% FEMLAB Model M-file % Generated 18-Mar-2002 20:23:25 by FEMLAB 2.1.0.127. flclear fem % FEMLAB Version clear vrsn; vrsn.name='FEMLAB 2.1'; vrsn.major=0; vrsn.build=127; fem.version=vrsn; % Space dimensions fem.sdim={'x','y'}; % Geometry clear s c p p=[0 0 5 15 25 25 25;0 100 0 15 30 45 100]; rb={1:7,[1 1 2 3 4 5 6;2 3 7 4 5 6 7],zeros(3,0),zeros(4,0)}; wt={zeros(1,0),ones(2,7),zeros(3,0),zeros(4,0)}; lr={[NaN NaN NaN NaN NaN NaN NaN],[0 1 0 1 1 1 1;1 0 1 0 0 0 0],zeros(2,0), ... zeros(2,0)}; CO1=solid2(p,rb,wt,lr); objs={CO1}; names={'CO1'}; s.objs=objs; s.name=names; objs={}; names={}; c.objs=objs; c.name=names; objs={}; names={}; p.objs=objs; p.name=names; drawstruct=struct('s',s,'c',c,'p',p); fem.draw=drawstruct; fem.geom=geomcsg(fem); % Recorded command sequence clear appl % Application mode 1 appl{1}.mode='flpdec2d(1,''dim'',{''u'',''u_t''},''sdim'',{''x'',''y''},''submode'',''std'',''tdiff'',''on'')'; appl{1}.name='c1'; appl{1}.dim={'u','u_t'}; appl{1}.border='off'; appl{1}.var={}; appl{1}.form='coefficient'; appl{1}.assign={'abscu1x';'abscu1x_c1';'absga1x';'absga1x_c1';'absux'; ... 'absux_c1'}; appl{1}.equ.da={{{'1'}}}; appl{1}.equ.c={{{'B*x'}}}; appl{1}.equ.al={{{'0';'0'}}}; appl{1}.equ.ga={{{'0';'B*x.*uy'}}}; appl{1}.equ.be={{{'2*B';'x'}}}; appl{1}.equ.a={{{'0'}}}; appl{1}.equ.f={{{'0'}}}; appl{1}.equ.ind=1; appl{1}.usage=1; appl{1}.bnd.q={{{'0'}},{{'0'}},{{'0'}},{{'0'}}}; appl{1}.bnd.g={{{'0'}},{{'0'}},{{'0'}},{{'0'}}}; appl{1}.bnd.h={{{'1'}},{{'1'}},{{'0'}},{{'1'}}}; appl{1}.bnd.r={{{'0'}},{{'x.^2/25'}},{{'0'}},{{'1'}}}; appl{1}.bnd.type={'dir','dir','dir','dir'}; appl{1}.bnd.ind=[1 2 3 4 4 4 4]; appl{1}.init.sd={{{'0'}}}; appl{1}.init.ind=1; fem.appl=appl; % Initialize mesh fem.mesh=meshinit(fem,... 'Out', {'mesh'},... 'jiggle', 'mean',... 'Hcurve', 0.29999999999999999,... 'Hgrad', 1.3,... 'Hpnt', {10,[]}); % Dimension fem.dim={{'u'}}; % Boundary conditions fem.border=0; % Usage fem.usage=1; % Problem form fem.form='general'; % Differentiation fem.diff={'ga','g','f','r'}; % Differentiation simplification fem.simplify='on'; % Differentiation rules fem.rules={}; % Define variables fem.variables={... 'D', 5,... 'B', 1.3}; % Define application mode variables fem.var={}; % Boundary conditions clear bnd bnd.q={{{'0'}},{{'0'}},{{'0'}},{{'0'}}}; bnd.g={{{'0'}},{{'0'}},{{'0'}},{{'0'}}}; bnd.h={{{'1'}},{{'1'}},{{'0'}},{{'1'}}}; bnd.r={{{'-u'}},{{'x./3-u'}},{{'0'}},{{'1-u'}}}; bnd.var={}; bnd.ind=[1 2 3 4 4 4 4]; fem.bnd=bnd; % PDE coefficients clear equ equ.da={{{'1'}}}; equ.c={{{'B*x','0';'0','B*x-B*x'}}}; equ.al={{{'0';'0'}}}; equ.ga={{{'-B*x.*ux';'B*x.*uy-B*x.*uy'}}}; equ.be={{{'2*B';'x'}}}; equ.a={{{'0'}}}; equ.f={{{'-(2*B.*ux+x.*uy)'}}}; equ.var={'absux_c1','sqrt(ux.^2+uy.^2)','absga1x_c1', ... 'sqrt(ga1x.^2+ga1y.^2)'}; equ.ind=1; fem.equ=equ; % Evaluate initial condition fem.init=asseminit(fem,... 'context','local',... 