mesh_collection.m

一个功能强大的非结构网格划分程序,可实现网格的自动剖分,及局部加密与质量控制

function mesh_collection(num)

%  MESH_COLLECTION: Collection of meshing examples from MESH2D users. 
%
%  mesh_collection(n) will run the nth example.
%
%  1. Simple square domain. Used for "driven cavity" CFD studies.
%
%  2. Rectangular domain with circular hole. Used in thermally coupled CFD
%     studies to examine the flow around a heated pipe.
%
%  3. Rectangular domain with circular hole and user defined size
%     functions. Used in a CFD study to examine vortex shedding about
%     cylinders.
%
%  4. Rectangular domain with 2 circular holes and user defined size
%     functions. Used in a CFD study to examine the unsteady flow between
%     cylinders.
%
%  5. Rectangular domain with square hole and user defined size functions.
%     Used in a CFD study to examine vortex shedding about square prisms.
%
%  6. 3 element airfoil with user defined size functions and boundary layer
%     size functions. Used in a CFD study to examin the lift/drag
%     characteristics.
%
%  7. U shaped domain.
%
%  8. Rectangular domain with step. Used for "backward facing step" CFD
%     studies.
%
%  9. NACA airfoil with boundary layer size functions. Used in a CFD study
%     to examine the lift/drag vs. alpha characteristics.
%
%  10. Wavy channel from Kong Zour. Used in a CFD study to examine unsteady
%      behaviour.
%
%  11. Tray of glass beads from Falk Hebe. Used in a CFD study to examine the flow
%      through past a collection of beads.
%
%  12. Coastline data from Francisco Garcia.
%
% I am always looking for new meshes to add to the collection, if you would
% like to contribute please send me an email with an m-file description of
% the NODE, EDGE, HDATA and OPTIONS used to setup the mesh.
%
% Darren Engwirda    : 2006-2007
% Email              : [e-mail]


switch(num)
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   case 1

      node  = [0,0; 1,0; 1,1; 0,1];

      hdata.hmax = 0.01;

      [p,t] = mesh2d(node,[],hdata);

      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   case 2

      theta = 0:pi/50:(2*pi-pi/50);
      x = cos(theta)/2;
      y = sin(theta)/2;

      node = [ x',y'; -5,-5; 5,-5; 5,15; -5,15];

      n = size(node,1)-4;
      edge = [(1:n-1)' (2:n)'; n,1; n+1,n+2; n+2,n+3; n+3,n+4; n+4,n+1];

      hdata.hmax = 0.175;
      [p,t] = mesh2d(node,edge,hdata);

      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   case 3

      theta = 0:pi/50:(2*pi-pi/50);
      x = cos(theta)/2;
      y = sin(theta)/2;

      node = [ x',y'; -5,-10; 25,-10; 25,10; -5,10];

      n = size(node,1)-4;
      edge = [(1:n-1)' (2:n)'; n,1; n+1,n+2; n+2,n+3; n+3,n+4; n+4,n+1];

      hdata.fun = @const_h;
      hdata.args = {-1,25,-3,3,0.1};
      options.dhmax = 0.2;

      [p,t] = mesh2d(node,edge,hdata,options);

      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   case 4

      theta = 0:pi/36:(2*pi-pi/36);
      x = cos(theta)/2;
      y = sin(theta)/2;

      cyL1 = [x' y'+1];
      cyL2 = [x' y'-1];
      box  = [-5,-10; 25,-10; 25,10; -5,10];

      n1 = size(cyL1,1);
      n2 = size(cyL2,1);
      c1 = [(1:n1-1)',(2:n1)'; n1,1];
      c2 = [(1:n2-1)',(2:n2)'; n2,1];
      c3 = [1,2; 2,3; 3,4; 4,1];

      node = [cyL1; cyL2; box];
      edge = [c1; c2+n1; c3+n1+n2];

      hdata.fun = @const_h;
      hdata.args = {-1,25,-4,4,0.2};

      [p,t] = mesh2d(node,edge,hdata);

      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   case 5

      node = [0,-10; 20,-10; 20,10; 0,10; 5,-0.5; 6,-0.5; 6,0.5; 5,0.5];
      edge = [1,2; 2,3; 3,4; 4,1; 5,6; 6,7; 7,8; 8,5];

      hdata.fun = @case5;
      hdata.edgeh = [5, 0.05; 6, 0.05; 7, 0.05; 8, 0.05];
      hdata.fun = @const_h;
      hdata.args = {5,20,-3,3,0.1};

      options.dhmax = 0.15;

