Mercurial > repos > public > sbplib
annotate +scheme/Wave2dCurve.m @ 1027:d6ab5ceba496 feature/advectionRV
Support variable wave speed and upwind operators in Utux
| author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
|---|---|
| date | Mon, 07 Jan 2019 16:35:04 +0100 |
| parents | 706d1c2b4199 |
| children |
| rev | line source |
|---|---|
| 0 | 1 classdef Wave2dCurve < scheme.Scheme |
| 2 properties | |
| 3 m % Number of points in each direction, possibly a vector | |
| 4 h % Grid spacing | |
|
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5 |
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6 grid |
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7 |
| 0 | 8 order % Order accuracy for the approximation |
| 9 | |
| 10 D % non-stabalized scheme operator | |
| 11 M % Derivative norm | |
| 12 c | |
| 13 J, Ji | |
| 14 a11, a12, a22 | |
| 15 | |
| 16 H % Discrete norm | |
| 17 Hi | |
| 18 H_u, H_v % Norms in the x and y directions | |
| 19 Hu,Hv % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir. | |
| 20 Hi_u, Hi_v | |
| 21 Hiu, Hiv | |
| 22 e_w, e_e, e_s, e_n | |
| 23 du_w, dv_w | |
| 24 du_e, dv_e | |
| 25 du_s, dv_s | |
| 26 du_n, dv_n | |
| 27 gamm_u, gamm_v | |
|
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28 lambda |
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29 |
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30 Dx, Dy % Physical derivatives |
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31 |
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32 x_u |
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33 x_v |
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34 y_u |
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35 y_v |
| 0 | 36 end |
| 37 | |
| 38 methods | |
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39 function obj = Wave2dCurve(g ,order, c, opSet) |
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40 default_arg('opSet',@sbp.D2Variable); |
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41 default_arg('c', 1); |
| 0 | 42 |
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43 warning('Use LaplaceCruveilinear instead') |
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44 |
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45 assert(isa(g, 'grid.Curvilinear')) |
| 0 | 46 |
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47 m = g.size(); |
| 0 | 48 m_u = m(1); |
| 49 m_v = m(2); | |
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50 m_tot = g.N(); |
| 0 | 51 |
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52 h = g.scaling(); |
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53 h_u = h(1); |
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54 h_v = h(2); |
| 0 | 55 |
| 56 % Operators | |
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57 ops_u = opSet(m_u, {0, 1}, order); |
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58 ops_v = opSet(m_v, {0, 1}, order); |
| 0 | 59 |
| 60 I_u = speye(m_u); | |
| 61 I_v = speye(m_v); | |
| 62 | |
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63 D1_u = ops_u.D1; |
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64 D2_u = ops_u.D2; |
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65 H_u = ops_u.H; |
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66 Hi_u = ops_u.HI; |
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67 e_l_u = ops_u.e_l; |
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68 e_r_u = ops_u.e_r; |
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69 d1_l_u = ops_u.d1_l; |
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70 d1_r_u = ops_u.d1_r; |
| 0 | 71 |
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72 D1_v = ops_v.D1; |
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73 D2_v = ops_v.D2; |
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74 H_v = ops_v.H; |
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75 Hi_v = ops_v.HI; |
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76 e_l_v = ops_v.e_l; |
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77 e_r_v = ops_v.e_r; |
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78 d1_l_v = ops_v.d1_l; |
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79 d1_r_v = ops_v.d1_r; |
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80 |
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81 Du = kr(D1_u,I_v); |
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82 Dv = kr(I_u,D1_v); |
| 0 | 83 |
| 84 % Metric derivatives | |
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85 coords = g.points(); |
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86 x = coords(:,1); |
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87 y = coords(:,2); |
| 0 | 88 |
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89 x_u = Du*x; |
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90 x_v = Dv*x; |
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91 y_u = Du*y; |
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92 y_v = Dv*y; |
