Mercurial > repos > public > sbplib

annotate +rv/constructDiffOps.m @ 1142:cff49fba3cc8 rv-interpolation

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Closing branch
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 05 Aug 2019 10:49:21 +0200
parents 1a5c8723c9be
children
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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1 function [D_rv, D_flux, DvDt, solutionPenalties, residualPenalties] = constructDiffOps(scheme, g, order, opSet, waveSpeed, BCs, fluxSplitting)
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2 default_arg('fluxSplitting',[]);
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3
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4 %% DiffOps for solution vector
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5 [D, solutionPenalties] = constructTotalFluxDiffOp(scheme, g, order, opSet, waveSpeed, BCs, fluxSplitting);
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6 D2 = constructSymmetricD2Operator(g, order, opSet);
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7 D_rv = @(v,viscosity)(D + D2(viscosity))*v;
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8
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9 %% DiffOps for residual viscosity
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10 [D_flux, residualPenalties] = constructTotalFluxDiffOp(scheme, g, max(order-2,2), opSet, waveSpeed, BCs, fluxSplitting);
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11 % DiffOp for flux in residual viscosity. Due to sign conventions of the implemnted schemes, we need to
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12 % change the sign.
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13 D_flux = -D_flux;
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14 D_flux = @(v) D_flux*v;
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15 % DiffOp for time derivative in residual viscosity
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16 DvDt = @(v)D*v;
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17
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18 %% DiffOps for residual viscosity
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19 % xl = g.getBoundary('l');
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20 % xr = g.getBoundary('r');
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21 % xlim = {xl, xr};
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22 % m_f = 2*(g.m()-1)+1;
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23 % g_f = grid.equidistant(m_f, xlim);
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24
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25 % [DvDt, residualPenalties] = constructTotalFluxDiffOp(scheme, g_f, 9, opSet, waveSpeed, BCs, fluxSplitting);
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26 % % DiffOp for flux in residual viscosity. Due to sign conventions of the implemnted schemes, we need to
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27 % % change the sign.
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28 % D_flux = -D;
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29 % D_flux = @(v) D_flux*v;
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30 % % DiffOp for time derivative in residual viscosity
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31 % DvDt = @(v)applyInterpDiffOp(g.points(), v, g_f.points(), DvDt);
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32 end
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33
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34 % function u = applyInterpDiffOp(x_c, u_c, x_f, D_f)
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35 % u_f = D_f*interp1(x_c,u_c,x_f,'linear');
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36 % u = u_f(ismember(x_f,x_c));
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37 % end
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38
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39 function [D, penalties] = constructTotalFluxDiffOp(scheme, grid, order, opSet, waveSpeed, BCs, fluxSplitting)
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40 if isequal(opSet, @sbp.D1Upwind)
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41 diffOp = scheme(grid, order, opSet, waveSpeed, fluxSplitting);
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42 else
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43 diffOp = scheme(grid, order, opSet, waveSpeed);
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44 end
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45 [D, penalties] = addClosuresToDiffOp(diffOp, BCs);
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46 end
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47
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48 function [D, penalties] = addClosuresToDiffOp(diffOp, BCs)
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49 D = diffOp.D;
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50 penalties = cell(size(BCs));
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51 for i = 1:size(BCs,1)
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52 for j = 1:size(BCs,2)
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53 [closure, penalties{i,j}] = diffOp.boundary_condition(BCs{i,j}.boundary, BCs{i,j}.type);
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54 D = D + closure;
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55 end
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56 end
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57 end
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58
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59 function D2 = constructSymmetricD2Operator(grid, order, opSet)
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60 % TODO:
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61 % Currently only implemented for upwind operators.
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62 % Remove this part once the time-dependent D2 operator is implemented for other opSets
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63 % or if it is decided that it should only be supported for upwind operators.
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64 assert(isequal(opSet,@sbp.D1Upwind))
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65
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66 m = grid.size();
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67 ops = cell(grid.D(),1);
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68 I = cell(grid.D(),1);
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69 for i = 1:grid.D()
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70 lim = {grid.x{i}(1), grid.x{i}(end)};
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71 ops{i} = opSet(m(i), lim, order);
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72 I{i} = speye(m(i));
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73 end
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74
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75 % TBD: How is this generalized to a loop over dimensions or similar?
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76 switch grid.D()
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77 case 1
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78 e_r = ops{1}.e_r;
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79 e_l = ops{1}.e_l;
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80 Dm = ops{1}.Dm;
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81 Dp = ops{1}.Dp;
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82 Hi = ops{1}.HI;
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83 B = e_r*e_r' - e_l*e_l';
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84 D2 = @(viscosity) Dm*spdiag(viscosity)*Dp-Hi*(B*spdiag(viscosity)*Dp);
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85 case 2
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86 e_e = kron(ops{1}.e_r,I{2});
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87 e_w = kron(ops{1}.e_l,I{2});
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88 Dm_x = kron(ops{1}.Dm,I{2});
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89 Dp_x = kron(ops{1}.Dp,I{2});
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90 H_x = kron(ops{1}.HI,I{2});
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91 B_x = e_e*e_e' - e_w*e_w';
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92 D2_x = @(viscosity) Dm_x*spdiag(viscosity)*Dp_x-H_x*(B_x*spdiag(viscosity)*Dp_x);
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93
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94 e_n = kron(I{1},ops{2}.e_r);
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95 e_s = kron(I{1},ops{2}.e_l);
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96 Dm_y = kron(I{1},ops{2}.Dm);
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97 Dp_y = kron(I{1},ops{2}.Dp);
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98 H_y = kron(I{1},ops{2}.HI);
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99 B_y = e_n*e_n' - e_s*e_s';
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100 D2_y = @(viscosity) Dm_y*spdiag(viscosity)*Dp_y-H_y*(B_y*spdiag(viscosity)*Dp_y);
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101 D2 = @(viscosity)D2_x(viscosity) + D2_y(viscosity);
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102 otherwise
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103 error('3D not yet implemented')
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
104 end
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
105 end