      [p,t] = mesh2d(node,edge,hdata,options);

      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   case 6

      temp = [
         0.027490  0.017991 0.899870  0.017200 0.052890 -0.021420 1.214624 -0.113530
         0.021231  0.013241 0.871260  0.019430 0.048640 -0.021060 1.193291 -0.106968
         0.011552  0.004325 0.835990  0.021190 0.043550 -0.019330 1.150970 -0.093895
         -0.004135 -0.011795 0.802400  0.021820 0.039060 -0.015140 1.123617 -0.085397
         -0.012160 -0.021418 0.766470  0.020920 0.037490 -0.009480 1.097197 -0.077260
         -0.018975 -0.031128 0.753490  0.019960 0.039190 -0.001600 1.058932 -0.065674
         -0.022844 -0.037478 0.735200  0.017900 0.043650  0.006190 1.034620 -0.058528
         -0.027273 -0.046152 0.729540  0.017030 0.048240  0.010880 0.996129 -0.047562
         -0.029451 -0.052343 0.718900  0.015170 0.055920  0.016870 0.967841 -0.039703
         -0.030201 -0.061288 0.709580  0.013210 0.062110  0.020990 0.953663 -0.035852
         -0.028411 -0.069148 0.701600  0.011010 0.072390  0.026910 0.940446 -0.032286
         -0.024596 -0.073614 0.690290  0.007120 0.083730  0.032240 0.926244 -0.028500
         -0.018756 -0.075514 0.682300  0.003430 0.104760  0.040220 0.917211 -0.026096
         -0.017118 -0.075335 0.676980 -0.000170 0.117300  0.044210 0.909167 -0.023871
         -0.016780 -0.076060 0.672990 -0.004160 0.134530  0.047900 0.905108 -0.022393
         -0.025493 -0.079097 0.669990 -0.011380 0.153460  0.050670 0.901391 -0.019944
         -0.035315 -0.082430 0.673320 -0.019060 0.168330  0.052460 0.900339 -0.012133
         -0.042170 -0.084269 0.677310 -0.020330 0.172890  0.052960 0.907722 -0.004509
         -0.049084 -0.085176 0.677310 -0.020960 0.182440  0.054030 0.915378 -0.001953
         -0.055933 -0.084663 0.668660 -0.021720 0.200270  0.055850 0.920255 -0.001185
         -0.059101 -0.083382 0.634730 -0.024850 0.203160  0.056150 0.926453 -0.000706
         -0.062122 -0.081635 0.602130 -0.028010 0.234300  0.058920 0.930333 -0.000745
         -0.066395 -0.076400 0.567860 -0.031570 0.266130  0.061280 0.937713 -0.000877
         -0.067831 -0.070173 0.534930 -0.034700 0.301060  0.063370 0.941848 -0.001212
         -0.067150 -0.063754 0.500670 -0.037820 0.335000  0.064970 0.950351 -0.002146
         -0.066302 -0.060865 0.466730 -0.040350 0.366270  0.066030 0.960400 -0.003718
         -0.063478 -0.055113 0.432470 -0.042250 0.401530  0.066770 0.971630 -0.005932
         -0.059726 -0.049766 0.400200 -0.043450 0.434460  0.067000 0.977522 -0.007257
         -0.053690 -0.043024 0.368260 -0.043910 0.468400  0.066730 0.989221 -0.010143
         -0.046491 -0.036434 0.333670 -0.043750 0.499000  0.066030 0.995344 -0.011797
         -0.034454 -0.026043 0.300070 -0.042880 0.533270  0.064740 1.001430 -0.013554
         -0.019737 -0.014303 0.267800 -0.041420 0.567860  0.062840 1.020150 -0.019516
         -0.006940 -0.004739 0.232870 -0.039160 0.599800  0.060480 1.034272 -0.024486
         0.008486  0.006239 0.202590 -0.036530 0.635400  0.057520 1.063809 -0.035726
         0.013998  0.010012 0.167000 -0.032930 0.668660  0.053560 1.097886 -0.050076
         0.019714  0.013891 0.136730 -0.029770 0.701260  0.049500 1.125638 -0.063296
         0.027025  0.018988 0.101460 -0.026280 0.734530  0.044940 1.155608 -0.079195
         0         0        0.084170 -0.024550 0.765140  0.040450 1.183517 -0.094908
         0         0        0.071120 -0.023250 0.799070  0.035100 1.214740 -0.113210
         0         0        0.067860 -0.022820 0.833330  0.029440 0         0
         0         0        0.061240 -0.022290 0.867930  0.023520 0         0
         0         0        0.054720 -0.021660 0.899870  0.017900 0         0];

