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{ 2D_STRETCH_XY.PDE
This example demonstrates moving meshes in 2D.
A Gaussian distribution is defined on a 2D mesh.
The mesh is then stretched to twice its initial size,
while the Gaussian remains fixed in space.
Output plots show that the Gaussian has retained its shape as
it moves through the mesh.
Mesh motion is imposed by explicit positions of the endpoints.
}
TITLE "stretching brick"
SELECT
regrid=off
VARIABLES
u
xm = move(x)
ym = move(y)
DEFINITIONS
Hl = 1/2
gwid = 0.15
u0 = exp(-(x^2+y^2)/gwid^2)
lmove = Hl + t
ms = gwid^2/u0
vx = dt(xm)
vy = dt(ym)
INITIAL VALUES
u = u0
dt(xm) = x/Hl
dt(ym) = y/Hl
EULERIAN EQUATIONS
U: dt(u)=0
Xm: div(grad(vx))=0
Ym: div(grad(vy))=0
BOUNDARIES
REGION 1
mesh_spacing = ms
START(-Hl,-Hl)
value(u)=0 nobc(xm) value(ym)=-lmove
line to (Hl,-Hl)
value(u)=0 value(xm)=lmove nobc(ym)
line to (Hl,Hl)
value(u)=0 nobc(xm) value(ym)=lmove
line to (-Hl,Hl)
value(u)=0 value(xm)=-lmove nobc(ym)
line to close
TIME 0 TO 0.5 by 0.01! 10
MONITORS
for cycle=1
grid(x,y) zoom(-Hl-1/2,-Hl-1/2, 2*Hl+1,2*Hl+1)
contour(u)
elevation(u,u0) from(-10*Hl,0) to (10*Hl,0) range (0,1)
elevation(u,u0) from(0,-10*Hl) to (0,10*Hl) range (0,1)
PLOTS
for time=0.1 by 0.1 to endtime
grid(x,y) zoom(-Hl-1/2,-Hl-1/2, 2*Hl+1,2*Hl+1)
contour(u)
contour(u-u0) as "True Total Error"
contour(space_error()) as "Estimated Step Error"
elevation(u,u0) from(-10*Hl,0) to (10*Hl,0) range (0,1)
elevation(vx) from(-10*Hl,0) to (10*Hl,0) range (0,1)
elevation(u,u0) from(0,-10*Hl) to (0,10*Hl) range (0,1)
elevation(vy) from(0,-10*Hl) to (0,10*Hl) range (0,1)
END