| 0 | 93 |
| 94 J = x_u.*y_v - x_v.*y_u; | |
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95 a11 = 1./J .* (x_v.^2 + y_v.^2); |
| 0 | 96 a12 = -1./J .* (x_u.*x_v + y_u.*y_v); |
| 97 a22 = 1./J .* (x_u.^2 + y_u.^2); | |
| 98 lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2)); | |
| 99 | |
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100 % Assemble full operators |
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101 L_12 = spdiags(a12, 0, m_tot, m_tot); |
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102 Duv = Du*L_12*Dv; |
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103 Dvu = Dv*L_12*Du; |
| 0 | 104 |
| 105 Duu = sparse(m_tot); | |
| 106 Dvv = sparse(m_tot); | |
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107 ind = grid.funcToMatrix(g, 1:m_tot); |
| 0 | 108 |
| 109 for i = 1:m_v | |
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110 D = D2_u(a11(ind(:,i))); |
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111 p = ind(:,i); |
| 0 | 112 Duu(p,p) = D; |
| 113 end | |
| 114 | |
| 115 for i = 1:m_u | |
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116 D = D2_v(a22(ind(i,:))); |
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117 p = ind(i,:); |
| 0 | 118 Dvv(p,p) = D; |
| 119 end | |
| 120 | |
| 121 obj.H = kr(H_u,H_v); | |
| 122 obj.Hi = kr(Hi_u,Hi_v); | |
| 123 obj.Hu = kr(H_u,I_v); | |
| 124 obj.Hv = kr(I_u,H_v); | |
| 125 obj.Hiu = kr(Hi_u,I_v); | |
| 126 obj.Hiv = kr(I_u,Hi_v); | |
| 127 | |
| 128 obj.e_w = kr(e_l_u,I_v); | |
| 129 obj.e_e = kr(e_r_u,I_v); | |
| 130 obj.e_s = kr(I_u,e_l_v); | |
| 131 obj.e_n = kr(I_u,e_r_v); | |
| 132 obj.du_w = kr(d1_l_u,I_v); | |
| 133 obj.dv_w = (obj.e_w'*Dv)'; | |
| 134 obj.du_e = kr(d1_r_u,I_v); | |
| 135 obj.dv_e = (obj.e_e'*Dv)'; | |
| 136 obj.du_s = (obj.e_s'*Du)'; | |
| 137 obj.dv_s = kr(I_u,d1_l_v); | |
| 138 obj.du_n = (obj.e_n'*Du)'; | |
| 370 | 139 obj.dv_n = kr(I_u,d1_r_v); |
| 376 | 140 |
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141 obj.x_u = x_u; |
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142 obj.x_v = x_v; |
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143 obj.y_u = y_u; |
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144 obj.y_v = y_v; |
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145 |
| 0 | 146 obj.m = m; |
| 147 obj.h = [h_u h_v]; | |
| 148 obj.order = order; | |
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149 obj.grid = g; |
| 0 | 150 |
| 151 obj.c = c; | |
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152 obj.J = spdiags(J, 0, m_tot, m_tot); |
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153 obj.Ji = spdiags(1./J, 0, m_tot, m_tot); |
| 0 | 154 obj.a11 = a11; |
| 155 obj.a12 = a12; | |
| 156 obj.a22 = a22; | |
| 157 obj.D = obj.Ji*c^2*(Duu + Duv + Dvu + Dvv); | |
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158 obj.lambda = lambda; |
| 0 | 159 |
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160 obj.Dx = spdiag( y_v./J)*Du + spdiag(-y_u./J)*Dv; |
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161 obj.Dy = spdiag(-x_v./J)*Du + spdiag( x_u./J)*Dv; |
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162 |
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163 obj.gamm_u = h_u*ops_u.borrowing.M.d1; |
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164 obj.gamm_v = h_v*ops_v.borrowing.M.d1; |
| 0 | 165 end |
| 166 | |
| 167 | |
| 168 % Closure functions return the opertors applied to the own doamin to close the boundary | |
| 169 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. | |
| 170 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. | |
| 171 % type is a string specifying the type of boundary condition if there are several. | |
| 172 % data is a function returning the data that should be applied at the boundary. | |
| 173 % neighbour_scheme is an instance of Scheme that should be interfaced to. | |
| 174 % neighbour_boundary is a string specifying which boundary to interface to. | |
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175 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter) |
| 0 | 176 default_arg('type','neumann'); |
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177 default_arg('parameter', []); |
| 0 | 178 |
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179 [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv , ~, ~, ~, scale_factor] = obj.get_boundary_ops(boundary); |
| 0 | 180 switch type |
| 181 % Dirichlet boundary condition | |
| 182 case {'D','d','dirichlet'} | |
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183 % v denotes the solution in the neighbour domain |
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184 tuning = 1.2; |
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185 % tuning = 20.2; |
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186 [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t] = obj.get_boundary_ops(boundary); |
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187 |
