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annotate +rv/constructDiffOps.m @ 1031:2ef20d00b386 feature/advectionRV

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For easier comparison, return both the first order and residual viscosity when evaluating the residual. Add the first order and residual viscosity to the state of the RungekuttaRV time steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 17 Jan 2019 10:25:06 +0100
parents 44c3ea38097e
children 1a5c8723c9be 2d7ba44340d0
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rev   line source
1021
cc61dde120cd Add upwind dissipation to the operator inside Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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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
1020
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4 %% DiffOps for solution vector
1021
cc61dde120cd Add upwind dissipation to the operator inside Utux2d
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5 [D, solutionPenalties] = constructTotalFluxDiffOp(scheme, grid, order, opSet, waveSpeed, BCs, fluxSplitting);
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6 D2 = constructSymmetricD2Operator(grid, 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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44c3ea38097e Fix minor issues in rv/constructDiffOps
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10 [D_flux, residualPenalties] = constructTotalFluxDiffOp(scheme, grid, 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 end
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18
1021
cc61dde120cd Add upwind dissipation to the operator inside Utux2d
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19 function [D, penalties] = constructTotalFluxDiffOp(scheme, grid, order, opSet, waveSpeed, BCs, fluxSplitting)
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20 if isequal(opSet, @sbp.D1Upwind)
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21 diffOp = scheme(grid, order, opSet, waveSpeed, fluxSplitting);
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22 else
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23 diffOp = scheme(grid, order, opSet, waveSpeed);
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24 end
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25 [D, penalties] = addClosuresToDiffOp(diffOp, BCs);
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26 end
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27
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28 function [D, penalties] = addClosuresToDiffOp(diffOp, BCs)
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29 D = diffOp.D;
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30 penalties = cell(size(BCs));
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31 for i = 1:size(BCs,1)
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32 for j = 1:size(BCs,2)
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33 [closure, penalties{i,j}] = diffOp.boundary_condition(BCs{i,j}.boundary, BCs{i,j}.type);
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34 D = D + closure;
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35 end
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36 end
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37 end
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38
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39 function D2 = constructSymmetricD2Operator(grid, order, opSet)
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40 % TODO:
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41 % Currently only implemented for upwind operators.
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42 % Remove this part once the time-dependent D2 operator is implemented for other opSets
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cc61dde120cd Add upwind dissipation to the operator inside Utux2d
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parents: 1020
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43 % or if it is decided that it should only be supported for upwind operators.
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44 assert(isequal(opSet,@sbp.D1Upwind))
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45
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46 m = grid.size();
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47 ops = cell(grid.D(),1);
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48 I = cell(grid.D(),1);
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49 for i = 1:grid.D()
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50 lim = {grid.x{i}(1), grid.x{i}(end)};
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51 ops{i} = opSet(m(i), lim, order);
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52 I{i} = speye(m(i));
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53 end
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54
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55 % TBD: How is this generalized to a loop over dimensions or similar?
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56 switch grid.D()
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57 case 1
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58 e_r = ops{1}.e_r;
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59 e_l = ops{1}.e_l;
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60 Dm = ops{1}.Dm;
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61 Dp = ops{1}.Dp;
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62 Hi = ops{1}.HI;
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63 B = e_r*e_r' - e_l*e_l';
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64 D2 = @(viscosity) Dm*spdiag(viscosity)*Dp-Hi*(B*spdiag(viscosity)*Dp);
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65 case 2
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66 e_e = kron(ops{1}.e_r,I{2});
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67 e_w = kron(ops{1}.e_l,I{2});
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68 Dm_x = kron(ops{1}.Dm,I{2});
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69 Dp_x = kron(ops{1}.Dp,I{2});
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70 H_x = kron(ops{1}.HI,I{2});
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71 B_x = e_e*e_e' - e_w*e_w';
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72 D2_x = @(viscosity) Dm_x*spdiag(viscosity)*Dp_x-H_x*(B_x*spdiag(viscosity)*Dp_x);
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73
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74 e_n = kron(I{1},ops{2}.e_r);
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75 e_s = kron(I{1},ops{2}.e_l);
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76 Dm_y = kron(I{1},ops{2}.Dm);
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77 Dp_y = kron(I{1},ops{2}.Dp);
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78 H_y = kron(I{1},ops{2}.HI);
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79 B_y = e_n*e_n' - e_s*e_s';
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80 D2_y = @(viscosity) Dm_y*spdiag(viscosity)*Dp_y-H_y*(B_y*spdiag(viscosity)*Dp_y);
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81 D2 = @(viscosity)D2_x(viscosity) + D2_y(viscosity);
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82 otherwise
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83 error('3D not yet implemented')
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84 end
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85 end