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Add upwind dissipation to the operator inside Utux2d
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 19 Dec 2018 20:00:27 +0100
parents f029b97dbc72
children 234c1c02ea39
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
950
cab047de7f5d Rename *2D schemes to *2d
Jonatan Werpers <jonatan@werpers.com>
parents: 948
diff changeset
1 classdef Utux2d < scheme.Scheme
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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2 properties
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Martin Almquist <martin.almquist@it.uu.se>
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3 m % Number of points in each direction, possibly a vector
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Martin Almquist <martin.almquist@it.uu.se>
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4 h % Grid spacing
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Martin Almquist <martin.almquist@it.uu.se>
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5 grid % Grid
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Martin Almquist <martin.almquist@it.uu.se>
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6 order % Order accuracy for the approximation
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Martin Almquist <martin.almquist@it.uu.se>
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7 v0 % Initial data
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8
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Martin Almquist <martin.almquist@it.uu.se>
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9 a % Wave speed a = [a1, a2];
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10 % Can either be a constant vector or a cell array of function handles.
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11
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Martin Almquist <martin.almquist@it.uu.se>
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12 H % Discrete norm
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13 H_x, H_y % Norms in the x and y directions
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14 Hi, Hx, Hy, Hxi, Hyi % Kroneckered norms
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15
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16 % Derivatives
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Martin Almquist <martin.almquist@it.uu.se>
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17 Dx, Dy
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18
1019
f029b97dbc72 Support upwind opSet in Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
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19 % Dissipation Operators
f029b97dbc72 Support upwind opSet in Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
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20 DissOpx, DissOpy
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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21
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Martin Almquist <martin.almquist@it.uu.se>
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22 % Boundary operators
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Martin Almquist <martin.almquist@it.uu.se>
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23 e_w, e_e, e_s, e_n
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24
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25 D % Total discrete operator
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26 end
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27
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28
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29 methods
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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30 function obj = Utux2d(g ,order, opSet, a, fluxSplitting)
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31
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
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32 default_arg('a',1/sqrt(2)*[1, 1]);
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33 default_arg('opSet',@sbp.D2Standard);
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34 default_arg('fluxSplitting',[]);
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35
948
3dd7f87c9a1b Use assertType(...) instead of assert(isa(...))
Jonatan Werpers <jonatan@werpers.com>
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36 assertType(g, 'grid.Cartesian');
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Martin Almquist <malmquist@stanford.edu>
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37 if iscell(a)
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38 a1 = grid.evalOn(g, a{1});
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39 a2 = grid.evalOn(g, a{2});
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40 a = {spdiag(a1), spdiag(a2)};
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41 else
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42 a = {a(1), a(2)};
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43 end
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44
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45 m = g.size();
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46 m_x = m(1);
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47 m_y = m(2);
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48 m_tot = g.N();
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49
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50 xlim = {g.x{1}(1), g.x{1}(end)};
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51 ylim = {g.x{2}(1), g.x{2}(end)};
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52 obj.grid = g;
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53
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54 % Operator sets
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Martin Almquist <martin.almquist@it.uu.se>
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55 ops_x = opSet(m_x, xlim, order);
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56 ops_y = opSet(m_y, ylim, order);
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Martin Almquist <martin.almquist@it.uu.se>
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57 Ix = speye(m_x);
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58 Iy = speye(m_y);
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59
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60 % Norms
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61 Hx = ops_x.H;
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62 Hy = ops_y.H;
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63 Hxi = ops_x.HI;
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64 Hyi = ops_y.HI;
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65
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66 obj.H_x = Hx;
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67 obj.H_y = Hy;
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68 obj.H = kron(Hx,Hy);
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69 obj.Hi = kron(Hxi,Hyi);
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70 obj.Hx = kron(Hx,Iy);
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71 obj.Hy = kron(Ix,Hy);
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72 obj.Hxi = kron(Hxi,Iy);
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73 obj.Hyi = kron(Ix,Hyi);
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74
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75 % Derivatives
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76 if (isequal(opSet,@sbp.D1Upwind))
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77 Dx = (ops_x.Dp + ops_x.Dm)/2;
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78 Dy = (ops_y.Dp + ops_y.Dm)/2;
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79 DissOpx = (ops_x.Dm - ops_x.Dp)/2;
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80 DissOpy = (ops_y.Dm - ops_y.Dp)/2;
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81 obj.Dx = kron(Dx,Iy);
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82 obj.Dy = kron(Ix,Dy);
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83 obj.DissOpx = kron(DissOpx,Iy);
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84 obj.DissOpy = kron(Ix,DissOpy);
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85 else
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86 Dx = ops_x.D1;
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87 Dy = ops_y.D1;
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88 obj.Dx = kron(Dx,Iy);
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89 obj.Dy = kron(Ix,Dy);
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90 end
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91
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92 % Boundary operators
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93 obj.e_w = kr(ops_x.e_l, Iy);
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94 obj.e_e = kr(ops_x.e_r, Iy);
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95 obj.e_s = kr(Ix, ops_y.e_l);
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96 obj.e_n = kr(Ix, ops_y.e_r);
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97
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98 obj.m = m;
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99 obj.h = [ops_x.h ops_y.h];
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100 obj.order = order;
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101 obj.a = a;
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102
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103 if (isequal(opSet,@sbp.D1Upwind))
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104 obj.D = -(a{1}*obj.Dx + a{2}*obj.Dy + fluxSplitting{1}*obj.DissOpx + fluxSplitting{2}*obj.DissOpy);
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105 else
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106 obj.D = -(a{1}*obj.Dx + a{2}*obj.Dy);
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107 end
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108
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109 end
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110 % Closure functions return the opertors applied to the own domain to close the boundary
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111 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
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112 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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113 % type is a string specifying the type of boundary condition if there are several.