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188 a_n = spdiag(coeff_n); |
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189 a_t = spdiag(coeff_t); |
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190 |
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191 F = (s * a_n * d_n' + s * a_t*d_t')'; |
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192 |
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193 u = obj; |
| 0 | 194 |
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195 b1 = gamm*u.lambda./u.a11.^2; |
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196 b2 = gamm*u.lambda./u.a22.^2; |
| 0 | 197 |
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198 tau = -1./b1 - 1./b2; |
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199 tau = tuning * spdiag(tau); |
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360
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200 sig1 = 1; |
| 0 | 201 |
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202 penalty_parameter_1 = halfnorm_inv_n*(tau + sig1*halfnorm_inv_t*F*e'*halfnorm_t)*e; |
| 0 | 203 |
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204 closure = obj.Ji*obj.c^2 * penalty_parameter_1*e'; |
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205 penalty = -obj.Ji*obj.c^2 * penalty_parameter_1; |
| 0 | 206 |
| 207 | |
| 208 % Neumann boundary condition | |
| 209 case {'N','n','neumann'} | |
| 210 c = obj.c; | |
| 211 | |
| 212 a_n = spdiags(coeff_n,0,length(coeff_n),length(coeff_n)); | |
| 213 a_t = spdiags(coeff_t,0,length(coeff_t),length(coeff_t)); | |
| 214 d = (a_n * d_n' + a_t*d_t')'; | |
| 215 | |
| 216 tau1 = -s; | |
| 217 tau2 = 0; | |
| 218 tau = c.^2 * obj.Ji*(tau1*e + tau2*d); | |
| 219 | |
| 220 closure = halfnorm_inv*tau*d'; | |
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221 penalty = -halfnorm_inv*tau; |
| 0 | 222 |
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223 % Characteristic boundary condition |
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224 case {'characteristic', 'char', 'c'} |
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225 default_arg('parameter', 1); |
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226 beta = parameter; |
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227 c = obj.c; |
| 0 | 228 |
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229 a_n = spdiags(coeff_n,0,length(coeff_n),length(coeff_n)); |
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230 a_t = spdiags(coeff_t,0,length(coeff_t),length(coeff_t)); |
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231 d = s*(a_n * d_n' + a_t*d_t')'; % outward facing normal derivative |
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232 |
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233 tau = -c.^2 * 1/beta*obj.Ji*e; |
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234 |
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451
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235 warning('is this right?! /c?') |
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236 closure{1} = halfnorm_inv*tau/c*spdiag(scale_factor)*e'; |
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237 closure{2} = halfnorm_inv*tau*beta*d'; |
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238 penalty = -halfnorm_inv*tau; |
| 0 | 239 |
| 240 % Unknown, boundary condition | |
| 241 otherwise | |
| 242 error('No such boundary condition: type = %s',type); | |
| 243 end | |
| 244 end | |
| 245 | |
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246 function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type) |
| 0 | 247 % u denotes the solution in the own domain |
| 248 % v denotes the solution in the neighbour domain | |
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249 tuning = 1.2; |
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250 % tuning = 20.2; |
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251 [e_u, d_n_u, d_t_u, coeff_n_u, coeff_t_u, s_u, gamm_u, halfnorm_inv_u_n, halfnorm_inv_u_t, halfnorm_u_t, I_u] = obj.get_boundary_ops(boundary); |
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252 [e_v, d_n_v, d_t_v, coeff_n_v, coeff_t_v, s_v, gamm_v, halfnorm_inv_v_n, halfnorm_inv_v_t, halfnorm_v_t, I_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary); |
| 0 | 253 |
|
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254 a_n_u = spdiag(coeff_n_u); |
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255 a_t_u = spdiag(coeff_t_u); |
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256 a_n_v = spdiag(coeff_n_v); |
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257 a_t_v = spdiag(coeff_t_v); |
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258 |
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259 F_u = (s_u * a_n_u * d_n_u' + s_u * a_t_u*d_t_u')'; |
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260 F_v = (s_v * a_n_v * d_n_v' + s_v * a_t_v*d_t_v')'; |
| 0 | 261 |
|
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262 u = obj; |
