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annotate +scheme/Euler1d.m @ 53:cca09cc5121d

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Changed default animation time to infinity.
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 11 Nov 2015 19:20:32 -0800
parents 75ebf5d3cfe5
children 2194cd385419
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1 classdef Euler1d < 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 N % Number of points total
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5 h % Grid spacing
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6 u % Grid values
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7 x % Values of x and y for each
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8 order % Order accuracy for the approximation
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9
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10 D % non-stabalized scheme operator
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11 Fx
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12 M % Derivative norm
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13 gamma
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14
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15 T
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16 p
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17 c
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20 H % Discrete norm
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21 Hi
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22 e_l, e_r, e_L, e_R;
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24 end
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25
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26 methods
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27 function obj = Euler1d(m,xlim,order,gama,opsGen,do_upwind)
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28 default_arg('opsGen',@sbp.Ordinary);
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29 default_arg('gama', 1.4);
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30 default_arg('do_upwind', false);
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31 gamma = gama;
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32
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33 [x, h] = util.get_grid(xlim{:},m);
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35 if do_upwind
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36 ops = spb.Upwind(m,h,order);
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37 Dp = ops.derivatives.Dp;
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38 Dm = ops.derivatives.Dm;
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40 printExpr('issparse(Dp)');
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41 printExpr('issparse(Dm)');
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43 D1 = (Dp + Dm)/2;
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44 else
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45 ops = opsGen(m,h,order);
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46 D1 = sparse(ops.derivatives.D1);
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47 end
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48
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49 H = sparse(ops.norms.H);
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50 Hi = sparse(ops.norms.HI);
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51 e_l = sparse(ops.boundary.e_1);
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52 e_r = sparse(ops.boundary.e_m);
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53
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54 I_x = speye(m);
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55 I_3 = speye(3);
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56
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57
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58 D1 = kr(D1, I_3);
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59 if do_upwind
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60 Ddisp = kr(Ddisp,I_3);
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61 end
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62
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63 % Norms
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64 obj.H = kr(H,I_3);
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65 obj.Hi = kr(Hi,I_3);
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66
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67 % Boundary operators
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68 obj.e_l = e_l;
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69 obj.e_r = e_r;
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70 obj.e_L = kr(e_l,I_3);
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71 obj.e_R = kr(e_r,I_3);
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72
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73 obj.m = m;
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74 obj.h = h;
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75 obj.order = order;
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76
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77 % Man har Q_t+F_x=0 i 1D Euler, där
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78 % q=[rho, rho*u, e]^T
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79 % F=[rho*u, rho*u^2+p, (e+p)*u] ^T
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80 % p=(gamma-1)*(e-rho*u^2/2);
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81
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82 %Solving on form q_t + F_x = 0
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83 function o = F(Q)
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84 % Flux: f = [q2; q2.^2/q1 + p(q); (q3+p(q))*q2/q1];
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85 o = [Q(2,:); Q(2,:).^2/Q(1,:) + p(Q); (Q(3,:)+p(Q)).*Q(2,:)./Q(1,:)];
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86 end
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87
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88 % Equation of state
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89 function o = p(Q)
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90 % Pressure p = (gamma-1)*(q3-q2.^2/q1/2)
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91 o = (gamma-1)*(Q(3,:)-Q(2,:).^2/Q(1,:)/2);
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92 end
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93
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94 function o = c(Q)
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95 % Speed of light c = sqrt(obj.gamma*p/rho);
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96 o = sqrt(gamma*p(Q)./Q(1,:));
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97 end
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98
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99
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100 % R =
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101 % [sqrt(2*(gamma-1))*rho , rho , rho ;
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102 % sqrt(2*(gamma-1))*rho*u , rho*(u+c) , rho*(u-c) ;
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103 % sqrt(2*(gamma-1))*rho*u^2/2, e+(gamma-1)*(e-rho*u^2/2)+rho*u*c, e+(gamma-1)*(e-rho*u^2/2)-rho*u*c]);
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104 function o = T(q)
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105 rho = q(1);
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106 u = q(2)/q(1);
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107 e = q(3);
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108
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109 c = sqrt(gamma*p(q)/rho);
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110
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111 sqrt2gamm = sqrt(2*(gamma-1));
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112
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113 o = [
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114 sqrt2gamm*rho , rho , rho ;
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115 sqrt2gamm*rho*u , rho*(u+c) , rho*(u-c) ;
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116 sqrt2gamm*rho*u^2/2, e+(gamma-1)*(e-rho*u^2/2)+rho*u*c , e+(gamma-1)*(e-rho*u^2/2)-rho*u*c
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117 ];
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118 % Devide columns by stuff to get rid of extra comp?
