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CATEGORIES:Engineering Fluids Group Seminar
SUMMARY:Accelerating time averaging by adding a Lie deriva
tive of an auxiliary function - Professor Sergei C
hernyshenko (Imperial College London)
DTSTART;TZID=Europe/London:20221104T124500
DTEND;TZID=Europe/London:20221104T134500
UID:TALK183482AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/183482
DESCRIPTION:Obtaining time-averaged quantities with sufficient
accuracy can be challenging computationally for s
ystems with a chaotic behaviour. We replace the q
uantity being averaged with another quantity havin
g the same average but such that it is easier to a
verage. If W(t) is a bounded differentiable functi
on\, then the infinite time average of its derivat
ive is zero. Hence\, rather than numerically avera
ging the quantity of interest\, which we will deno
te F\, one can average F+dW/dt. We explore first t
he simplest way of choosing W(t)\, which is to ens
ure that the fluctuation amplitude of F+dW/dt is s
maller than the fluctuation amplitude of F. For th
is\, F and dW/dt should be correlated. This can of
ten be achieved by taking W(t)=V(x(t))\, where x i
s the state of the dynamical system. The talk will
discuss our tests of this idea. (A spoiler: the a
cceleration is only moderate but is worth doing be
cause it is easy. Further improvement requires pro
gress on interesting and challenging problems.) \n
LOCATION:LR12
CONTACT:Paras Vadher
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