jawa0 / jakmt

Ideal Gas Simulation using Kinetic Molecular Theory (KMT)

jakmt - Ideal Gas Simulation using Kinetic Molecular Theory (KMT)

Overview

• Simulate a gas by simulating the individual molecules as idealized balls bouncing off each other.
• Kinetic Molecular Theory (KMT) Assumptions
  • The molecules are modeled as spheres that bounce off each other, and off the walls of the container, undergoing fully elastic collisions.
  • Other than collisions, the molecules have no other interactions with each other, or the walls of the container. For instance, no electronic attraction or repulsion.

Why not use a continuous media fluid-simulation approach, like they do in computer graphics? What about Navier-Stokes? Why simulate individual molecules?

• I want the fluid to be compressible
  • I want to be able to simulate shock-waves by e.g. sending a sphere at high speed through the gas.
• I'm not mathed-up enough yet to implement Navier-Stokes. See: Bridson. Fluid Simulation for Computer Graphics.

See Wikipedia's page on the Kinetic Theory of Gases. Or this summary of kinetic theory on HyperPhysics.

Building / Running

To build jakmt, you'll need cmake. Running cmake generates the Makefile for your system, which you then build.

Assuming that you're in the jakmt repository directory:

mkdir build
cd build
cmake ..
make
./jakmt

Challenges

There's lots of molecules. LOTS.

There are Na = 6.02E23 molecules of gas in a mole. A mole is like a dozen, but for molecules. It's just a unit of counting. That's a 6 followed by 23 zeroes: 600,000,000,000,000,000,000,000. At Standard Temperature and Pressure (STP), which is 0 degrees C and 1 bar of pressure, one mole of ideal gas has a volume of 22.7L.

How many molecules are there in one cubic millimetre? 1 mm^3 = 10^-9 m^3 22.7 L/mol ~= 0.02 m^3/mol <=> 50 mol/m^3

1mm^3 contains 3E16 molecules! That's 30,000,000,000,000,000

So, in 2019 that's a bit beyond my ability to simulate. How about a cubic micro-metre?

1 cubic micron contains 3E7 molecules

That's 30 million. Okay, so let's try to simulate 30 million molecules bouncing around. Go!

Current Performance

Doing O(n^2) collision detection on 30M particles will take about 34 days on my 2017 laptop. :/

TODO

• Implement a collision query acceleration data structure, so we're not doing O(n^2) collision detection. I'm going to try Thatcher Ulrich's Loose Octrees.
• Multithreading
• GPU acceleration
• Distribute across multiple machines

Current Performance

My 2017 Mac Laptop

=====================================================
jaKMT - Kinetic Molecular Theory Ideal Gas Simulation
=====================================================
Number of hardware threads supported: 4
  NOTE: Currently only using one thread.

C++ high-resolution clock period: 1 / 1000000000
=====================================================

Allocating memory for 2 buffers of 30000000 particles...
Finished allocating memory.
Allocation took 1.98674 seconds.

Simulation time step: 1e-09 s
Simulation box side: 1e-06 m
Molecule kinetic diameter: 3.64e-10 m
	=> 0.000182 box widths
Initial speed coordinate: 500 m/s
	=> 0.5 box widths / step
Initializing particle positions and velocities...
Num particles per lattice edge: 311
(-0.498392, -0.498392, -0.498392)
Stepping particles...
Particle step took 1.63687 seconds.
Finding collisions...
0...
Checked 0 out of 4.5e+14 pairs.
Percent done:   0.0000 %
100...
Checked 2.99999e+09 out of 4.5e+14 pairs.
Percent done:   0.0007 %
Pairs processed since last update: 2.99999e+09
Took 19 seconds.
Collision pairs processed per second: 1.57894e+08
Remaining time: 791.663 hours.
First collision time: 0.00358602
200...
Checked 5.99998e+09 out of 4.5e+14 pairs.
Percent done:   0.0013 %
Pairs processed since last update: 2.99998e+09
Took 19 seconds.
Collision pairs processed per second: 1.57894e+08
Remaining time: 791.66 hours.
First collision time: 0.00358602
300...
Checked 8.99995e+09 out of 4.5e+14 pairs.
Percent done:   0.0020 %
Pairs processed since last update: 2.99997e+09
Took 18 seconds.
Collision pairs processed per second: 1.66665e+08
Remaining time: 749.991 hours.
First collision time: 0.00358602
400...
Checked 1.19999e+10 out of 4.5e+14 pairs.
Percent done:   0.0027 %
Pairs processed since last update: 2.99996e+09
Took 20 seconds.
Collision pairs processed per second: 1.49998e+08
Remaining time: 833.321 hours.
First collision time: 0.00358602
500...
Checked 1.49999e+10 out of 4.5e+14 pairs.
Percent done:   0.0033 %
Pairs processed since last update: 2.99995e+09
Took 18 seconds.
Collision pairs processed per second: 1.66664e+08
Remaining time: 749.986 hours.
First collision time: 0.00326668