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annotate +multiblock/+domain/Circle.m @ 1198:2924b3a9b921 feature/d2_compatible

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Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
author Martin Almquist <malmquist@stanford.edu>
date Fri, 16 Aug 2019 14:30:28 -0700
parents 9be370486d36
children
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588
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1 classdef Circle < multiblock.DefCurvilinear
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2 properties
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3 r, c
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4
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5 hs
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6 r_arc
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7 omega
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8 end
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9
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10 methods
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11 function obj = Circle(r, c, hs)
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12 default_arg('r', 1);
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13 default_arg('c', [0; 0]);
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14 default_arg('hs', 0.435);
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15
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16
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17 % alpha = 0.75;
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18 % hs = alpha*r/sqrt(2);
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19
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20 % Square should not be a square, it should be an arc. The arc radius
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21 % is chosen so that the three angles of the meshes are all equal.
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22 % This gives that the (half)arc opening angle of should be omega = pi/12
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23 omega = pi/12;
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24 r_arc = hs*(2*sqrt(2))/(sqrt(3)-1); % = hs* 1/sin(omega)
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25 c_arc = c - [(1/(2-sqrt(3))-1)*hs; 0];
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26
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27 cir = parametrization.Curve.circle(c,r,[-pi/4 pi/4]);
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28
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29 c2 = cir(0);
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30 c3 = cir(1);
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31
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32 s1 = [-hs; -hs];
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33 s2 = [ hs; -hs];
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34 s3 = [ hs; hs];
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35 s4 = [-hs; hs];
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36
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37 sp2 = parametrization.Curve.line(s2,c2);
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38 sp3 = parametrization.Curve.line(s3,c3);
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39
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40 Se1 = parametrization.Curve.circle(c_arc,r_arc,[-omega, omega]);
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41 Se2 = Se1.rotate(c,pi/2);
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42 Se3 = Se2.rotate(c,pi/2);
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43 Se4 = Se3.rotate(c,pi/2);
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44
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45
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46 S = parametrization.Ti(Se1,Se2,Se3,Se4).rotate_edges(-1);
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47
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48 A = parametrization.Ti(sp2, cir, sp3.reverse, Se1.reverse);
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49 B = A.rotate(c,1*pi/2).rotate_edges(-1);
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50 C = A.rotate(c,2*pi/2).rotate_edges(-1);
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51 D = A.rotate(c,3*pi/2).rotate_edges(0);
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52
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53 blocks = {S,A,B,C,D};
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54 blocksNames = {'S','A','B','C','D'};
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55
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56 conn = cell(5,5);
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57 conn{1,2} = {'e','w'};
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58 conn{1,3} = {'n','s'};
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59 conn{1,4} = {'w','s'};
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60 conn{1,5} = {'s','w'};
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61
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62 conn{2,3} = {'n','e'};
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63 conn{3,4} = {'w','e'};
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64 conn{4,5} = {'w','s'};
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65 conn{5,2} = {'n','s'};
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66
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67 boundaryGroups = struct();
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68 boundaryGroups.E = multiblock.BoundaryGroup({{2,'e'}});
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69 boundaryGroups.N = multiblock.BoundaryGroup({{3,'n'}});
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70 boundaryGroups.W = multiblock.BoundaryGroup({{4,'n'}});
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71 boundaryGroups.S = multiblock.BoundaryGroup({{5,'e'}});
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72 boundaryGroups.all = multiblock.BoundaryGroup({{2,'e'},{3,'n'},{4,'n'},{5,'e'}});
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73
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74 obj = obj@multiblock.DefCurvilinear(blocks, conn, boundaryGroups, blocksNames);
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75
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76 obj.r = r;
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77 obj.c = c;
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78 obj.hs = hs;
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79 obj.r_arc = r_arc;
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80 obj.omega = omega;
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81 end
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82
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83 function ms = getGridSizes(obj, m)
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84 m_S = m;
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85
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86 % m_Radial
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87 s = 2*obj.hs;
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88 innerArc = obj.r_arc*obj.omega;
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89 outerArc = obj.r*pi/2;
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90 shortSpoke = obj.r-s/sqrt(2);
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91 x = (1/(2-sqrt(3))-1)*obj.hs;
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92 longSpoke = (obj.r+x)-obj.r_arc;
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93 m_R = parametrization.equal_step_size((innerArc+outerArc)/2, m_S, (shortSpoke+longSpoke)/2);
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94
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95 ms = {[m_S m_S], [m_R m_S], [m_S m_R], [m_S m_R], [m_R m_S]};
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96 end
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97 end
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98 end