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263 v = neighbour_scheme; |
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264 |
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265 b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2; |
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266 b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2; |
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267 b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2; |
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268 b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2; |
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269 |
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270 tau = -1./(4*b1_u) -1./(4*b1_v) -1./(4*b2_u) -1./(4*b2_v); |
|
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271 tau = tuning * spdiag(tau); |
| 0 | 272 sig1 = 1/2; |
| 83 | 273 sig2 = -1/2; |
| 0 | 274 |
|
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275 penalty_parameter_1 = halfnorm_inv_u_n*(e_u*tau + sig1*halfnorm_inv_u_t*F_u*e_u'*halfnorm_u_t*e_u); |
| 0 | 276 penalty_parameter_2 = halfnorm_inv_u_n * sig2 * e_u; |
| 277 | |
| 278 | |
|
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279 closure = obj.Ji*obj.c^2 * ( penalty_parameter_1*e_u' + penalty_parameter_2*F_u'); |
| 83 | 280 penalty = obj.Ji*obj.c^2 * (-penalty_parameter_1*e_v' + penalty_parameter_2*F_v'); |
| 0 | 281 end |
| 282 | |
| 283 % Ruturns the boundary ops and sign for the boundary specified by the string boundary. | |
| 284 % The right boundary is considered the positive boundary | |
|
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285 % |
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286 % I -- the indecies of the boundary points in the grid matrix |
|
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287 function [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t, I, scale_factor] = get_boundary_ops(obj, boundary) |
|
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288 |
|
337
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289 % gridMatrix = zeros(obj.m(2),obj.m(1)); |
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290 % gridMatrix(:) = 1:numel(gridMatrix); |
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291 |
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292 ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m)); |
|
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293 |
| 0 | 294 switch boundary |
| 295 case 'w' | |
| 296 e = obj.e_w; | |
| 297 d_n = obj.du_w; | |
| 298 d_t = obj.dv_w; | |
| 299 s = -1; | |
| 300 | |
|
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301 I = ind(1,:); |
|
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302 coeff_n = obj.a11(I); |
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303 coeff_t = obj.a12(I); |
|
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304 scale_factor = sqrt(obj.x_v(I).^2 + obj.y_v(I).^2); |
| 0 | 305 case 'e' |
| 306 e = obj.e_e; | |
| 307 d_n = obj.du_e; | |
| 308 d_t = obj.dv_e; | |
| 309 s = 1; | |
| 310 | |
|
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311 I = ind(end,:); |
|
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312 coeff_n = obj.a11(I); |
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313 coeff_t = obj.a12(I); |
|
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314 scale_factor = sqrt(obj.x_v(I).^2 + obj.y_v(I).^2); |
| 0 | 315 case 's' |
| 316 e = obj.e_s; | |
| 317 d_n = obj.dv_s; | |
| 318 d_t = obj.du_s; | |
| 319 s = -1; | |
| 320 | |
|
337
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|
321 I = ind(:,1)'; |
|
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322 coeff_n = obj.a22(I); |
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323 coeff_t = obj.a12(I); |
|
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324 scale_factor = sqrt(obj.x_u(I).^2 + obj.y_u(I).^2); |
| 0 | 325 case 'n' |
| 326 e = obj.e_n; | |
| 327 d_n = obj.dv_n; | |
| 328 d_t = obj.du_n; | |
| 329 s = 1; | |
| 330 | |
|
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331 I = ind(:,end)'; |
|
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332 coeff_n = obj.a22(I); |
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333 coeff_t = obj.a12(I); |
|
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334 scale_factor = sqrt(obj.x_u(I).^2 + obj.y_u(I).^2); |
| 0 | 335 otherwise |
| 336 error('No such boundary: boundary = %s',boundary); | |
| 337 end | |
| 338 | |
| 339 switch boundary | |
| 340 case {'w','e'} | |
| 341 halfnorm_inv_n = obj.Hiu; | |
| 342 halfnorm_inv_t = obj.Hiv; | |
| 343 halfnorm_t = obj.Hv; | |
| 344 gamm = obj.gamm_u; | |
| 345 case {'s','n'} | |
| 346 halfnorm_inv_n = obj.Hiv; | |
| 347 halfnorm_inv_t = obj.Hiu; | |
| 348 halfnorm_t = obj.Hu; | |
| 349 gamm = obj.gamm_v; | |
| 350 end | |
| 351 end | |
| 352 | |
| 353 function N = size(obj) | |
| 354 N = prod(obj.m); | |
| 355 end | |
| 356 | |
| 357 | |
| 358 end | |
| 359 end |