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annotate +scheme/Burgers2d.m @ 1223:9fddc8749445 rv_diffOp_test

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Closing branch
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 05 Aug 2019 10:48:37 +0200
parents 0c906f7ab8bf
children
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1149
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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1 classdef Burgers2d < scheme.Scheme
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2 properties
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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3 grid % Physical grid
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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4 order % Order accuracy for the approximation
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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5
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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6 D % Non-stabilized scheme operator
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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7 H % Discrete norm
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1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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8 H_x, H_y % Norms in the x and y directions
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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9 Hi % Kroneckered norm inverse
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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10 % Boundary operators
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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11 e_w, e_e, e_s, e_n
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a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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12 end
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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13
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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14 methods
1149
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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15 function obj = Burgers2d(g, order, pde_form, fluxSplitting, opSet)
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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parents: 1147
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16 default_arg('opSet',@sbp.D2Standard);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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17 default_arg('fluxSplitting',{@(v)max(abs(v)),@(v)max(abs(v))});
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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18 assertType(g, 'grid.Cartesian');
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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19
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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20 m = g.size();
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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21 m_x = m(1);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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22 m_y = m(2);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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23 m_tot = g.N();
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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parents: 1147
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24
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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25 xlim = {g.x{1}(1), g.x{1}(end)};
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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26 ylim = {g.x{2}(1), g.x{2}(end)};
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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27 obj.grid = g;
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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parents: 1147
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28
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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29 % Operator sets
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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parents: 1147
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30 ops_x = opSet(m_x, xlim, order);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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31 ops_y = opSet(m_y, ylim, order);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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32 Ix = speye(m_x);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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parents: 1147
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33 Iy = speye(m_y);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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parents: 1147
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34
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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35 % Norms
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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36 Hx = ops_x.H;
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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37 Hy = ops_y.H;
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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38 Hxi = ops_x.HI;
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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39 Hyi = ops_y.HI;
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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parents: 1147
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40
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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41 obj.H_x = Hx;
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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parents: 1147
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42 obj.H_y = Hy;
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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43 obj.H = kron(Hx,Hy);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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44 obj.Hi = kron(Hxi,Hyi);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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45
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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46 % Derivatives
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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47 if (isequal(opSet,@sbp.D1Upwind))
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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48 Dx = kron((ops_x.Dp + ops_x.Dm)/2,Iy);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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49 Dy = kron(Ix,(ops_y.Dp + ops_y.Dm)/2);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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50 DissOpx = kron((ops_x.Dm - ops_x.Dp)/2,Iy);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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51 DissOpy = kron(Ix,(ops_y.Dm - ops_y.Dp)/2);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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parents: 1147
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52 D1 = Dx + Dy;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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53 switch pde_form
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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parents: 1147
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54 case 'skew-symmetric'
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parents: 1147
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55 switch length(fluxSplitting)
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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56 case 1
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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57 DissOp = DissOpx + DissOpy;
1221
0c906f7ab8bf Attempt to reduce unnessecary operations when using the RV diffOps. Does not seem to improve efficiency at this stage.
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parents: 1149
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58 obj.D = @(v) -(1/3*D1*(v.*v) + (1/3*spdiag(v)*D1 + fluxSplitting{1}(v)*DissOp)*v);
1149
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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59 case 2
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60 obj.D = @(v) -(1/3*D1*(v.*v) + (1/3*spdiag(v)*D1 + fluxSplitting{1}(v)*DissOpx + fluxSplitting{2}(v)*DissOpy)*v);
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61 end
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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62 case 'conservative'
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parents: 1147
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63 switch length(fluxSplitting)
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parents: 1147
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64 case 1
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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65 DissOp = DissOpx + DissOpy;
1221
0c906f7ab8bf Attempt to reduce unnessecary operations when using the RV diffOps. Does not seem to improve efficiency at this stage.
