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annotate +scheme/Utux2D.m @ 666:2d85f17a8aec feature/utux2D
Add possibility for damping terms at interpolation interface.
| author | Martin Almquist <malmquist@stanford.edu> |
|---|---|
| date | Mon, 16 Oct 2017 21:56:12 -0700 |
| parents | b7b3c11fab4d |
| children | f4595f14d696 |
| rev | line source |
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| 591 | 1 classdef Utux2D < scheme.Scheme |
| 2 properties | |
| 3 m % Number of points in each direction, possibly a vector | |
| 4 h % Grid spacing | |
| 5 grid % Grid | |
| 6 order % Order accuracy for the approximation | |
| 7 v0 % Initial data | |
| 8 | |
| 9 a % Wave speed a = [a1, a2]; | |
| 10 | |
| 11 H % Discrete norm | |
| 595 | 12 H_x, H_y % Norms in the x and y directions |
| 13 Hi, Hx, Hy, Hxi, Hyi % Kroneckered norms | |
| 591 | 14 |
| 15 % Derivatives | |
| 16 Dx, Dy | |
| 17 | |
| 18 % Boundary operators | |
| 19 e_w, e_e, e_s, e_n | |
| 20 | |
| 21 D % Total discrete operator | |
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22 |
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23 % String, type of interface coupling |
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24 % Default: 'upwind' |
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25 % Other: 'centered' |
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26 coupling_type |
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27 |
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28 % String, type of interpolation operators |
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29 % Default: 'AWW' (Almquist Wang Werpers) |
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30 % Other: 'MC' (Mattsson Carpenter) |
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31 interpolation_type |
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32 |
| 591 | 33 |
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34 % Cell array, damping on upwstream and downstream sides. |
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35 interpolation_damping |
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36 |
| 591 | 37 end |
| 38 | |
| 39 | |
| 40 methods | |
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41 function obj = Utux2D(g ,order, opSet, a, coupling_type, interpolation_type, interpolation_damping) |
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42 |
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43 default_arg('interpolation_damping',{0,0}); |
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44 default_arg('interpolation_type','AWW'); |
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45 default_arg('coupling_type','upwind'); |
| 591 | 46 default_arg('a',1/sqrt(2)*[1, 1]); |
| 47 default_arg('opSet',@sbp.D2Standard); | |
| 48 assert(isa(g, 'grid.Cartesian')) | |
| 49 | |
| 50 m = g.size(); | |
| 51 m_x = m(1); | |
| 52 m_y = m(2); | |
| 53 m_tot = g.N(); | |
| 54 | |
| 595 | 55 xlim = {g.x{1}(1), g.x{1}(end)}; |
| 56 ylim = {g.x{2}(1), g.x{2}(end)}; | |
| 591 | 57 obj.grid = g; |
| 58 | |
| 59 % Operator sets | |
| 60 ops_x = opSet(m_x, xlim, order); | |
| 61 ops_y = opSet(m_y, ylim, order); | |
| 62 Ix = speye(m_x); | |
| 63 Iy = speye(m_y); | |
| 64 | |
| 65 % Norms | |
| 66 Hx = ops_x.H; | |
| 67 Hy = ops_y.H; | |
| 68 Hxi = ops_x.HI; | |
| 69 Hyi = ops_y.HI; | |
| 595 | 70 |
| 71 obj.H_x = Hx; | |
| 72 obj.H_y = Hy; | |
| 591 | 73 obj.H = kron(Hx,Hy); |
| 74 obj.Hi = kron(Hxi,Hyi); | |
| 75 obj.Hx = kron(Hx,Iy); | |
| 76 obj.Hy = kron(Ix,Hy); | |
| 77 obj.Hxi = kron(Hxi,Iy); | |
| 78 obj.Hyi = kron(Ix,Hyi); | |
| 79 | |
| 80 % Derivatives | |
| 81 Dx = ops_x.D1; | |
| 82 Dy = ops_y.D1; | |
| 83 obj.Dx = kron(Dx,Iy); | |
| 84 obj.Dy = kron(Ix,Dy); | |
| 85 | |
| 86 % Boundary operators | |
| 87 obj.e_w = kr(ops_x.e_l, Iy); | |
| 88 obj.e_e = kr(ops_x.e_r, Iy); | |
| 89 obj.e_s = kr(Ix, ops_y.e_l); | |
| 90 obj.e_n = kr(Ix, ops_y.e_r); | |
| 91 | |
| 92 obj.m = m; | |
| 93 obj.h = [ops_x.h ops_y.h]; | |
| 94 obj.order = order; | |
| 595 | 95 obj.a = a; |
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96 obj.coupling_type = coupling_type; |
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97 obj.interpolation_type = interpolation_type; |
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98 obj.interpolation_damping = interpolation_damping; |
| 591 | 99 obj.D = -(a(1)*obj.Dx + a(2)*obj.Dy); |
| 100 | |
| 101 end | |
| 102 % Closure functions return the opertors applied to the own domain to close the boundary | |
| 103 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. | |
| 104 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. | |
| 105 % type is a string specifying the type of boundary condition if there are several. | |
| 106 % data is a function returning the data that should be applied at the boundary. | |
| 107 % neighbour_scheme is an instance of Scheme that should be interfaced to. | |
| 108 % neighbour_boundary is a string specifying which boundary to interface to. | |
| 109 function [closure, penalty] = boundary_condition(obj,boundary,type) | |
| 110 default_arg('type','dirichlet'); | |
| 111 | |
| 112 sigma = -1; % Scalar penalty parameter | |
| 113 switch boundary | |
| 114 case {'w','W','west','West'} | |
| 595 | 115 tau = sigma*obj.a(1)*obj.e_w*obj.H_y; |
| 591 | 116 closure = obj.Hi*tau*obj.e_w'; |
| 117 | |
| 118 case {'s','S','south','South'} | |
| 595 | 119 tau = sigma*obj.a(2)*obj.e_s*obj.H_x; |
| 591 | 120 closure = obj.Hi*tau*obj.e_s'; |
| 121 end | |
| 122 penalty = -obj.Hi*tau; | |
