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annotate +scheme/Utux2D.m @ 595:2a2f34778ded feature/utux2D

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Make Utux2D work
author Martin Almquist <malmquist@stanford.edu>
date Tue, 26 Sep 2017 13:26:25 -0700
parents 39554f2de783
children 0f9d20dbb7ce
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Martin Almquist <martin.almquist@it.uu.se>
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1 classdef Utux2D < scheme.Scheme
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2 properties
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3 m % Number of points in each direction, possibly a vector
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4 h % Grid spacing
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5 grid % Grid
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6 order % Order accuracy for the approximation
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7 v0 % Initial data
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8
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9 a % Wave speed a = [a1, a2];
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10
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11 H % Discrete norm
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12 H_x, H_y % Norms in the x and y directions
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13 Hi, Hx, Hy, Hxi, Hyi % Kroneckered norms
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14
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15 % Derivatives
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16 Dx, Dy
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17
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18 % Boundary operators
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19 e_w, e_e, e_s, e_n
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20
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21 D % Total discrete operator
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22
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23 end
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24
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25
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26 methods
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27 function obj = Utux2D(g ,order, opSet, a)
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28
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29 default_arg('a',1/sqrt(2)*[1, 1]);
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30 default_arg('opSet',@sbp.D2Standard);
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31 assert(isa(g, 'grid.Cartesian'))
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32
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33 m = g.size();
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34 m_x = m(1);
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35 m_y = m(2);
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36 m_tot = g.N();
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37
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38 xlim = {g.x{1}(1), g.x{1}(end)};
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39 ylim = {g.x{2}(1), g.x{2}(end)};
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40 obj.grid = g;
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41
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42 % Operator sets
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43 ops_x = opSet(m_x, xlim, order);
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44 ops_y = opSet(m_y, ylim, order);
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45 Ix = speye(m_x);
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46 Iy = speye(m_y);
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47
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48 % Norms
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49 Hx = ops_x.H;
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50 Hy = ops_y.H;
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51 Hxi = ops_x.HI;
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52 Hyi = ops_y.HI;
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53
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54 obj.H_x = Hx;
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55 obj.H_y = Hy;
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56 obj.H = kron(Hx,Hy);
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57 obj.Hi = kron(Hxi,Hyi);
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58 obj.Hx = kron(Hx,Iy);
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59 obj.Hy = kron(Ix,Hy);
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60 obj.Hxi = kron(Hxi,Iy);
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61 obj.Hyi = kron(Ix,Hyi);
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62
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63 % Derivatives
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64 Dx = ops_x.D1;
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65 Dy = ops_y.D1;
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66 obj.Dx = kron(Dx,Iy);
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67 obj.Dy = kron(Ix,Dy);
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68
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69 % Boundary operators
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70 obj.e_w = kr(ops_x.e_l, Iy);
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71 obj.e_e = kr(ops_x.e_r, Iy);
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72 obj.e_s = kr(Ix, ops_y.e_l);
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73 obj.e_n = kr(Ix, ops_y.e_r);
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74
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75 obj.m = m;
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76 obj.h = [ops_x.h ops_y.h];
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77 obj.order = order;
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78 obj.a = a;
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79 obj.D = -(a(1)*obj.Dx + a(2)*obj.Dy);
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80
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81 end
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82 % Closure functions return the opertors applied to the own domain to close the boundary
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83 % 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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84 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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85 % type is a string specifying the type of boundary condition if there are several.
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86 % data is a function returning the data that should be applied at the boundary.
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87 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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88 % neighbour_boundary is a string specifying which boundary to interface to.
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89 function [closure, penalty] = boundary_condition(obj,boundary,type)
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90 default_arg('type','dirichlet');
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91
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92 sigma = -1; % Scalar penalty parameter
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93 switch boundary
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94 case {'w','W','west','West'}
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95 tau = sigma*obj.a(1)*obj.e_w*obj.H_y;
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96 closure = obj.Hi*tau*obj.e_w';
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97
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98 case {'s','S','south','South'}
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99 tau = sigma*obj.a(2)*obj.e_s*obj.H_x;
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100 closure = obj.Hi*tau*obj.e_s';
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101 end
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102 penalty = -obj.Hi*tau;
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103
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104 end
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105
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106 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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107
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108 % Get neighbour boundary operator
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109 switch neighbour_boundary
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110 case {'e','E','east','East'}
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111 e_neighbour = neighbour_scheme.e_e;
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112 case {'w','W','west','West'}
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113 e_neighbour = neighbour_scheme.e_w;
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114 case {'n','N','north','North'}
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115 e_neighbour = neighbour_scheme.e_n;
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116 case {'s','S','south','South'}
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117 e_neighbour = neighbour_scheme.e_s;
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118 end
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119
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120 % Upwind coupling
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121 sigma_ds = -1; %"Downstream" penalty
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122 sigma_us = 0; %"Upstream" penalty
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123
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124 switch boundary
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125 case {'w','W','west','West'}
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126 tau = sigma_ds*obj.a(1)*obj.e_w*obj.H_y;
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127 closure = obj.Hi*tau*obj.e_w';
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128 case {'e','E','east','East'}
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129 tau = sigma_us*obj.a(1)*obj.e_e*obj.H_y;
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130 closure = obj.Hi*tau*obj.e_e';
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131 case {'s','S','south','South'}
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132 tau = sigma_ds*obj.a(2)*obj.e_s*obj.H_x;
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133 closure = obj.Hi*tau*obj.e_s';
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134 case {'n','N','north','North'}
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135 tau = sigma_us*obj.a(2)*obj.e_n*obj.H_x;
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136 closure = obj.Hi*tau*obj.e_n';
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137 end
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138 penalty = -obj.Hi*tau*e_neighbour';
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139
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140 end
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141
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142 function N = size(obj)
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143 N = obj.m;
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144 end
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145
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146 end
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147
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148 methods(Static)
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149 % Calculates the matrices needed for the inteface coupling between boundary bound_u of scheme schm_u
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150 % and bound_v of scheme schm_v.
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151 % [uu, uv, vv, vu] = inteface_coupling(A,'r',B,'l')
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152 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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153 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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154 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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155 end
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156 end
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157 end