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annotate +scheme/Burgers2D.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 a6f34de60044
children
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1 classdef Burgers2D < scheme.Scheme
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2 properties
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3 grid % Physical grid
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4 order % Order accuracy for the approximation
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5
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6 D % Non-stabilized scheme operator
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7 H % Discrete norm
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8 H_inv % Norm inverse
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9 halfnorm_inv % Cell array halfnorm operators
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10 e_l % Cell array of left boundary operators
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11 e_r % Cell array of right boundary operators
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12 d_l % Cell array of left boundary derivative operators
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13 d_r % Cell array of right boundary derivative operators
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14 end
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15
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16 methods
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17 function obj = Burgers2D(g, operator_type, order, dissipation)
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18 if ~isa(g, 'grid.Cartesian') || g.D() ~= 2
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19 error('Grid must be 2d cartesian');
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20 end
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21
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22 obj.grid = g;
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23 obj.order = order;
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24
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25 % Create cell array of 1D operators. For example D1_1d{1} = D1_x, D1_1d{2} = D1_y.
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26 [Dp_1d, Dm_1d, H_1d, H_inv_1d, d_l_1d, d_r_1d, e_l_1d, e_r_1d, I, DissipationOp_1d] = ...
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27 obj.assemble1DOperators(g, operator_type, order, dissipation);
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28
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29 %% 2D-operators
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30 % D1
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31 D1_1d{1} = (Dp_1d{1} + Dp_1d{1})/2;
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32 D1_1d{2} = (Dp_1d{2} + Dp_1d{2})/2;
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33 D1_2d = obj.extendOperatorTo2D(D1_1d, I);
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34 D1 = D1_2d{1} + D1_2d{2};
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35 % D2
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36
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37 Dp_2d = obj.extendOperatorTo2D(Dp_1d, I);
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38 Dm_2d = obj.extendOperatorTo2D(Dm_1d, I);
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39 D2 = @(viscosity) Dm_2d{1}*spdiag(viscosity)*Dp_2d{1} + Dm_2d{2}*spdiag(viscosity)*Dp_2d{2};
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40 % m = g.size();
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41 % ind = grid.funcToMatrix(g, 1:g.N());
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42 % for i = 1:g.D()
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43 % D2_2d{i} = sparse(zeros(g.N()));
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44 % end
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45 % % x-direction
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46 % for i = 1:m(2)
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47 % p = ind(:,i);
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48 % D2_2d{1}(p,p) = @(viscosity) D2_1d{1}(viscosity(p));
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49 % end
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50 % % y-direction
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51 % for i = 1:m(1)
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52 % p = ind(i,:);
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53 % D2_2d{2}(p,p) = @(viscosity) D2_1d{2}(viscosity(p));
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54 % end
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55 % D2 = D2_2d{1} + D2_2d{2};
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56
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57 obj.d_l = obj.extendOperatorTo2D(d_l_1d, I);
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58 obj.d_r = obj.extendOperatorTo2D(d_r_1d, I);
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59 obj.e_l = obj.extendOperatorTo2D(e_l_1d, I);
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60 obj.e_r = obj.extendOperatorTo2D(e_r_1d, I);
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61 obj.H = kron(H_1d{1},H_1d{2});
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62 obj.H_inv = kron(H_inv_1d{1},H_inv_1d{2});
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63 obj.halfnorm_inv = obj.extendOperatorTo2D(H_inv_1d, I);
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64
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65 % Dissipation operator
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66 switch dissipation
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67 case 'on'
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68 DissOp_2d = obj.extendOperatorTo2D(DissipationOp_1d, I);
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69 DissOp = DissOp_2d{1} + DissOp_2d{2};
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70 obj.D = @(v, viscosity) -1/2*D1*v.^2 + (D2(viscosity) + max(abs(v))*DissOp)*v;
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71 case 'off'
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72 obj.D = @(v, viscosity) -1/2*D1*v.^2 + D2(viscosity)*v;
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73 end
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74 end
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75
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76 % Closure functions return the operators applied to the own doamin to close the boundary
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77 % 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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78 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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79 % type is a string specifying the type of boundary condition if there are several.
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80 % data is a function returning the data that should be applied at the boundary.
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81 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
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82 default_arg('type','robin');
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83 default_arg('data',0);
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84 [e, d, halfnorm_inv, i_b, s] = obj.get_boundary_ops(boundary);
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85 switch type
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86 % Stable robin-like boundary conditions ((u+-abs(u))*u/3 - eps*u_x)) with +- at left/right boundary
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87 case {'R','robin'}
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88 p = s*halfnorm_inv*e;
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89 closure = @(v, viscosity) p*(((v(i_b)-s*abs(v(i_b)))/3).*(v(i_b)) - ((viscosity(i_b)).*d*v));
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90 switch class(data)
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91 case 'double'
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92 penalty = s*p*data;
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93 case 'function_handle'
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94 penalty = @(t) s*p*data(t);
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95 otherwise
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96 error('Wierd data argument!')
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97 end
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98 otherwise
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99 error('No such boundary condition: type = %s',type);
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100 end
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101 end
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102
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103 % Ruturns the boundary ops, half-norm, boundary indices and sign for the boundary specified by the string boundary.