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114 % data is a function returning the data that should be applied at the boundary.
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115 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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116 % neighbour_boundary is a string specifying which boundary to interface to.
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117 function [closure, penalty] = boundary_condition(obj,boundary,type)
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118 default_arg('type','dirichlet');
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119
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120 sigma = -1; % Scalar penalty parameter
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121 switch boundary
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122 case {'w','W','west','West'}
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123 tau = sigma*obj.a{1}*obj.e_w*obj.H_y;
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124 closure = obj.Hi*tau*obj.e_w';
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125
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126 case {'s','S','south','South'}
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127 tau = sigma*obj.a{2}*obj.e_s*obj.H_x;
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128 closure = obj.Hi*tau*obj.e_s';
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129 end
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130 penalty = -obj.Hi*tau;
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131
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132 end
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133
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134 % type Struct that specifies the interface coupling.
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135 % Fields:
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136 % -- couplingType String, type of interface coupling
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137 % % Default: 'upwind'. Other: 'centered'
942
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138 % -- interpolation: type of interpolation, default 'none'
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139 % -- interpolationDamping: damping on upstream and downstream sides, when using interpolation.
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140 % Default {0,0} gives zero damping.
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diff changeset
141 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
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142
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diff changeset
143 defaultType.couplingType = 'upwind';
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144 defaultType.interpolation = 'none';
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Martin Almquist <malmquist@stanford.edu>
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145 defaultType.interpolationDamping = {0,0};
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
146 default_struct('type', defaultType);
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147
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148 switch type.interpolation
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149 case {'none', ''}
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150 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
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151 case {'op','OP'}
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152 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
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153 otherwise
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154 error('Unknown type of interpolation: %s ', type.interpolation);
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155 end
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156 end
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157
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158 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
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159 couplingType = type.couplingType;
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160
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161 % Get neighbour boundary operator
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162 switch neighbour_boundary
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163 case {'e','E','east','East'}
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164 e_neighbour = neighbour_scheme.e_e;
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165 case {'w','W','west','West'}
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166 e_neighbour = neighbour_scheme.e_w;
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167 case {'n','N','north','North'}
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168 e_neighbour = neighbour_scheme.e_n;
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169 case {'s','S','south','South'}
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170 e_neighbour = neighbour_scheme.e_s;
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171 end
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172
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173 switch couplingType
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174
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175 % Upwind coupling (energy dissipation)
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176 case 'upwind'
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177 sigma_ds = -1; %"Downstream" penalty
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178 sigma_us = 0; %"Upstream" penalty
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179
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180 % Energy-preserving coupling (no energy dissipation)
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181 case 'centered'
605
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182 sigma_ds = -1/2; %"Downstream" penalty
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183 sigma_us = 1/2; %"Upstream" penalty
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184
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185 otherwise
942
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186 error(['Interface coupling type ' couplingType ' is not available.'])
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187 end
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188
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189 switch boundary
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190 case {'w','W','west','West'}
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191 tau = sigma_ds*obj.a{1}*obj.e_w*obj.H_y;
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192 closure = obj.Hi*tau*obj.e_w';
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193 penalty = -obj.Hi*tau*e_neighbour';
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194 case {'e','E','east','East'}
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195 tau = sigma_us*obj.a{1}*obj.e_e*obj.H_y;
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196 closure = obj.Hi*tau*obj.e_e';
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197 penalty = -obj.Hi*tau*e_neighbour';
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198 case {'s','S','south','South'}
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199 tau = sigma_ds*obj.a{2}*obj.e_s*obj.H_x;
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200 closure = obj.Hi*tau*obj.e_s';
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201 penalty = -obj.Hi*tau*e_neighbour';
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202 case {'n','N','north','North'}
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203 tau = sigma_us*obj.a{2}*obj.e_n*obj.H_x;
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204 closure = obj.Hi*tau*obj.e_n';
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205 penalty = -obj.Hi*tau*e_neighbour';
605
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206 end
610
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207
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208 end
610
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209
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diff changeset
210 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
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211
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212 % User can request special interpolation operators by specifying type.interpOpSet
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213 default_field(type, 'interpOpSet', @sbp.InterpOpsOP);
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214
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diff changeset
215 interpOpSet = type.interpOpSet;
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216 couplingType = type.couplingType;
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217 interpolationDamping = type.interpolationDamping;
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218
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219 % Get neighbour boundary operator
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220 switch neighbour_boundary
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221 case {'e','E','east','East'}
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diff changeset
222 e_neighbour = neighbour_scheme.e_e;
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223 case {'w','W','west','West'}
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224 e_neighbour = neighbour_scheme.e_w;
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225 case {'n','N','north','North'}
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226 e_neighbour = neighbour_scheme.e_n;
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227 case {'s','S','south','South'}
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228 e_neighbour = neighbour_scheme.e_s;
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229 end
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230
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diff changeset
231 switch couplingType
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232
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233 % Upwind coupling (energy dissipation)
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234 case 'upwind'
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235 sigma_ds = -1; %"Downstream" penalty
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236 sigma_us = 0; %"Upstream" penalty
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237
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diff changeset
238 % Energy-preserving coupling (no energy dissipation)
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diff changeset
239 case 'centered'
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diff changeset
240 sigma_ds = -1/2; %"Downstream" penalty
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diff changeset
241 sigma_us = 1/2; %"Upstream" penalty
666
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diff changeset
242
914
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diff changeset
243 otherwise
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diff changeset
244 error(['Interface coupling type ' couplingType ' is not available.'])
