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Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 24 Jan 2019 09:05:44 +0100
parents c322a9454d75
children 3108963cc42c 0c906f7ab8bf
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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
diff changeset
1 classdef Burgers2d < scheme.Scheme
1008
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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
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>
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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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parents: 1147
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11 e_w, e_e, e_s, e_n
1008
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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12 end
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13
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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parents:
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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
diff changeset
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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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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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.
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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.
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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.
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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.
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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.
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.
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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.
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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;
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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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'
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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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.
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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;
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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58 obj.D = @(v) -(1/3*D1*v.*v + (1/3*spdiag(v)*D1 + fluxSplitting{1}(v)*DissOp)*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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59 case 2
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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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);
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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61 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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62 case 'conservative'
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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63 switch length(fluxSplitting)
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64 case 1
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parents: 1147
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65 DissOp = DissOpx + DissOpy;
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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66 obj.D = @(v) -(1/2*D1*v.*v + fluxSplitting{1}(v)*DissOp*v);
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parents: 1147
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67 case 2
1fe48cbd379a Change Burgers2d to inviscid formulation. Rewrite to use opSets and fix the implementation of the Dirichlet conditions.
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68 obj.D = @(v) -(1/2*D1*v.*v + (fluxSplitting{1}(v)*DissOpx + fluxSplitting{2}(v)*DissOpy)*v);
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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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73 Dx = kron(ops_x.D1,Iy);
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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;
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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
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parents:
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83
1149
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84 % Boundary operators
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85 obj.e_w = kr(ops_x.e_l, Iy);
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86 obj.e_e = kr(ops_x.e_r, Iy);
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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>
parents: 1147
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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
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92
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
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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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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.
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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
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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;
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106 tau = @(v) s*magnitude*obj.Hi*e*H_b*spdiag((v(index)-s*abs(v(index)))/2);
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107 closure = @(v) tau(v)*v(index);
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108 penalty = @(v) -tau(v);
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109
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110
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111 % tau = s*e*H_b;
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112 % closure = @(v) (obj.Hi*tau)*(((v(index)-s*abs(v(index)))/3).*v(index));
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113 % penalty = -obj.Hi*tau;
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114 otherwise
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115 error('No such boundary condition: type = %s',type);
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116 end
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117
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118
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119 end
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120
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121 % Ruturns the boundary ops, half-norm, boundary indices and sign for the boundary specified by the string boundary.
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122 % The right boundary for each coordinate direction is considered the positive boundary
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123 function [e, H_b, index, s] = get_boundary_ops(obj, boundary)
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124 ind = grid.funcToMatrix(obj.grid, 1:obj.grid.N());
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125 switch boundary
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126 case {'w', 'W', 'west', 'West'}
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127 e = obj.e_w;
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128 H_b = obj.H_y;
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129 index = ind(1,:);
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130 s = -1;
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131 case {'e', 'E', 'east', 'East'}
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132 e = obj.e_e;
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133 H_b = obj.H_y;
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134 index = ind(end,:);
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135 s = 1;
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136 case {'s', 'S', 'south', 'South'}
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137 e = obj.e_s;
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138 H_b = obj.H_x;
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139 index = ind(:,1);
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140 s = -1;
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141 case {'n', 'N', 'north', 'North'}
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142 e = obj.e_n;
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143 H_b = obj.H_x;
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diff changeset
144 index = ind(:,end);
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145 s = 1;
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146 otherwise
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147 error('No such boundary: boundary = %s',boundary);
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148 end
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149 end
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150
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151 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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152 error('An interface function does not exist yet');
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153 end
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154
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155 function N = size(obj)
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156 N = obj.grid.m;
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157 end
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158 end
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159 end