{Epot_2D_4el.PDE - Electric POTential D.Bakewell 22:30 Tu/14/12/1999 } title 'time-dependent 2D electric potential' SELECT regrid=off { use fixed grid for 2D problems } ! regrid=on {enable adaptive grid - warning can take too long} COORDINATES cartesian(x,y) VARIABLES Phi {Electric potential} Ex {Flux in X direction} Ey {Flux in X direction} XgrdE2 YgrdE2 DEFINITIONS om=10^(-1) EW=80*om {External boundary Width} EH=100*om {External boundary Height} IW=10*om {Internal electrode boundary Width} IH=1*om {Internal electrode boundary Height} IG=10*om {Internal boundary - gap between electrodes} a=0 {External rectangular boundary horizontal & vertical origin} b=a+EW c=a+EH h1c=10*om {First Internal rectangular boundary horizontal centre} vc=50*om {First Internal rectangular boundary vertical centre} d1=h1c-IW/2. e=vc-IH/2. f1=h1c+IW/2. g=vc+IH/2. V=1. d2=d1+IW+IG f2=f1+IW+IG d3=d2+IW+IG f3=f2+IW+IG d4=d3+IW+IG f4=f3+IW+IG EQUATIONS div[grad(Phi)]=0 {2D Laplace's equation } dx(Phi)=-Ex {for monitoring Electric field in X direction} dy(Phi)=-Ey {for monitoring Electric field in Y direction} Ex*dx(Ex)+Ey*dx(Ey)=XgrdE2 {grad E^2 in X dirctn} Ex*dy(Ex)+Ey*dy(Ey)=YgrdE2 {grad E^2 in Y dirctn} {2*Ey*dy(Ey)=grdEy2} BOUNDARIES Region 1 { define region 2 RECTANGLE boundary on horizontal plane } start (a,a) Value(Phi)=0 line to (b,a) Value(Phi)=0 {Neumann(Phi)=0} { natural(Phi)=0} line to (b,c) Value(Phi)=0 line to (a,c) {natural(Phi)=0} Value(Phi)=0 line to finish Value(Phi)=V start (d1,e) line to (f1,e) to (f1,g) to (d1,g) to finish Value(Phi)=-V start (d2,e) line to (f2,e) to (f2,g) to (d2,g) to finish Value(Phi)=V start (d3,e) line to (f3,e) to (f3,g) to (d3,g) to finish Value(Phi)=-V start (d4,e) line to (f4,e) to (f4,g) to (d4,g) to finish time 0 to 0.05 by 0.01 { establish time range and initial timestep } !PLOTS MONITORS for cycle=1 contour(Phi) contour(Ex) contour(Ey) contour(XgrdE2) contour(YgrdE2) HISTORIES history(Phi) at (10*om,10*om) END 8745