Advection (Part 2). Hank Childs, University of Oregon. October 18 th , 2013. Announcements. Bonus OH Mon 1-2 Quiz on Weds Project #4 is out, due Mon. Today’s lecture: Review of advection Overview of project 4 More particle advection usages.
Hank Childs, University of Oregon
X = B-A
This is an ordinary differential equation (ODE).
S(t0) = p0
S(ti) = AdvanceStep(S(t(i-1))
ShouldContinue(): keep stepping as long as it returns true
How to do an advance?
S1 = AdvanceStep(S0)
S4 = AdvanceStep(S3)
S2 = AdvanceStep(S1)
This picture is misleading:
steps are typically much smaller.
Answer: ((0.99, 1.98, 0.99), 0.01)
v(ti+h, pi+h*k3) = k4
v(ti+h/2, pi+h/2*k2) = k3
v(ti, pi) = k1
v(ti+h/2, pi+h/2*k1) = k2
Evaluate 4 velocities, use combination
to calculate pi+1
Quiz: which one is time and which one is distance?
Streamlines in the “fish tank”
Will do an example on the board
Generation of Accurate Integral Surfaces in Time-Dependent Vector Fields. C. Garth, H. Krishnan, X. Tricoche, T. Bobach, K. I. Joy. In IEEE TVCG, 14(6):1404–1411, 2007
Vortex system behind ellipsoid