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104 % The right boundary for each coordinate direction is considered the positive boundary
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105 function [e, d, halfnorm_inv, ind_boundary, s] = get_boundary_ops(obj,boundary)
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106 ind = grid.funcToMatrix(obj.grid, 1:obj.grid.N());
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107 switch boundary
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108 case 'w'
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109 e = obj.e_l{1};
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
110 d = obj.d_l{1};
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
111 halfnorm_inv = obj.halfnorm_inv{1};
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
112 ind_boundary = ind(1,:);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
113 s = -1;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
114 case 'e'
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
115 e = obj.e_r{1};
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parents:
diff changeset
116 d = obj.d_r{1};
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
117 halfnorm_inv = obj.halfnorm_inv{1};
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
118
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
119 ind_boundary = ind(end,:);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
120 s = 1;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
121 case 's'
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
122 e = obj.e_l{2};
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
123 d = obj.d_l{2};
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
124 halfnorm_inv = obj.halfnorm_inv{2};
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
125 ind_boundary = ind(:,1);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
126 s = -1;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
127 case 'n'
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
128 e = obj.e_r{2};
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parents:
diff changeset
129 d = obj.d_r{2};
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parents:
diff changeset
130 halfnorm_inv = obj.halfnorm_inv{2};
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
131 ind_boundary = ind(:,end);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
132 s = 1;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
133 otherwise
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
134 error('No such boundary: boundary = %s',boundary);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
135 end
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
136 end
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
137
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
138 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
139 error('An interface function does not exist yet');
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
140 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
141
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
142 function N = size(obj)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
143 N = obj.grid.m;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
144 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
145 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
146
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
147 methods(Static)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
148 function [Dp, Dm, H, Hi, d_l, d_r, e_l, e_r, I, DissipationOp] = assemble1DOperators(g, operator_type, order, dissipation)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
149 dim = g.D();
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
150 I = cell(dim,1);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
151 D1 = cell(dim,1);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
152 D2 = cell(dim,1);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
153 H = cell(dim,1);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
154 Hi = cell(dim,1);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
155 e_l = cell(dim,1);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
156 e_r = cell(dim,1);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
157 d1_l = cell(dim,1);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
158 d1_r = cell(dim,1);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
159 DissipationOp = cell(dim,1);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
160 for i = 1:dim
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
161 switch operator_type
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
162 % case 'narrow'
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
163 % ops = sbp.D4Variable(g.m(i), g.lim{i}, order);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
164 % D1{i} = ops.D1;
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parents:
diff changeset
165 % D2{i} = ops.D2;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
166 % d_l{i} = ops.d1_l';
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
167 % d_r{i} = ops.d1_r';
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
168 % if (strcmp(dissipation,'on'))
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
169 % DissipationOp{i} = -1*sbp.dissipationOperator(g.m(i), order, ops.HI);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
170 % end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
171 % case 'upwind-'
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
172 % ops = sbp.D1Upwind(g.m(i), g.lim{i}, order);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
173 % D1{i} = (ops.Dp + ops.Dm)/2;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
174 % D2{i} = @(viscosity) ops.Dp*spdiag(viscosity)*ops.Dm;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
175 % d_l{i} = ops.e_l'*ops.Dm;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
176 % d_r{i} = ops.e_r'*ops.Dm;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
177 % if (strcmp(dissipation,'on'))
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
178 % DissipationOp{i} = (ops.Dp-ops.Dm)/2;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
179 % end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
180 case 'upwind+'
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
181 ops = sbp.D1Upwind(g.m(i), g.lim{i}, order);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
182 Dp{i} = ops.Dp;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
183 Dm{i} = ops.Dm;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
184 % D1{i} = (ops.Dp + ops.Dm)/2;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
185 % D2{i} = @(viscosity) ops.Dm*spdiag(viscosity)*ops.Dp;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
186 d_l{i} = ops.e_l'*ops.Dp;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
187 d_r{i} = ops.e_r'*ops.Dp;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
188 if (strcmp(dissipation,'on'))
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
189 DissipationOp{i} = (ops.Dp-ops.Dm)/2;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
190 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
191 % case 'upwind+-'
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
192 % ops = sbp.D1Upwind(g.m(i), g.lim{i}, order);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
193 % D1{i} = (ops.Dp + ops.Dm)/2;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
194 % D2{i} = @(viscosity) (ops.Dp*spdiag(viscosity)*ops.Dm + ops.Dm*spdiag(viscosity)*ops.Dp)/2;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
195 % d_l{i} = ops.e_l'*D1;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
196 % d_r{i} = ops.e_r'*D1;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
197 % if (strcmp(dissipation,'on'))
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
198 % DissipationOp{i} = (ops.Dp-ops.Dm)/2;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
199 % end
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
200 otherwise
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
201 error('Other operator types not yet supported', operator_type);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
202 end
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
203 H{i} = ops.H;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
204 Hi{i} = ops.HI;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
205 e_l{i} = ops.e_l;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
206 e_r{i} = ops.e_r;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
207 I{i} = speye(g.m(i));
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
208 end
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
209 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
210 function op_2d = extendOperatorTo2D(op, I)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
211 op_2d{1} = kr(op{1}, I{2});
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
212 op_2d{2} = kr(I{1}, op{2});
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
213 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
214 end
a6f34de60044 First attempt at implementing Burgers in 2D with RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
215 end