Recursive model for body in fluid

mercredi 31 juillet 2013

Good evening,

I've been trying to wrap my head around this problem for some time and I just can't seem to get it straight.

What I am trying to achieve:

I want to program a recursive model that calculates the position of a moving body in a fluid after a certain time.

What i have done already

I got as far as to simulate the movement due to a force applied at the center of the object.

In pseudo-code

Spoiler

for the speed at t = n

//calculate the drag force due to v_n-1 Wikipedia reference

F_d = 0.5*ρ*v_n-1²*C_d*A //

// add any external force that may have been applied when n-1<=t<n and the gravitational force

F_tot= F_d+F_ext+F_g

// calculate the acceleration of the object at n

a_n=F_tot/m

// assume the acceleration constant for dt so the velocity becomes

v = v_n-1 + a_n*dt

// calculate the new coordinates of the object based on v_n

This works fine as long as the time step dt is small enough (0<dt<0.00001)

The amount of calculations is too high. So i decided to approximate some more by limiting the rate of change of the drag force F_d.est = MAX(const,F_d)

This leads to a decent approximation with about a factor 100 less calculations per second (0<dt<0.001), which i think is sufficient. I observed a 10% disparity between the original and the approximation after 10^7 iterations.

What i'm struggling with

1) I'm stumped on how to model the angular motion when a force is applied a distance d from the center of the object

2) Is there a way to make the approximate the whole model more precisely but with the same dt = 0.001

If anyone has tips on how I can improve I would greatly appreciate it.

MrsTMouse