      slat = temp(:,1:2);
      wing = temp(:,3:6);
      flap = temp(:,7:8);

      slat = slat(slat(:,1)~=0,:);
      flap = flap(flap(:,1)~=0,:);
      wing = [wing(:,1:2); wing(:,3:4)];
      box  = [-0.75,-1; 2.25,-1; 2.25,1; -0.75,1];

      n1 = size(slat,1);
      n2 = size(wing,1);
      n3 = size(flap,1);
      c1 = [(1:n1-1)',(2:n1)'; n1,1];
      c2 = [(1:n2-1)',(2:n2)'; n2,1];
      c3 = [(1:n3-1)',(2:n3)'; n3,1];
      c4 = [1,2; 2,3; 3,4; 4,1];

      node = [slat; wing; flap; box];
      edge = [c1; c2+n1; c3+n1+n2; c4+n1+n2+n3];

      options.dhmax = 0.15;

      hdata.edgeh(:,1) = [unique(c1(:)); unique(c2(:))+n1; unique(c3(:))+n1+n2];
      hdata.edgeh(:,2) = 0.001;

      [p,t] = mesh2d(node,edge,hdata,options);

      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   case 7

      node  = [0,0; 4,0; 4,1; 2,1; 2,2; 4,2; 4,3; 0,3];

      hdata.hmax = 0.05;

      [p,t] = mesh2d(node,[],hdata);

      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   case 8

      node = [-2,1; 1,1; 1,0; 20,0; 20,2; -2,2];

      hdata.hmax = 0.1;
      hdata.fun = @const_h;
      hdata.args = {-1,5,0,2,0.05};

      options.dhmax = 0.1;

      [p,t] = mesh2d(node,[],hdata,options);
      
%       in = inpoly(p,node);
%       ti = sum(in(t),2)>0;
%       [p,t] = refine(p,t,ti);
%       patch('faces',t,'vertices',p,'facecolor','none','edgecolor','b');
      save('D:\backingface.mat','p','t');

      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   case 9

      wing = [
         1.00003  0.00126
         0.99730  0.00170
         0.98914  0.00302
         0.97563  0.00518
         0.95693  0.00812
         0.93324  0.01176
         0.90482  0.01602
         0.87197  0.02079
         0.83506  0.02597
         0.79449  0.03145
         0.75070  0.03712
         0.70417  0.04285
         0.65541  0.04854
         0.60496  0.05405
         0.55335  0.05924
         0.50117  0.06397
         0.44897  0.06811
         0.39733  0.07150
         0.34681  0.07402
         0.29796  0.07554
         0.25131  0.07597
         0.20738  0.07524
         0.16604  0.07320
         0.12732  0.06915
         0.09230  0.06265
         0.06203  0.05382
         0.03730  0.04324
         0.01865  0.03176
         0.00628  0.02030
         0.00015  0.00956
         0.00000  0.00000
         0.00533 -0.00792
         0.01557 -0.01401
         0.03029 -0.01870
         0.04915 -0.02248
         0.07195 -0.02586
         0.09868 -0.02922
         0.12954 -0.03282
         0.16483 -0.03660
         0.20483 -0.04016
         0.24869 -0.04283
         0.29531 -0.04446
         0.34418 -0.04510
         0.39476 -0.04482
         0.44650 -0.04371
         0.49883 -0.04188
         0.55117 -0.03945
         0.60296 -0.03655
         0.65360 -0.03327
         0.70257 -0.02975
         0.74930 -0.02607
         0.79330 -0.02235
         0.83407 -0.01866
         0.87118 -0.01512
         0.90420 -0.01180
         0.93279 -0.00880
         0.95661 -0.00621
         0.97543 -0.00410
         0.98901 -0.00254
         0.99722 -0.00158
         0.99997 -0.00126];

      wing = rotate(wing,2.5);
      wall = [-1,-2; 2,-2; 2,2; -1,2];

      nwing = size(wing,1);
      nwall = size(wall,1);

      cwing = [(1:nwing-1)', (2:nwing)'; nwing, 1];
      cwall = [(1:nwall-1)', (2:nwall)'; nwall, 1];

      edge = [cwing; cwall+nwing];
      node = [wing; wall];

      hdata.edgeh(:,1) = (1:size(cwing,1))';
      hdata.edgeh(:,2) = 0.0025;

      options.dhmax = 0.1;

