Kinetic Theory
Pressure Single molecule momentum change on wall collision: Time between collisions on 1 wall: Single molecule x force: vx l
Pressure n molecule x force: 2- and 3-D velocity magnitude: Total force (both directions each axis):
Pressure Force on one out of 4 or 6 walls: RMS velocity: Force: 2D 3D Force on one out of 4 or 6 walls: RMS velocity: Force: Pressure:
Ideal Gas Law
Maxwell-Boltzmann Distribution
D2Q9 Velocity Distribution a |ea| wa faeq (r=1) 4/9 1 1/9 2 All 4: 3 4 5 √2 1/36 6 7 8
D2Q9 Velocity Distribution |ea| feq |ea|2feq 4/9 1 √2 1/9 2/9 vrms2 2/3
D2Q9 LBM