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annotate +scheme/AdvectionRV2D.m @ 1023:defc9d0cc1f2 feature/advectionRV

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Remove incorrect assertion of the number of BC:s
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 07 Jan 2019 12:06:49 +0100
parents 87809b4762c9
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
1009
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1 classdef AdvectionRV2D < scheme.Scheme
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2 properties
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3 grid % Physical grid
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4 order % Order accuracy for the approximation
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5
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6 D % Non-stabilized scheme operator
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7 H % Discrete norm
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8 H_inv % Norm inverse
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9 halfnorm_inv % Cell array of inverse halfnorm operators
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10 e_l % Cell array of left boundary operators
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11 e_r % Cell array of right boundary operators
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12 d_l % Cell array of left boundary derivative operators
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13 d_r % Cell array of right boundary derivative operators
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14 waveSpeed
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15 end
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16
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17 methods
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18 function obj = AdvectionRV2D(g, operator_type, order, dissipation, waveSpeed)
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19 if ~isa(g, 'grid.Cartesian') || g.D() ~= 2
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20 error('Grid must be 2d cartesian');
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21 end
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22
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23 obj.grid = g;
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24 obj.order = order;
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25
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26 % Create cell array of 1D operators. For example D1_1d{1} = D1_x, D1_1d{2} = D1_y.
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27 [Dp_1d, Dm_1d, H_1d, H_inv_1d, d_l_1d, d_r_1d, e_l_1d, e_r_1d, I, DissipationOp_1d] = ...
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28 obj.assemble1DOperators(g, operator_type, order, dissipation);
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29
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30 %% 2D-operators
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31 % D1
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32 D1_1d{1} = (Dp_1d{1} + Dp_1d{1})/2;
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33 D1_1d{2} = (Dp_1d{2} + Dp_1d{2})/2;
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34 D1_2d = obj.extendOperatorTo2D(D1_1d, I);
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35 D1 = D1_2d{1} + D1_2d{2};
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36 % D2
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37
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38 Dp_2d = obj.extendOperatorTo2D(Dp_1d, I);
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39 Dm_2d = obj.extendOperatorTo2D(Dm_1d, I);
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40 D2 = @(viscosity) Dm_2d{1}*spdiag(viscosity)*Dp_2d{1} + Dm_2d{2}*spdiag(viscosity)*Dp_2d{2};
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41 % m = g.size();
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42 % ind = grid.funcToMatrix(g, 1:g.N());
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43 % for i = 1:g.D()
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44 % D2_2d{i} = sparse(zeros(g.N()));
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45 % end
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46 % % x-direction
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47 % for i = 1:m(2)
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48 % p = ind(:,i);
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49 % D2_2d{1}(p,p) = @(viscosity) D2_1d{1}(viscosity(p));
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50 % end
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51 % % y-direction
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52 % for i = 1:m(1)
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53 % p = ind(i,:);
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54 % D2_2d{2}(p,p) = @(viscosity) D2_1d{2}(viscosity(p));
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55 % end
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56 % D2 = D2_2d{1} + D2_2d{2};
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57
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58 obj.d_l = obj.extendOperatorTo2D(d_l_1d, I);
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59 obj.d_r = obj.extendOperatorTo2D(d_r_1d, I);
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60 obj.e_l = obj.extendOperatorTo2D(e_l_1d, I);
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61 obj.e_r = obj.extendOperatorTo2D(e_r_1d, I);
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62 obj.H = kron(H_1d{1},H_1d{2});
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63 obj.H_inv = kron(H_inv_1d{1},H_inv_1d{2});
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64 obj.halfnorm_inv = obj.extendOperatorTo2D(H_inv_1d, I);
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65 obj.waveSpeed = waveSpeed;
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66
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67 % Dissipation operator
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68 switch dissipation
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69 case 'on'
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70 DissOp_2d = obj.extendOperatorTo2D(DissipationOp_1d, I);
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71 DissOp = DissOp_2d{1} + DissOp_2d{2};
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72 % max(abs()) or just abs()?
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73 obj.D = @(v, viscosity) (-waveSpeed.*D1 + D2(viscosity) + abs(waveSpeed).*DissOp)*v;
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74 case 'off'
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75 obj.D = @(v, viscosity) (-waveSpeed.*D1 + D2(viscosity))*v;
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76 end
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77 end
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78
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79 % Closure functions return the operators applied to the own doamin to close the boundary
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80 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other domain.
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81 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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82 % type is a string specifying the type of boundary condition if there are several.
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83 % data is a function returning the data that should be applied at the boundary.
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84 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
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85 default_arg('type','robin');
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86 default_arg('data',0);
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87 [e, d, halfnorm_inv, i_b, s] = obj.get_boundary_ops(boundary);
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88 switch type
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89 case {'D', 'dirichlet'}
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90 p = s*halfnorm_inv*e;
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91 closure = @(v,viscosity) p*(v(i_b));
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92 case {'N', 'nuemann'}
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93 p = s*halfnorm_inv*e;
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94 closure = @(v,viscosity) p*(viscosity(i_b).*d*v);
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95 case {'R', 'robin'}
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96 p = s*halfnorm_inv*e;
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97 closure = @(v, viscosity) p*(obj.waveSpeed(i_b).*v(i_b) - 2*viscosity(i_b).*d*v);
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98 otherwise
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99 error('No such boundary condition: type = %s',type);
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100 end
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101 switch class(data)
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102 case 'double'
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103 penalty = s*p*data;
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104 case 'function_handle'
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105 penalty = @(t) s*p*data(t);
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106 otherwise
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107 error('Wierd data argument!')