'init', struct('sd',{{{{'0'}}}},'ind',{1})); % Solve problem fem.sol=femlin(fem,... 'out', {'sol'},... 'context','local',... 'sd', 'off',... 'Epoint', 'gauss2',... 'Nullfun','flnullorth',... 'Tpoint', 'gauss2',... 'Solcomp',1,... 'method', 'eliminate'); % Save current mesh restart.mesh=fem.mesh; restart.usage=fem.usage; % Plot solution postplot(fem,... 'context','local',... 'contdata',{'u','cont','on'},... 'contlevels',18,... 'contstyle','color',... 'contlabel','off',... 'contmaxmin','off',... 'contbar','on',... 'contmap','cool',... 'geom', 'on',... 'geomcol','bginv',... 'view', [0 90],... 'title', 'Contour: u (u) ',... 'renderer','zbuffer',... 'solnum', 1,... 'axisvisible','on') % Dimension fem.dim={{'u'}}; % Boundary conditions fem.border=0; % Usage fem.usage=1; % Problem form fem.form='general'; % Differentiation fem.diff={'ga','g','f','r'}; % Differentiation simplification fem.simplify='on'; % Differentiation rules fem.rules={}; % Define variables fem.variables={... 'D', 5,... 'B', 1.3}; % Define application mode variables fem.var={}; % Boundary conditions clear bnd bnd.q={{{'0'}},{{'0'}},{{'0'}},{{'0'}}}; bnd.g={{{'0'}},{{'0'}},{{'0'}},{{'0'}}}; bnd.h={{{'1'}},{{'1'}},{{'0'}},{{'1'}}}; bnd.r={{{'-u'}},{{'x/D-u'}},{{'0'}},{{'1-u'}}}; bnd.var={}; bnd.ind=[1 2 3 4 4 4 4]; fem.bnd=bnd; % PDE coefficients clear equ equ.da={{{'1'}}}; equ.c={{{'B*x','0';'0','B*x-B*x'}}}; equ.al={{{'0';'0'}}}; equ.ga={{{'-B*x.*ux';'B*x.*uy-B*x.*uy'}}}; equ.be={{{'2*B';'x'}}}; equ.a={{{'0'}}}; equ.f={{{'-(2*B.*ux+x.*uy)'}}}; equ.var={'absux_c1','sqrt(ux.^2+uy.^2)','absga1x_c1', ... 'sqrt(ga1x.^2+ga1y.^2)'}; equ.ind=1; fem.equ=equ; % Evaluate initial condition fem.init=asseminit(fem,... 'context','local',... 'init', struct('sd',{{{{'0'}}}},'ind',{1})); % Solve problem fem.sol=femlin(fem,... 'out', {'sol'},... 'context','local',... 'sd', 'off',... 'Epoint', 'gauss2',... 'Nullfun','flnullorth',... 'Tpoint', 'gauss2',... 'Solcomp',1,... 'method', 'eliminate'); % Save current mesh restart.mesh=fem.mesh; restart.usage=fem.usage; % Plot solution postplot(fem,... 'context','local',... 'contdata',{'u','cont','on'},... 'contlevels',18,... 'contstyle','color',... 'contlabel','off',... 'contmaxmin','off',... 'contbar','on',... 'contmap','cool',... 'geom', 'on',... 'geomcol','bginv',... 'view', [0 90],... 'title', 'Contour: u (u) ',... 'renderer','zbuffer',... 'solnum', 1,... 'axisvisible','on') % Refine mesh fem.mesh=meshrefine(fem,... 'out', {'mesh'},... 'rmethod','regular'); % Refine mesh fem.mesh=meshrefine(fem,... 'out', {'mesh'},... 'rmethod','regular'); % Dimension fem.dim={{'u'}}; % Boundary conditions fem.border=0; % Usage fem.usage=1; % Problem form fem.form='general'; % Differentiation fem.diff={'ga','g','f','r'}; % Differentiation simplification fem.simplify='on'; % Differentiation rules fem.rules={}; % Define variables fem.variables={... 'D', 5,... 