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annotate +rv/constructDiffOps.m @ 1021:cc61dde120cd feature/advectionRV

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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 5359a61cb4d9
children defc9d0cc1f2
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1021
cc61dde120cd Add upwind dissipation to the operator inside Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1020
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1 function [D_rv, D_flux, DvDt, solutionPenalties, residualPenalties] = constructDiffOps(scheme, grid, order, opSet, waveSpeed, BCs, fluxSplitting)
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2 default_arg('fluxSplitting',[]);
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3 assert(size(BCs,1) == grid.D());
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cc61dde120cd Add upwind dissipation to the operator inside Utux2d
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4
1020
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5 %% DiffOps for solution vector
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cc61dde120cd Add upwind dissipation to the operator inside Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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6 [D, solutionPenalties] = constructTotalFluxDiffOp(scheme, grid, order, opSet, waveSpeed, BCs, fluxSplitting);
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7 D2 = constructSymmetricD2Operator(grid, order, opSet);
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8 D_rv = @(v,viscosity)(D + D2(viscosity))*v;
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9
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10 %% DiffOps for residual viscosity
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cc61dde120cd Add upwind dissipation to the operator inside Utux2d
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11 [D_flux, residualPenalties] = constructTotalFluxDiffOp(scheme, grid, order-2, opSet, waveSpeed, BCs, fluxSplitting);
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12 % DiffOp for flux in residual viscosity. Due to sign conventions of the implemnted schemes, we need to
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13 % change the sign.
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14 D_flux = -D_flux;
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15 D_flux = @(v) D_flux*v;
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16 % DiffOp for time derivative in residual viscosity
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17 DvDt = @(v)D*v;
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18 end
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19
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cc61dde120cd Add upwind dissipation to the operator inside Utux2d
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20 function [D, penalties] = constructTotalFluxDiffOp(scheme, grid, order, opSet, waveSpeed, BCs, fluxSplitting)
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21 if isequal(opSet, @sbp.D1Upwind)
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22 assert(size(fluxSplitting,1) == grid.D());
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23 diffOp = scheme(grid, order, opSet, waveSpeed, fluxSplitting);
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24 else
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25 diffOp = scheme(grid, order, opSet, waveSpeed);
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26 end
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27 [D, penalties] = addClosuresToDiffOp(diffOp, BCs);
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28 end
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29
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30 function [D, penalties] = addClosuresToDiffOp(diffOp, BCs)
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31 D = diffOp.D;
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32 penalties = cell(size(BCs));
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33 for i = 1:size(BCs,1)
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34 for j = 1:size(BCs,2)
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35 [closure, penalties{i,j}] = diffOp.boundary_condition(BCs{i,j}.boundary, BCs{i,j}.type);
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36 D = D + closure;
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37 end
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38 end
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39 end
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40
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41 function D2 = constructSymmetricD2Operator(grid, order, opSet)
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42 % TODO:
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43 % Currently only implemented for upwind operators.
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44 % Remove this part once the time-dependent D2 operator is implemented for other opSets
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parents: 1020
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45 % or if it is decided that it should only be supported for upwind operators.
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46 assert(isequal(opSet,@sbp.D1Upwind))
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47
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48 m = grid.size();
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49 ops = cell(grid.D(),1);
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50 I = cell(grid.D(),1);
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51 for i = 1:grid.D()
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52 lim = {grid.x{i}(1), grid.x{i}(end)};
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53 ops{i} = opSet(m(i), lim, order);
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54 I{i} = speye(m(i));
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55 end
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56
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57 % TBD: How is this generalized to a loop over dimensions or similar?
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58 switch grid.D()
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59 case 1
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60 e_r = ops{1}.e_r;
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61 e_l = ops{1}.e_l;
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62 Dm = ops{1}.Dm;
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63 Dp = ops{1}.Dp;
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64 Hi = ops{1}.HI;
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65 B = e_r*e_r' - e_l*e_l';
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66 D2 = @(viscosity) Dm*spdiag(viscosity)*Dp-Hi*(B*spdiag(viscosity)*Dp);
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67 case 2
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68 e_e = kron(ops{1}.e_r,I{2});
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69 e_w = kron(ops{1}.e_l,I{2});
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70 Dm_x = kron(ops{1}.Dm,I{2});
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71 Dp_x = kron(ops{1}.Dp,I{2});
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72 H_x = kron(ops{1}.HI,I{2});
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73 B_x = e_e*e_e' - e_w*e_w';
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74 D2_x = @(viscosity) Dm_x*spdiag(viscosity)*Dp_x-H_x*(B_x*spdiag(viscosity)*Dp_x);
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75
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76 e_n = kron(I{1},ops{2}.e_r);
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77 e_s = kron(I{1},ops{2}.e_l);
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78 Dm_y = kron(I{1},ops{2}.Dm);
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79 Dp_y = kron(I{1},ops{2}.Dp);
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80 H_y = kron(I{1},ops{2}.HI);
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81 B_y = e_n*e_n' - e_s*e_s';
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82 D2_y = @(viscosity) Dm_y*spdiag(viscosity)*Dp_y-H_y*(B_y*spdiag(viscosity)*Dp_y);
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83 D2 = @(viscosity)D2_x(viscosity) + D2_y(viscosity);
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84 otherwise
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85 error('3D not yet implemented')
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86 end
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87 end