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108 end
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109 end
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110
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111 % Ruturns the boundary ops, half-norm, boundary indices and sign for the boundary specified by the string boundary.
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112 % The right boundary for each coordinate direction is considered the positive boundary
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113 function [e, d, halfnorm_inv, ind_boundary, s] = get_boundary_ops(obj,boundary)
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114 ind = grid.funcToMatrix(obj.grid, 1:obj.grid.N());
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115 switch boundary
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116 case 'w'
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117 e = obj.e_l{1};
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118 d = obj.d_l{1};
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119 halfnorm_inv = obj.halfnorm_inv{1};
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120 ind_boundary = ind(1,:);
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121 s = -1;
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diff changeset
122 case 'e'
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123 e = obj.e_r{1};
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124 d = obj.d_r{1};
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125 halfnorm_inv = obj.halfnorm_inv{1};
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126
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127 ind_boundary = ind(end,:);
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128 s = 1;
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129 case 's'
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130 e = obj.e_l{2};
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131 d = obj.d_l{2};
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132 halfnorm_inv = obj.halfnorm_inv{2};
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133 ind_boundary = ind(:,1);
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134 s = -1;
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diff changeset
135 case 'n'
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136 e = obj.e_r{2};
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137 d = obj.d_r{2};
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138 halfnorm_inv = obj.halfnorm_inv{2};
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139 ind_boundary = ind(:,end);
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140 s = 1;
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141 otherwise
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142 error('No such boundary: boundary = %s',boundary);
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143 end
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144 end
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145
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diff changeset
146 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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147 error('An interface function does not exist yet');
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148 end
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149
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150 function N = size(obj)
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151 N = obj.grid.m;
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152 end
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153 end
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154
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155 methods(Static)
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156 function [Dp, Dm, H, Hi, d_l, d_r, e_l, e_r, I, DissipationOp] = assemble1DOperators(g, operator_type, order, dissipation)
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157 dim = g.D();
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158 I = cell(dim,1);
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159 D1 = cell(dim,1);
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160 D2 = cell(dim,1);
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161 H = cell(dim,1);
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162 Hi = cell(dim,1);
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163 e_l = cell(dim,1);
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164 e_r = cell(dim,1);
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165 d1_l = cell(dim,1);
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166 d1_r = cell(dim,1);
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167 DissipationOp = cell(dim,1);
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168 for i = 1:dim
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169 switch operator_type
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170 % case 'narrow'
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171 % ops = sbp.D4Variable(g.m(i), g.lim{i}, order);
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172 % D1{i} = ops.D1;
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173 % D2{i} = ops.D2;
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174 % d_l{i} = ops.d1_l';
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175 % d_r{i} = ops.d1_r';
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176 % if (strcmp(dissipation,'on'))
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177 % DissipationOp{i} = -1*sbp.dissipationOperator(g.m(i), order, ops.HI);
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178 % end
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179 % case 'upwind-'
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180 % ops = sbp.D1Upwind(g.m(i), g.lim{i}, order);
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181 % D1{i} = (ops.Dp + ops.Dm)/2;
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182 % D2{i} = @(viscosity) ops.Dp*spdiag(viscosity)*ops.Dm;
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183 % d_l{i} = ops.e_l'*ops.Dm;
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184 % d_r{i} = ops.e_r'*ops.Dm;
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185 % if (strcmp(dissipation,'on'))
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186 % DissipationOp{i} = (ops.Dp-ops.Dm)/2;
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187 % end
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188 case 'upwind+'
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189 ops = sbp.D1Upwind(g.m(i), g.lim{i}, order);
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190 Dp{i} = ops.Dp;
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191 Dm{i} = ops.Dm;
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192 % D1{i} = (ops.Dp + ops.Dm)/2;
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193 % D2{i} = @(viscosity) ops.Dm*spdiag(viscosity)*ops.Dp;
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194 d_l{i} = ops.e_l'*ops.Dp;
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195 d_r{i} = ops.e_r'*ops.Dp;
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196 if (strcmp(dissipation,'on'))
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197 DissipationOp{i} = (ops.Dp-ops.Dm)/2;
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198 end
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199 % case 'upwind+-'
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200 % ops = sbp.D1Upwind(g.m(i), g.lim{i}, order);
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201 % D1{i} = (ops.Dp + ops.Dm)/2;
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202 % D2{i} = @(viscosity) (ops.Dp*spdiag(viscosity)*ops.Dm + ops.Dm*spdiag(viscosity)*ops.Dp)/2;
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203 % d_l{i} = ops.e_l'*D1;
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204 % d_r{i} = ops.e_r'*D1;
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205 % if (strcmp(dissipation,'on'))
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206 % DissipationOp{i} = (ops.Dp-ops.Dm)/2;
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207 % end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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diff changeset
208 otherwise
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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diff changeset
209 error('Other operator types not yet supported', operator_type);
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diff changeset
210 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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diff changeset
211 H{i} = ops.H;
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diff changeset
212 Hi{i} = ops.HI;
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diff changeset
213 e_l{i} = ops.e_l;
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diff changeset
214 e_r{i} = ops.e_r;
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diff changeset
215 I{i} = speye(g.m(i));
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216 end
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217 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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diff changeset
218 function op_2d = extendOperatorTo2D(op, I)
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parents:
diff changeset
219 op_2d{1} = kr(op{1}, I{2});
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diff changeset
220 op_2d{2} = kr(I{1}, op{2});
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221 end
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222 end
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diff changeset
223 end