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annotate +scheme/Burgers2d.m @ 1197:433c89bf19e0 feature/rv

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Merge with default
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 07 Aug 2019 15:23:42 +0200
parents 6cb03209f0a7
children
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rev   line source
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
diff changeset
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
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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
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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.
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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.
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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.
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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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parents: 1147
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11 e_w, e_e, e_s, e_n
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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
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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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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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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.
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19
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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20 m = g.size();
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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21 m_x = m(1);
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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22 m_y = m(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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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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24
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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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.
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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.
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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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28
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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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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30 ops_x = opSet(m_x, xlim, order);
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parents: 1147
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31 ops_y = opSet(m_y, ylim, order);
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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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33 Iy = speye(m_y);
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34
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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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;
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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.
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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;
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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.
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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.
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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.
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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);
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3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
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parents: 1149
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50 DissOpx = kron((ops_x.Dp - ops_x.Dm)/2,Iy);
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
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51 DissOpy = kron(Ix,(ops_y.Dp - ops_y.Dm)/2);
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1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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52 D1 = Dx + Dy;
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parents: 1147
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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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54 case 'skew-symmetric'
1155
336ee37a0617 Change penalty term and add missing semicolon
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55 D = -1/3*D1;
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56 switch length(fluxSplitting)
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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57 case 1
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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58 DissOp = DissOpx + DissOpy;
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3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
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parents: 1149
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59 obj.D = @(v) D*(v.*v) + (spdiags(v,0,m_tot,m_tot)*D + fluxSplitting{1}(v)*DissOp)*v;
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1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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60 case 2
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parents: 1149
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61 obj.D = @(v) D*(v.*v) + (spdiags(v,0,m_tot,m_tot)*D + fluxSplitting{1}(v)*DissOpx + fluxSplitting{2}(v)*DissOpy)*v;
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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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62 end
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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63 case 'conservative'
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parents: 1149
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64 D = -1/2*D1;
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parents: 1147
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65 switch length(fluxSplitting)
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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66 case 1
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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67 DissOp = DissOpx + DissOpy;
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3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
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parents: 1149
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68 % TODO: Check if we can use fluxSplitting{1} here instead
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
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parents: 1149
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69 obj.D = @(v) D*(v.*v) + max(abs(v))*DissOp*v;
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parents: 1147
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70 case 2
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71 obj.D = @(v) D*(v.*v) + (fluxSplitting{1}(v)*DissOpx + fluxSplitting{2}(v)*DissOpy)*v;
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parents: 1147
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72 end
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73
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74 end
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75 else
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parents: 1147
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76 Dx = kron(ops_x.D1,Iy);
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parents: 1147
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77 Dy = kron(Ix,ops_y.D1);
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parents: 1147
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78 D1 = Dx + Dy;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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79 switch pde_form
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parents: 1147
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80 case 'skew-symmetric'
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6cb03209f0a7 Add missing semicolon
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parents: 1155
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81 D = -1/3*D1;
1154
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1149
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82 obj.D = @(v) D*(v.*v) + spdiags(v,0,m_tot,m_tot)*D*v;
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parents: 1147
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83 case 'conservative'
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parents: 1149
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84 D = -1/2*D1;
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1149
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85 obj.D = @(v) D*(v.*v);
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parents: 1147
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86 end
1008
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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87 end
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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parents:
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88
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parents: 1147
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89 % Boundary operators
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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90 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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91 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1147
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92 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>
parents: 1147
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93 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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94
1149
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95 obj.order = order;
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a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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parents:
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96 end
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97
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98 % Closure functions return the operators applied to the own doamin to close the boundary
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99 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other domain.
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100 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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101 % type is a string specifying the type of boundary condition if there are several.
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102 function [closure, penalty] = boundary_condition(obj,boundary,type)
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103 default_arg('type','dirichlet');
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104 s = obj.getBoundarySign(boundary);
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105 e = obj.getBoundaryOperator('e', boundary);
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106 indices = obj.getBoundaryIndices(boundary);
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107 H_1d = obj.getOneDirectionalNorm(boundary);
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108 switch type
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109 case {'D', 'd', 'dirichlet', 'Dirichlet'}
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110 penalty_parameter = 1/3;
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111 Tau = s*penalty_parameter*obj.Hi*e*H_1d/2;
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112 m = obj.grid.m;
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113 tau = @(v) Tau*spdiags((v(indices)-s*abs(v(indices))),0,m(1),m(2));
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114 closure = @(v) Tau*((v(indices)-s*abs(v(indices))).*v(indices));
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115 penalty = @(v) -tau(v);
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116 otherwise
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117 error('No such boundary condition: type = %s',type);
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118 end
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119
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120
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121 end
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122
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123 % Returns the boundary sign. The right boundary is considered the positive boundary
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124 % boundary -- string
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125 function s = getBoundarySign(obj, boundary)
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126 assertIsMember(boundary, {'w', 'e', 's', 'n'})
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127 switch boundary
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128 case {'e','n'}
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129 s = 1;
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130 case {'w','s'}
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131 s = -1;
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132 end
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133 end
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134
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135 % Returns the boundary operator op for the boundary specified by the string boundary.
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136 % op -- string
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137 % boundary -- string
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138 function o = getBoundaryOperator(obj, op, boundary)
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139 assertIsMember(op, {'e'})
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140 assertIsMember(boundary, {'w', 'e', 's', 'n'})
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141
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142 o = obj.([op, '_', boundary]);
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143 end
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144
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145 % Returns square boundary quadrature matrix, of dimension
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146 % corresponding to the number of boundary points
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147 %
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148 % boundary -- string
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149 function H_b = getBoundaryQuadrature(obj, boundary)
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150 assertIsMember(boundary, {'w', 'e', 's', 'n'})
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151 H_b = obj.(['H_', boundary]);
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152 end
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153
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154 % Returns square boundary quadrature matrix, of dimension
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155 % corresponding to the number of boundary points
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156 %
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157 % boundary -- string
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158 function H_1d = getOneDirectionalNorm(obj, boundary)
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159 assertIsMember(boundary, {'w', 'e', 's', 'n'})
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160 switch boundary
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161 case {'w','e'}
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162 H_1d = obj.H_y;
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163 case {'s','n'}
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164 H_1d = obj.H_x;
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165 end
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166 end
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167
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168 % Returns the indices of the boundary points in the grid matrix
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169 % boundary -- string
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170 function I = getBoundaryIndices(obj, boundary)
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171 assertIsMember(boundary, {'w', 'e', 's', 'n'})
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172
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173 ind = grid.funcToMatrix(obj.grid, 1:prod(obj.grid.m));
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174 switch boundary
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175 case 'w'
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176 I = ind(1,:);
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177 case 'e'
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178 I = ind(end,:);
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179 case 's'
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180 I = ind(:,1)';
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181 case 'n'
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182 I = ind(:,end)';
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183 end
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184 end
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185
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186 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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187 error('An interface function does not exist yet');
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188 end
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189
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190 function N = size(obj)
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191 N = obj.grid.m;
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192 end
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193 end
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194 end