'B', 1.3}; % Define application mode variables fem.var={}; % Boundary conditions clear bnd bnd.q={{{'0'}},{{'0'}},{{'0'}},{{'0'}}}; bnd.g={{{'0'}},{{'0'}},{{'0'}},{{'0'}}}; bnd.h={{{'1'}},{{'1'}},{{'0'}},{{'1'}}}; bnd.r={{{'-u'}},{{'0.2*x-u'}},{{'0'}},{{'1-u'}}}; bnd.var={}; bnd.ind=[1 2 3 4 4 4 4]; fem.bnd=bnd; % PDE coefficients clear equ equ.da={{{'1'}}}; equ.c={{{'B*x','0';'0','B*x-B*x'}}}; equ.al={{{'0';'0'}}}; equ.ga={{{'-B*x.*ux';'B*x.*uy-B*x.*uy'}}}; equ.be={{{'2*B';'x'}}}; equ.a={{{'0'}}}; equ.f={{{'-(2*B.*ux+x.*uy)'}}}; equ.var={'absux_c1','sqrt(ux.^2+uy.^2)','absga1x_c1', ... 'sqrt(ga1x.^2+ga1y.^2)'}; equ.ind=1; fem.equ=equ; % Evaluate initial condition fem.init=asseminit(fem,... 'context','local',... 'init', struct('sd',{{{{'0'}}}},'ind',{1})); % Solve problem fem.sol=femlin(fem,... 'out', {'sol'},... 'context','local',... 'sd', 'off',... 'Epoint', 'gauss2',... 'Nullfun','flnullorth',... 'Tpoint', 'gauss2',... 'Solcomp',1,... 'method', 'eliminate'); % Save current mesh restart.mesh=fem.mesh; restart.usage=fem.usage; % Plot solution postplot(fem,... 'context','local',... 'contdata',{'u','cont','on'},... 'contlevels',18,... 'contstyle','color',... 'contlabel','off',... 'contmaxmin','off',... 'contbar','on',... 'contmap','cool',... 'geom', 'on',... 'geomcol','bginv',... 'view', [0 90],... 'title', 'Contour: u (u) ',... 'renderer','zbuffer',... 'solnum', 1,... 'axisvisible','on') % Plot solution postplot(fem,... 'context','local',... 'contdata',{'u','cont','on'},... 'contlevels',18,... 'contstyle','color',... 'contlabel','off',... 'contmaxmin','off',... 'contbar','on',... 'contmap','cool',... 'geom', 'on',... 'geomcol','bginv',... 'view', [0 90],... 'title', 'Contour: u (u) ',... 'renderer','zbuffer',... 'solnum', 1,... 'axisvisible','on') % Plot solution postplot(fem,... 'context','local',... 'contdata',{'u','cont','on'},... 'contlevels',18,... 'contstyle','color',... 'contlabel','off',... 'contmaxmin','off',... 'contbar','on',... 'contmap','cool',... 'geom', 'on',... 'geomcol','bginv',... 'view', [0 90],... 'title', 'Contour: u (u) ',... 'renderer','zbuffer',... 'solnum', 1,... 'axisvisible','on') % Plot solution postplot(fem,... 'context','local',... 'contdata',{'u','cont','on'},... 'contlevels',18,... 'contstyle','color',... 'contlabel','off',... 'contmaxmin','off',... 'contbar','on',... 'contmap','cool',... 'geom', 'on',... 'geomcol','bginv',... 'view', [0 90],... 'title', 'Contour: u (u) ',... 'renderer','zbuffer',... 'solnum', 1,... 'axisvisible','on') % Dimension fem.dim={{'u'}}; % Boundary conditions fem.border=0; % Usage fem.usage=1; % Problem form fem.form='general'; % Differentiation fem.diff={'ga','g','f','r'}; % Differentiation simplification fem.simplify='on'; % Differentiation rules fem.rules={}; % Define variables fem.variables={... 'D', 5,... 'B', 1.3}; % Define application mode variables fem.var={}; % Boundary conditions clear bnd bnd.q={{{'0'}},{{'0'}},{{'0'}},{{'0'}}}; bnd.g={{{'0'}},{{'0'}},{{'0'}},{{'0'}}}; bnd.h={{{'1'}},{{'1'}},{{'0'}},{{'1'}}}; bnd.r={{{'-u'}},{{'0.04*x.