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66 obj.D = @(v) -(1/2*D1*spdiag(v) + fluxSplitting{1}(v)*DissOp);
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67 case 2
1221
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68 obj.D = @(v) -(1/2*D1*spdiag(v) + (fluxSplitting{1}(v)*DissOpx + fluxSplitting{2}(v)*DissOpy));
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parents: 1147
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69 end
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70
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71 end
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72 else
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parents: 1147
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73 Dx = kron(ops_x.D1,Iy);
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parents: 1147
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74 Dy = kron(Ix,ops_y.D1);
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parents: 1147
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75 D1 = Dx + Dy;
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76 switch pde_form
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77 case 'skew-symmetric'
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78 obj.D = @(v) -(1/3*D1*(v.*v) + 1/3*spdiag(v)*D1*v);
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79 case 'conservative'
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80 obj.D = @(v) -1/2*D1*(v.*v);
1149
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parents: 1147
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81 end
1008
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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parents:
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82 end
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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83
1149
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84 % Boundary operators
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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85 obj.e_w = kr(ops_x.e_l, Iy);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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parents: 1147
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86 obj.e_e = kr(ops_x.e_r, Iy);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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parents: 1147
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87 obj.e_s = kr(Ix, ops_y.e_l);
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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88 obj.e_n = kr(Ix, ops_y.e_r);
1008
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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parents:
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89
1149
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90 obj.order = order;
1008
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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91 end
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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parents:
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92
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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93 % Closure functions return the operators applied to the own doamin to close the boundary
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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parents:
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94 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other domain.
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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parents:
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95 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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96 % type is a string specifying the type of boundary condition if there are several.
1149
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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97 function [closure, penalty] = boundary_condition(obj,boundary,type)
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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98 default_arg('type','dirichlet');
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99 [e, H_b, index, s] = obj.get_boundary_ops(boundary);
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100 switch type
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101 % Stable dirchlet-like boundary conditions (u+-abs(u))*u/3
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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102 % with +- at left/right boundaries in each coordinate direction
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103 case {'D', 'd', 'dirichlet', 'Dirichlet'}
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104
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105 magnitude = 2/3;
1221
0c906f7ab8bf Attempt to reduce unnessecary operations when using the RV diffOps. Does not seem to improve efficiency at this stage.
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106 Tau = s*magnitude*obj.Hi*e*H_b;
0c906f7ab8bf Attempt to reduce unnessecary operations when using the RV diffOps. Does not seem to improve efficiency at this stage.
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107 tau = @(v) Tau*spdiag((v(index)-s*abs(v(index)))/2);
0c906f7ab8bf Attempt to reduce unnessecary operations when using the RV diffOps. Does not seem to improve efficiency at this stage.
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108 closure = @(v) tau(v)*e';
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diff changeset
109 penalty = @(v) -tau(v);
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diff changeset
110
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diff changeset
111
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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diff changeset
112 % tau = s*e*H_b;
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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113 % closure = @(v) (obj.Hi*tau)*(((v(index)-s*abs(v(index)))/3).*v(index));
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114 % penalty = -obj.Hi*tau;
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115 otherwise
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116 error('No such boundary condition: type = %s',type);
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117 end
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118
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119
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120 end
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121
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122 % Ruturns the boundary ops, half-norm, boundary indices and sign for the boundary specified by the string boundary.
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123 % The right boundary for each coordinate direction is considered the positive boundary
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124 function [e, H_b, index, s] = get_boundary_ops(obj, boundary)
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125 ind = grid.funcToMatrix(obj.grid, 1:obj.grid.N());
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126 switch boundary
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127 case {'w', 'W', 'west', 'West'}
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128 e = obj.e_w;
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129 H_b = obj.H_y;
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130 index = ind(1,:);
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131 s = -1;
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132 case {'e', 'E', 'east', 'East'}
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133 e = obj.e_e;
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134 H_b = obj.H_y;
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135 index = ind(end,:);
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136 s = 1;
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137 case {'s', 'S', 'south', 'South'}
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diff changeset
138 e = obj.e_s;
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diff changeset
139 H_b = obj.H_x;
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diff changeset
140 index = ind(:,1);
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141 s = -1;
1149
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diff changeset
142 case {'n', 'N', 'north', 'North'}
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diff changeset
143 e = obj.e_n;
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diff changeset
144 H_b = obj.H_x;
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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diff changeset
145 index = ind(:,end);
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146 s = 1;
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147 otherwise
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148 error('No such boundary: boundary = %s',boundary);
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149 end
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150 end
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151
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152 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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153 error('An interface function does not exist yet');
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154 end
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155
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156 function N = size(obj)
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157 N = obj.grid.m;
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158 end
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159 end
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160 end