| 123 | |
| 124 end | |
| 125 | |
| 126 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) | |
| 127 | |
| 128 % Get neighbour boundary operator | |
| 129 switch neighbour_boundary | |
| 130 case {'e','E','east','East'} | |
| 131 e_neighbour = neighbour_scheme.e_e; | |
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132 m_neighbour = neighbour_scheme.m(2); |
| 591 | 133 case {'w','W','west','West'} |
| 134 e_neighbour = neighbour_scheme.e_w; | |
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135 m_neighbour = neighbour_scheme.m(2); |
| 591 | 136 case {'n','N','north','North'} |
| 137 e_neighbour = neighbour_scheme.e_n; | |
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138 m_neighbour = neighbour_scheme.m(1); |
| 591 | 139 case {'s','S','south','South'} |
| 140 e_neighbour = neighbour_scheme.e_s; | |
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141 m_neighbour = neighbour_scheme.m(1); |
| 591 | 142 end |
| 143 | |
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144 switch obj.coupling_type |
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145 |
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146 % Upwind coupling (energy dissipation) |
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147 case 'upwind' |
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148 sigma_ds = -1; %"Downstream" penalty |
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149 sigma_us = 0; %"Upstream" penalty |
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150 |
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151 % Energy-preserving coupling (no energy dissipation) |
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152 case 'centered' |
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153 sigma_ds = -1/2; %"Downstream" penalty |
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154 sigma_us = 1/2; %"Upstream" penalty |
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155 |
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156 otherwise |
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157 error(['Interface coupling type ' coupling_type ' is not available.']) |
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158 end |
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159 |
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160 % Check grid ratio for interpolation |
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161 switch boundary |
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162 case {'w','W','west','West','e','E','east','East'} |
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163 m = obj.m(2); |
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164 case {'s','S','south','South','n','N','north','North'} |
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165 m = obj.m(1); |
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166 end |
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167 grid_ratio = m/m_neighbour; |
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168 if grid_ratio ~= 1 |
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169 |
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170 [ms, index] = sort([m, m_neighbour]); |
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171 orders = [obj.order, neighbour_scheme.order]; |
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172 orders = orders(index); |
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173 |
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174 switch obj.interpolation_type |
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175 case 'MC' |
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176 interpOpSet = sbp.InterpMC(ms(1),ms(2),orders(1),orders(2)); |
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177 if grid_ratio < 1 |
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178 I_neighbour2local_us = interpOpSet.IF2C; |
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179 I_neighbour2local_ds = interpOpSet.IF2C; |
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180 I_local2neighbour_us = interpOpSet.IC2F; |
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181 I_local2neighbour_ds = interpOpSet.IC2F; |
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182 elseif grid_ratio > 1 |
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183 I_neighbour2local_us = interpOpSet.IC2F; |
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184 I_neighbour2local_ds = interpOpSet.IC2F; |
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185 I_local2neighbour_us = interpOpSet.IF2C; |
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186 I_local2neighbour_ds = interpOpSet.IF2C; |
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187 end |
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188 case 'AWW' |
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189 %String 'C2F' indicates that ICF2 is more accurate. |
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190 interpOpSetF2C = sbp.InterpAWW(ms(1),ms(2),orders(1),orders(2),'F2C'); |
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191 interpOpSetC2F = sbp.InterpAWW(ms(1),ms(2),orders(1),orders(2),'C2F'); |
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192 if grid_ratio < 1 |
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193 % Local is coarser than neighbour |
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194 I_neighbour2local_us = interpOpSetC2F.IF2C; |
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195 I_neighbour2local_ds = interpOpSetF2C.IF2C; |