^2-u'}},{{'0'}},{{'1-u'}}}; bnd.var={}; bnd.ind=[1 2 3 4 4 4 4]; fem.bnd=bnd; % PDE coefficients clear equ equ.da={{{'1'}}}; equ.c={{{'B*x','0';'0','B*x-B*x'}}}; equ.al={{{'0';'0'}}}; equ.ga={{{'-B*x.*ux';'B*x.*uy-B*x.*uy'}}}; equ.be={{{'2*B';'x'}}}; equ.a={{{'0'}}}; equ.f={{{'-(2*B.*ux+x.*uy)'}}}; equ.var={'absux_c1','sqrt(ux.^2+uy.^2)','absga1x_c1', ... 'sqrt(ga1x.^2+ga1y.^2)'}; equ.ind=1; fem.equ=equ; % Evaluate initial condition fem.init=asseminit(fem,... 'context','local',... 'init', struct('sd',{{{{'0'}}}},'ind',{1})); % Solve problem fem.sol=femlin(fem,... 'out', {'sol'},... 'context','local',... 'sd', 'off',... 'Epoint', 'gauss2',... 'Nullfun','flnullorth',... 'Tpoint', 'gauss2',... 'Solcomp',1,... 'method', 'eliminate'); % Save current mesh restart.mesh=fem.mesh; restart.usage=fem.usage; % Plot solution postplot(fem,... 'context','local',... 'contdata',{'u','cont','on'},... 'contlevels',18,... 'contstyle','color',... 'contlabel','off',... 'contmaxmin','off',... 'contbar','on',... 'contmap','cool',... 'geom', 'on',... 'geomcol','bginv',... 'view', [0 90],... 'title', 'Contour: u (u) ',... 'renderer','zbuffer',... 'solnum', 1,... 'axisvisible','on') % Plot solution postplot(fem,... 'context','local',... 'contdata',{'u','cont','on'},... 'contlevels',18,... 'contstyle','color',... 'contlabel','off',... 'contmaxmin','off',... 'contbar','on',... 'contmap','cool',... 'geom', 'on',... 'geomcol','bginv',... 'view', [0 90],... 'title', 'Contour: u (u) ',... 'renderer','zbuffer',... 'solnum', 1,... 'axisvisible','on') % Plot solution postplot(fem,... 'context','local',... 'contdata',{'u','cont','on'},... 'contlevels',19,... 'contstyle','color',... 'contlabel','off',... 'contmaxmin','off',... 'contbar','on',... 'contmap','cool',... 'arrowdata',{'uy','-ux'},... 'arrowcolor',[1 0 0],... 'arrowscale','auto',... 'arrowstyle','proportional',... 'arrowxspacing',15,... 'arrowyspacing',30,... 'arrowmaxmin','off',... 'geom', 'on',... 'geomcol','bginv',... 'view', [0 90],... 'title', 'Contour: u (u) Arrow: [uy (uy),-ux] ',... 'renderer','zbuffer',... 'solnum', 1,... 'axisvisible','on') % Plot solution postplot(fem,... 'context','local',... 'contdata',{'u','cont','on'},... 'contlevels',19,... 'contstyle','color',... 'contlabel','off',... 'contmaxmin','off',... 'contbar','on',... 'contmap','cool',... 'geom', 'on',... 'geomcol','bginv',... 'view', [0 90],... 'title', 'Contour: u (u) ',... 'renderer','zbuffer',... 'solnum', 1,... 'axisvisible','on') % Plot solution postplot(fem,... 'context','local',... 'contdata',{'u','cont','on'},... 'contlevels',19,... 'contstyle','color',... 'contlabel','off',... 'contmaxmin','off',... 'contbar','on',... 'contmap','jet',... 'geom', 'on',... 'geomcol','bginv',... 'view', [0 90],... 'title', 'Contour: u (u) ',... 'renderer','zbuffer',... 'solnum', 1,... 'axisvisible','on')