2D_StretchX

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{

This example demonstrates moving meshes in 2D.

A 1D Gaussian distribution is defined on a 2D mesh.

The mesh is then stretched to twice its initial X size,

while the Gaussian remains fixed in space.

Mesh motion is imposed by explicit positions of the endpoints.

}

TITLE "2D brick stretching in x"

VARIABLES

xm = move(x)

DEFINITIONS

Hl = 1/2

wid = 0.01

gwid = 0.15

u0= exp(-x^2/gwid^2)

lmove = Hl + t

INITIAL VALUES

u= u0

vx = x/Hl

EQUATIONS

U: dt(u)=100*dyy(u)

Vx: div(grad(vx)) = 0

Xm: dt(xm) = vx

BOUNDARIES

REGION 1

START(-Hl,0) Line to (Hl,0)

value(u)=0 value(vx)=1 value(xm)=lmove

line to (Hl,wid)

natural(u)=0 nobc(vx) nobc(xm)

line to (-Hl,wid)

value(u)=0 value(vx)=-1 value(xm)=-lmove

line to close

TIME 0 TO 0.5 by 0.01

MONITORS

for time=0

grid(x,10*y) as "Initial mesh"

contour(vx)

for cycle=1

grid(x,10*y)

contour(u) zoom(-2*Hl,0, 4*Hl,2*wid)

contour(vx) zoom(-2*Hl,0, 4*Hl,2*wid)

contour(dt(xm)) zoom(-2*Hl,0, 4*Hl,2*wid)

elevation(u,u0) from(-10*Hl,wid/2) to (10*Hl,wid/2) range (0,1)

elevation(vx) from(-10*Hl,wid/2) to (10*Hl,wid/2) range (0,1)

elevation(dt(xm)) from(-10*Hl,wid/2) to (10*Hl,wid/2) range (0,1)

PLOTS