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119 end
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120
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121 function o = Fx(q)
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122 Q = reshape(q,3,m);
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123 o = reshape(F(Q),3*m,1);
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124 o = D1*o;
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125 end
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126
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127
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128 % A=R*Lambda*inv(R), där Lambda=diag(u, u+c, u-c) (c är ljudhastigheten)
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129 % c^2=gamma*p/rho
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130 % function o = A(rho,u,e)
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131 % end
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132 if do_upwind
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133 obj.D = @(q)-Fx(q) + Ddisp*(1)*u;
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134 else
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135 obj.D = @(q)-Fx(q);
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136 end
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137
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138 obj.Fx = @Fx;
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139 obj.T = @T;
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140 obj.u = x;
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141 obj.x = kr(x,ones(3,1));
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142 obj.p = @p;
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143 obj.c = @c;
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144 obj.gamma = gamma;
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145 end
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146
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147
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148 % Enforces the boundary conditions
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149 % w+ = R*w- + g(t)
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150 function closure = boundary_condition(obj,boundary, type, varargin)
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151 [e_s,e_S,s] = obj.get_boundary_ops(boundary);
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152
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153 % Boundary condition on form
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154 % w_in = R*w_out + g, where g is data
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155
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156 % How to handle when the number of BC we want to set changes
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157 % How to handel u = 0 as an example
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158
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159 % Måste sätta in s och fixa tecken som de ska vara
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160
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161 % Kanske ska man tala om vilka karakteristikor som är in och ut i anropet
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162 % Man kan sen kolla om det stämmer (men hur blir det med u=0?)
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163 % Och antingen tillåta att man skickar in flera alternativ och väljer automatiskt
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164 % eller låta koden utanför bestämma vilken penalty som ska appliceras.
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165
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166 switch type
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167 case 'wall'
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168 closure = obj.boundary_condition_wall(boundary);
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169 otherwise
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170 error('Unsupported bc type: %s', type);
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171 end
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172
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173 % T = obj.T(e_S*v);
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174
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175 % c = sqrt(gamma*p/rho);
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176 % l = [u, u+c, u-c];
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177
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178 % p_in = find(s*l <= 0);
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179 % p_ot = find(s*l > 0);
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180
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181 % p = [p_in, p_ot] % Permutation to sort
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182 % pt(p) = 1:length(p); % Inverse permutation
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183
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184 % L_in = diag(abs(l(p_in)));
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185 % L_ot = diag(abs(l(p_ot)));
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186
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187 % Lambda = diag(u, u+c, u-c);
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188
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189 % tau = -e_S*sparse(T*[L_in; R'*L_in]); % Något med pt
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190
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191
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192 % w_s = T'*(e_S*v);
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193 % w_in = w_s(p_in);
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194 % w_ot = w_s(p_ot);
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195
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196
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197 % function closure_fun(q,t)
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198 % obj.Hi * tau * (w_in - R*w_ot - g(t));
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199 % end
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200
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201 % function closure_fun_indep(q,t)
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202 % obj.Hi * tau * (w_in - R*w_ot - g;
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203 % end
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204
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205
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206 % switch class(g)
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207 % case 'double'
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208 % closure = @closure_fun;
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209 % case 'function_handle'
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210 % closure = @closure_fun_indep;
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211 % otherwise
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212 % error('Wierd data argument!');
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213 % end
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214
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215 end
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216
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217 % Set wall boundary condition v = 0.
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218 function closure = boundary_condition_wall(obj,boundary)
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219 [e_s,e_S,s] = obj.get_boundary_ops(boundary);
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220
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221 % v = 0 corresponds to
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222 % L = [0 1 0];
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223 % g = 0
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224 %
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225 % Tp =
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226 % R = -(u-c)/(u+c)
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227
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228 % tau = alpha * (u+c)
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229 % (alpha+1)(u+c) + 1/4* alpha^2|u-c| <= 0
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230 % 4*(alpha+1)(u+c) + alpha^2|u-c| <= 0
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231 % 4 * (alpha+1)(u+c) + alpha^2|u| + alpha^2*c <= 0
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232 % |u|*(sgn(u)*4 + sgn(u)*4*alpha + alpha^2) + c*(4 + 4alpha + alpha^2) <= 0
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233 % |u|*(alpha^2 + 4*sgn(u)*alpha + 4*sgn(u)) + c*(alpha+2)^2 <= 0
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234 % |u|*[(alpha + 2*sgn(u))^2 - 4*(sgn(u)-1)] + c*(alpha+2)^2 <= 0
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235
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236
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237 % om vi låtsas att u = 0:
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238 % (alpha+1)c + 1/4 * alpha^2*c <= 0
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239 % alpha^2 + 4*alpha +4 <= 0
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240 % (alpha + 2)^2 <= 0
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241 % alpha = -2 gives tau = -2*c;
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242
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243
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244 % Vill vi sätta penalty på karateristikan som är nära noll också eller vill
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245 % vi låta den vara fri?
