Second Computational Aeroacoustics (CAA) Workshop on ...

where
Find the scattered sound field for _v = 8rr.
(0.2)2 sinwt.
GiveD(0) = lira rp2 for0 = 90 ° to 180 ° at A0 = 1 degree (--=
State your grid specification and At used in the Computation.
Problem 2
time average).
This is the same as problem 1 above except that there is no time periodic source; i.e.,
S = 0 in equation (3). Consider an initial value problem with initial conditions t = 0,
u = v = 0, and
Find p(t) at the three points A (r = 5,0 = 90°), B (r = 5,0 = 135°), C (r = 5,0 = 180°).
Give p(t) from t = 6 to t = 10 with At = 0.01. State the grid specification and the At
used in the computation.
Problem 3
Solve the axisymmetric linearized Euler equations to predict the scattering of acoustic
waves from a sphere. The governing equations (including the acoustic source) are given by
[i][i]I
0 0 0
+N =
p
--_ + Aexp(-B(gn2)((x - x,) 2 + r2))cos(wt)
The length scale is given by the radius of the sphere, R. The ambient speed of sound,
ao,, and the ambient density, po_, are used as the velocity and density scales, respectively.
The pressure is nondimensionalized by 2
p_ao_ and time is scaled by R/a_. For the source,
use A = 0.01, B = 16, xs = 2 and w = 20rr.
There are no constraints on the maximum size of the domain or number of grid points;
although, CPU time will be used in part to assess the algorithm.
Submit the RMS pressure along the circle x 2 + y2 = 25 at A0 = 1 °, 0 measured from
the x-axis. The computer used, CPU time per timestep, the number of timesteps per
period of the source, the number of grid points and CPU memory per grid point should
also be reported.
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