Sample Problems > Usage > Accuracy > rotating

{

ROTATING_SHAPE.PDE

This test rotates a sinusoidal shape around a center at a fixed timestep of one degree per timestep

to demonstrate the degradation of the shape after one, two and three circuits.

}

title 'One Degree per Timestep'

select

fixdt ! use a fixed timestep

errlim=1e-4

variables

definitions

wide=1

rad=sqrt((x+0.5)^2+y^2)

! define the initial shape as one pulse of (cos(ang)+1)

u0 = if(rad < 0.25) then 0.5*(cos(4*rad*pi)+1) else 0

vel = vector(-y,x)

initial values

u = u0

equations

dt(u) + dot(vel,grad(u)) = 0

boundaries

! define a square region to rotate in

Region 1

start(-wide,-wide) value(u)=0

line to(wide,-wide) to(wide,wide) to(-wide,wide) to close

time=0 to 6*pi by pi/180 ! one degree per timestep

monitors

for t=0 by pi/4 to endtime

grid(x,y)

contour(u)

plots

for t=0 by 2*pi to endtime

grid(x,y)

contour(u)

report(globalmax(u))

report(globalmax_x(u))

surface(u)

contour(u-u0)

contour(dxx(u)) contour(dxy(u)) contour(dyy(u))

for t=2*pi

elevation(u, u0) from(-1,0) to (1,0)

for t=4*pi

elevation(u, u0) from(-1,0) to (1,0)

for t=6*pi

elevation(u, u0) from(-1,0) to (1,0)

end

rotating_shape