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246
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247
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248 switch s
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249 case -1
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250 p_in = 2;
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251 p_zero = 1;
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252 p_ot = 3;
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253 case 1
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254 p_in = 3;
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255 p_zero = 1;
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256 p_ot = 2;
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257 otherwise
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258 error();
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259 end
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260
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261 p = [p_in, p_zero, p_ot]; % Permutation to sort
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262 pt(p) = 1:length(p); % Inverse permutation
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263
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264 function o = closure_fun(q)
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265
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266 q_s = e_S'*q;
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267 rho = q_s(1);
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268 u = q_s(2)/rho;
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269 c = obj.c(q_s);
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270
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271 T = obj.T(q_s);
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272 R = -(u-c)/(u+c);
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273 % l = [u, u+c, u-c];
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274
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275 % p_in = find(s*l <= 0);
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276 % p_ot = find(s*l > 0);
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277
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278
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279 tau1 = -2*c;
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280 tau2 = [0; 0]; % Penalty only on ingoing char.
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281
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282 % L_in = diag(abs(l(p_in)));
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283 % L_ot = diag(abs(l(p_ot)));
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284
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285 tauHat = [tau1; tau2];
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286 tau = -s*e_S*sparse(T*tauHat(pt));
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287
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288 w_s = inv(T)*q_s;
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289 % w_s = T\q_s;
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290 % w_s = Tinv * q_s; % Med analytisk matris
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291 w_in = w_s(p_in);
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292 w_ot = w_s(p_ot);
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293
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294 o = obj.Hi * tau * (w_in - R*w_ot);
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295 end
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296
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297 closure = @closure_fun;
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298 end
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299
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300 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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301 error('NOT DONE')
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302 % u denotes the solution in the own domain
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303 % v denotes the solution in the neighbour domain
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304 [e_u,d1_u,d2_u,d3_u,s_u,gamm_u,delt_u, halfnorm_inv] = obj.get_boundary_ops(boundary);
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305 [e_v,d1_v,d2_v,d3_v,s_v,gamm_v,delt_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
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306
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307 tuning = 2;
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308
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309 alpha_u = obj.alpha;
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310 alpha_v = neighbour_scheme.alpha;
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311
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312 tau1 = ((alpha_u/2)/delt_u + (alpha_v/2)/delt_v)/2*tuning;
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313 % tau1 = (alpha_u/2 + alpha_v/2)/(2*delt_u)*tuning;
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314 tau4 = s_u*alpha_u/2;
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315
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316 sig2 = ((alpha_u/2)/gamm_u + (alpha_v/2)/gamm_v)/2*tuning;
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317 sig3 = -s_u*alpha_u/2;
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318
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319 phi2 = s_u*1/2;
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320
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321 psi1 = -s_u*1/2;
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322
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323 tau = tau1*e_u + tau4*d3_u;
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324 sig = sig2*d1_u + sig3*d2_u ;
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325 phi = phi2*d1_u ;
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326 psi = psi1*e_u ;
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327
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328 closure = halfnorm_inv*(tau*e_u' + sig*d1_u' + phi*alpha_u*d2_u' + psi*alpha_u*d3_u');
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329 penalty = -halfnorm_inv*(tau*e_v' + sig*d1_v' + phi*alpha_v*d2_v' + psi*alpha_v*d3_v');
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330 end
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331
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332 % Ruturns the boundary ops and sign for the boundary specified by the string boundary.
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333 % The right boundary is considered the positive boundary
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334 function [e,E,s] = get_boundary_ops(obj,boundary)
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335 switch boundary
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336 case 'l'
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337 e = obj.e_l;
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338 E = obj.e_L;
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339 s = -1;
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340 case 'r'
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341 e = obj.e_r;
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342 E = obj.e_R;
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343 s = 1;
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344 otherwise
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345 error('No such boundary: boundary = %s',boundary);
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346 end
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347 end
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348
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349 function N = size(obj)
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350 N = prod(obj.m);
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351 end
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352
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353 end
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354 end