method" to descrete each formula. And I also adopted "The Jacobi Method" as a iterative method to solve Poisson Eq. There are some for loops in functions that solve Advection Eqation because of complicated conditions.

ENVIRONMENTS

	Version etc
Machine	FMVA77GR
OS	Ubuntu 20.04.2 LTS
CPU	Intel(R) Core(TM) i7-2670QM CPU @ 2.20GHz
Python	3.8.10
conda	4.10.3
numpy	1.19.2
matplotlib	3.3.2

USAGE

This simulation is assuming a 2D room. It has height and width. Variable lx means its Width and ly does its height. When you want to do a 3D room, lx means its widt, ly means its depth and lz means its height. I put variables below.

Variable	Explanation
lx, ly, lz	The Lengths of Imaginary Room [m].
DELT	The Micro Time. Default is 0.01[s].
DELL	The Micro Length of The Micro Volume. Default is 0.1[m].
divlx, divly	Divided Numbers in x, y Directions.
ux, uy	Fluid Velocities in x, y Directions at Point (x, y)ndarray.
vx, vy	Temporary Velocities in x, y Directions.
ux_ast	Calculated Velocity in x Direction at Point (x, y)ndarray.
uy_ast	Calculated Velocity in y Direction at Point (x, y)ndarray.
div	Calculated Divergence at Point (x, y)ndarray(This Must be Nearly Zero).
RHO	Density(Uniform). Default is 1.293kg/m^3.
MU	The Dinamic Viscosity Coeficient. Default is 1.82e-8[Pa s].
h	Fan Height.
v0	The First Velocity Condition.
EPS	Tiny Error Constance That Evaluate Pressure. Default is 1e-8.
CNT_MAX	The Number That You Wanna Repeat. Default is 10000[times].
p	The Presure at Point (x, y).
fx, fy	The Forces in x, y Directions at Point (x, y)ndarray.
save	If You Want to Build Animation File in the Script, Set 'False'. If You Want to Build Animation File after Outputing All Img files, Set 'True'. Default is 'False'.
Main script file is simulater.py, so run this file or import this file to simulate.
Args in main function is lx, ly, (lz when you want to simulate 3D room), h, v0, theta, time_range and save.
I put the meanings of each arge above.
Output format is a animation file(animation_v0_theta.mp4) written by ffmpeg.
This will be created in this current directory.

EXSAMPLE

$ python simulater.py 2D

Example Result

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If you want to watch Example movie, visit my Google Drive. This is a 30s movie and might be a little bit heavy(9.3MB).

REFERENCE

https://warp.da.ndl.go.jp/info:ndljp/pid/3481431/www.eto.titech.ac.jp/contents/sub03/chapter01.html https://www.imi.kyushu-u.ac.jp/PDF/Hirose_20160612.pdf

Thank you for seeing my repository!