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196 I_local2neighbour_us = interpOpSetC2F.IC2F; |
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197 I_local2neighbour_ds = interpOpSetF2C.IC2F; |
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198 elseif grid_ratio > 1 |
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199 % Local is finer than neighbour |
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200 I_neighbour2local_us = interpOpSetF2C.IC2F; |
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201 I_neighbour2local_ds = interpOpSetC2F.IC2F; |
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202 I_local2neighbour_us = interpOpSetF2C.IF2C; |
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203 I_local2neighbour_ds = interpOpSetC2F.IF2C; |
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204 end |
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205 otherwise |
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206 error(['Interpolation type ' obj.interpolation_type ... |
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207 ' is not available.' ]); |
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208 end |
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209 |
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210 else |
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211 % No interpolation required |
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212 I_neighbour2local_us = speye(m,m); |
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213 I_neighbour2local_ds = speye(m,m); |
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214 end |
| 591 | 215 |
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216 int_damp_us = obj.interpolation_damping{1}; |
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217 int_damp_ds = obj.interpolation_damping{2}; |
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218 |
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219 I = speye(m,m); |
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220 I_back_forth_us = I_neighbour2local_us*I_local2neighbour_us; |
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221 I_back_forth_ds = I_neighbour2local_ds*I_local2neighbour_ds; |
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222 |
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223 |
| 591 | 224 switch boundary |
| 225 case {'w','W','west','West'} | |
| 595 | 226 tau = sigma_ds*obj.a(1)*obj.e_w*obj.H_y; |
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227 closure = obj.Hi*tau*obj.e_w'; |
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228 penalty = -obj.Hi*tau*I_neighbour2local_ds*e_neighbour'; |
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229 |
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230 beta = int_damp_ds*obj.a(1)... |
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231 *obj.e_w*obj.H_y; |
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232 closure = closure + obj.Hi*beta*(I_back_forth_ds - I)*obj.e_w'; |
| 591 | 233 case {'e','E','east','East'} |
| 595 | 234 tau = sigma_us*obj.a(1)*obj.e_e*obj.H_y; |
| 591 | 235 closure = obj.Hi*tau*obj.e_e'; |
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236 penalty = -obj.Hi*tau*I_neighbour2local_us*e_neighbour'; |
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237 |
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238 beta = int_damp_us*obj.a(1)... |
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239 *obj.e_e*obj.H_y; |
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240 closure = closure + obj.Hi*beta*(I_back_forth_us - I)*obj.e_e'; |
| 591 | 241 case {'s','S','south','South'} |
| 595 | 242 tau = sigma_ds*obj.a(2)*obj.e_s*obj.H_x; |
| 591 | 243 closure = obj.Hi*tau*obj.e_s'; |
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244 penalty = -obj.Hi*tau*I_neighbour2local_ds*e_neighbour'; |
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245 |
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246 beta = int_damp_ds*obj.a(2)... |
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247 *obj.e_s*obj.H_x; |
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248 closure = closure + obj.Hi*beta*(I_back_forth_ds - I)*obj.e_s'; |
| 591 | 249 case {'n','N','north','North'} |
| 595 | 250 tau = sigma_us*obj.a(2)*obj.e_n*obj.H_x; |
| 591 | 251 closure = obj.Hi*tau*obj.e_n'; |
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252 penalty = -obj.Hi*tau*I_neighbour2local_us*e_neighbour'; |
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253 |
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254 beta = int_damp_us*obj.a(2)... |
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255 *obj.e_n*obj.H_x; |
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256 closure = closure + obj.Hi*beta*(I_back_forth_us - I)*obj.e_n'; |
| 591 | 257 end |
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258 |
| 591 | 259 |
| 260 end | |
| 261 | |
| 262 function N = size(obj) | |
| 263 N = obj.m; | |
| 264 end | |
| 265 | |
| 266 end | |
| 267 | |
| 268 methods(Static) | |
| 269 % Calculates the matrices needed for the inteface coupling between boundary bound_u of scheme schm_u | |
| 270 % and bound_v of scheme schm_v. | |
| 271 % [uu, uv, vv, vu] = inteface_coupling(A,'r',B,'l') | |
| 272 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v) | |
| 273 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v); | |
| 274 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u); | |
| 275 end | |
| 276 end | |
| 277 end |