      [p,t] = mesh2d(node,edge,hdata,options);

      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   case 10

      % DEFINE GEOMETRY
      H   = 1;                % Height
      L   = 5;                % Length
      n   = 4;                % Cycles
      k   = 2*pi*n*H/L;
      dx  = 0.05;             % Streamwise spatial increment
      x   = 0:dx:L;
      num = length(x);

      % Wavy channel walls
      ytop = 1+0.1*cos(k*x);

      node = [0,0; L,0; x(num:-1:1)' ytop(num:-1:1)'];

      hdata.hmax = 0.05;

      [p,t] = mesh2d(node,[],hdata);

      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   case 11

      % A mesh for an industrial process from an engineer in Germany (for a CFD
      % study invloving fluid transport through a tray of glass beads...) which
      % caused eariler versions of mesh2d big problems...


      Radius  = 2;                    % Radius des Kreises
      xNumber = 15;                    % Anzahl in x-Richtung
      yNumber = 8;                    % Anzahl in y-Richtung
      Anzahl  = xNumber*yNumber;      % Anzahl der Kreise
      Abstand = 2*Radius+1;           % Abstand der Kreise
      dtheta  = 0.1;                 % Schrittweite der Winkelaul"osung

      theta = 0:pi*dtheta:(2*pi-pi*dtheta);

      x = zeros(Anzahl,length(theta));
      y = x;
      Radii = 1.5+rand(Anzahl,1);

      % setzen der Kreise
      for i = 1:Anzahl
         x(i,:) = Radii(i)*cos(theta);
         y(i,:) = Radii(i)*sin(theta);
         dy = floor((i-1)/xNumber);
         dx = (i-1)-dy*xNumber;
         node((i-1)*20+1:i*20,1) = [x(i,:)'+dx*Abstand];
         node((i-1)*20+1:i*20,2)  = [y(i,:)'-dy*Abstand];
      end

      % setzen des begrenzenden Rechtecks
      node = [    node(1:Anzahl*20,1) node(1:Anzahl*20,2)
         -3                  -((yNumber-1)*5+3)
         ((xNumber-1)*5+3)    -((yNumber-1)*5+3)
         ((xNumber-1)*5+3)    3
         -3                  3
         ];


      n = size(node,1)-4;

      cnect = [(1:n-1)' (2:n)'
         n        1
         n+1      n+2
         n+2      n+3
         n+3      n+4
         n+4      n+1
         ];

      for i = 1:Anzahl
         cnect(i*20,2) = 1+(i-1)*20;
      end

      options.dhmax = 0.3;

      [p,t] = mesh2d(node,cnect,[],options);

      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   case 12

      p1=[
         2875871	2394144
         2875959	2394053
         2876044	2394049
         2876132	2393952
         2876228	2393952
         2876312	2393861
         2877032	2393861
         2877121	2393763
         2877474	2393760
         2877573	2393670
         2877928	2393675
         2878015	2393579
         2878111	2393579
         2878200	2393481
         2878380	2393485
         2878462	2393387
         2878645	2393387
         2878734	2393290
         2879005	2393296
         2879095	2393206
         2879178	2393206
         2879585	2392777
         2879585	2392685
         2879675	2392589
         2879675	2392122
         2879582	2392026
         2879582	2391929
         2879453	2391794
         2879364	2391794
         2879316	2391750
         2879316	2391466
         2879540	2391230
         2879633	2391230
         2879717	2391134
         2880885	2391137
         2881112	2390897
         2881109	2390618
         2881246	2390484
         2881335	2390484
         2881599	2390196
         2881691	2390196
         2882278	2389589
         2882278	2389492
         2882366	2389401
         2882366	2389304
         2882674	2388979
         2883663	2388982
         2883752	2388885
         2883934	2388885
         2884024	2388788
         2884195	2388792
         2884290	2388694
         2884741	2388694
         2884825	2388602
         2885097	2388599
         2885186	2388509
         2885457	2388509
         2885542	2388411
         2885904	2388411
         2885993	2388320
         2886175	2388317
         2886259	2388220
         2886445	2388220
         2886528	2388129
         2886622	2388129
         2886707	2388037
         2886983	2388037
         2887072	2387941
         2887245	2387944
         2887335	2387847
         2887962	2387847
         2888052	2387754
         2888235	2387941
         2888505	2387941
         2888595	2387849