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245 end
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diff changeset
246
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diff changeset
247 int_damp_us = interpolationDamping{1};
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248 int_damp_ds = interpolationDamping{2};
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249
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diff changeset
250 % u denotes the solution in the own domain
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251 % v denotes the solution in the neighbour domain
942
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diff changeset
252 % Find the number of grid points along the interface
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diff changeset
253 switch boundary
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diff changeset
254 case {'w','e'}
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255 m_u = obj.m(2);
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256 case {'s','n'}
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257 m_u = obj.m(1);
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258 end
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259 m_v = size(e_neighbour, 2);
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260
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261 % Build interpolation operators
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262 intOps = interpOpSet(m_u, m_v, obj.order, neighbour_scheme.order);
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263 Iu2v = intOps.Iu2v;
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264 Iv2u = intOps.Iv2u;
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265
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266 I_local2neighbour_ds = intOps.Iu2v.bad;
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267 I_local2neighbour_us = intOps.Iu2v.good;
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268 I_neighbour2local_ds = intOps.Iv2u.good;
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269 I_neighbour2local_us = intOps.Iv2u.bad;
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270
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271 I_back_forth_us = I_neighbour2local_us*I_local2neighbour_us;
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272 I_back_forth_ds = I_neighbour2local_ds*I_local2neighbour_ds;
666
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273
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274
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275 switch boundary
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276 case {'w','W','west','West'}
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277 tau = sigma_ds*obj.a{1}*obj.e_w*obj.H_y;
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278 closure = obj.Hi*tau*obj.e_w';
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279 penalty = -obj.Hi*tau*I_neighbour2local_ds*e_neighbour';
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280
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281 beta = int_damp_ds*obj.a{1}...
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282 *obj.e_w*obj.H_y;
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283 closure = closure + obj.Hi*beta*I_back_forth_ds*obj.e_w' - obj.Hi*beta*obj.e_w';
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284 case {'e','E','east','East'}
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285 tau = sigma_us*obj.a{1}*obj.e_e*obj.H_y;
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286 closure = obj.Hi*tau*obj.e_e';
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287 penalty = -obj.Hi*tau*I_neighbour2local_us*e_neighbour';
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288
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289 beta = int_damp_us*obj.a{1}...
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290 *obj.e_e*obj.H_y;
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291 closure = closure + obj.Hi*beta*I_back_forth_us*obj.e_e' - obj.Hi*beta*obj.e_e';
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292 case {'s','S','south','South'}
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293 tau = sigma_ds*obj.a{2}*obj.e_s*obj.H_x;
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294 closure = obj.Hi*tau*obj.e_s';
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295 penalty = -obj.Hi*tau*I_neighbour2local_ds*e_neighbour';
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296
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297 beta = int_damp_ds*obj.a{2}...
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298 *obj.e_s*obj.H_x;
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299 closure = closure + obj.Hi*beta*I_back_forth_ds*obj.e_s' - obj.Hi*beta*obj.e_s';
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300 case {'n','N','north','North'}
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301 tau = sigma_us*obj.a{2}*obj.e_n*obj.H_x;
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302 closure = obj.Hi*tau*obj.e_n';
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303 penalty = -obj.Hi*tau*I_neighbour2local_us*e_neighbour';
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304
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305 beta = int_damp_us*obj.a{2}...
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306 *obj.e_n*obj.H_x;
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307 closure = closure + obj.Hi*beta*I_back_forth_us*obj.e_n' - obj.Hi*beta*obj.e_n';
591
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308 end
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459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
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309
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310
591
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311 end
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312
591
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313 function N = size(obj)
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314 N = obj.m;
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315 end
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316
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317 end
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318
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319 methods(Static)
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320 % Calculates the matrices needed for the inteface coupling between boundary bound_u of scheme schm_u
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321 % and bound_v of scheme schm_v.
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322 % [uu, uv, vv, vu] = inteface_coupling(A,'r',B,'l')
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323 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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324 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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325 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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326 end
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327 end
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328 end