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annotate +scheme/Burgers1d.m @ 1037:2d7ba44340d0 feature/burgers1d

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Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 18 Jan 2019 09:02:02 +0100
parents 2b9bdb22baec
children 8537fdd6830a
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
1034
2676ad79f994 Rename Burgers1D to Burgers1d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 853
diff changeset
1 classdef Burgers1d < scheme.Scheme
814
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
2 properties
832
5573913a0949 Merged with default, and updated +scheme/Burgers1D accordingly
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 831
diff changeset
3 grid % Physical grid
814
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parents:
diff changeset
4 order % Order accuracy for the approximation
832
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parents: 831
diff changeset
5
815
fae41958af4f Add support for artificial viscosity to the 1d burgers scheme.
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
diff changeset
6 params
814
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7
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
8 D % Non-stabalized scheme operator
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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9 H % Discrete norm
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
10 Hi % Norm inverse
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
11 e_l
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
12 e_r
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
13 d_l
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
14 d_r
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
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diff changeset
15 end
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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16
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
17 methods
1034
2676ad79f994 Rename Burgers1D to Burgers1d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 853
diff changeset
18 function obj = Burgers1d(grid, pde_form, operator_type, order, dissipation, params)
832
5573913a0949 Merged with default, and updated +scheme/Burgers1D accordingly
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 831
diff changeset
19 assert(grid.D == 1);
5573913a0949 Merged with default, and updated +scheme/Burgers1D accordingly
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 831
diff changeset
20 assert(grid.size() == length(params.eps));
5573913a0949 Merged with default, and updated +scheme/Burgers1D accordingly
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 831
diff changeset
21 m = grid.size();
5573913a0949 Merged with default, and updated +scheme/Burgers1D accordingly
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 831
diff changeset
22 lim = grid.lim{1}; % Ugly, and only applicable for cartesian grids.
815
fae41958af4f Add support for artificial viscosity to the 1d burgers scheme.
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
diff changeset
23 switch operator_type
fae41958af4f Add support for artificial viscosity to the 1d burgers scheme.
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
diff changeset
24 case 'narrow'
833
9f4c45a2d271 Support narrow stencil operators of order 6
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 832
diff changeset
25 ops = sbp.D4Variable(m, lim, order);
815
fae41958af4f Add support for artificial viscosity to the 1d burgers scheme.
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
diff changeset
26 D1 = ops.D1;
834
f1f0bf087e1c Add support for artificial viscosity
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
diff changeset
27 D2 = ops.D2;
844
9e4e0576ca0f Only compute dissipation operator when requested
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 834
diff changeset
28 if (strcmp(dissipation,'on'))
9e4e0576ca0f Only compute dissipation operator when requested
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 834
diff changeset
29 DissipationOp = -1*sbp.dissipationOperator(m, order, ops.HI);
9e4e0576ca0f Only compute dissipation operator when requested
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 834
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30 end
834
f1f0bf087e1c Add support for artificial viscosity
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
diff changeset
31 d_l = ops.d1_l';
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
diff changeset
32 d_r = ops.d1_r';
852
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
33 case 'upwind-'
834
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
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34 ops = sbp.D1Upwind(m, lim, order);
f1f0bf087e1c Add support for artificial viscosity
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
diff changeset
35 D1 = (ops.Dp + ops.Dm)/2;
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1e057b0f2fed Add RK6 with residual viscosity update and reduce computational effort of spatial scheme
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 844
diff changeset
36 D2 = @(eps) ops.Dp*spdiag(eps)*ops.Dm;
852
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
37 if (strcmp(dissipation,'on'))
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
38 DissipationOp = (ops.Dp-ops.Dm)/2;
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
39 end
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
40 d_l = ops.e_l'*ops.Dm;
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
41 d_r = ops.e_r'*ops.Dm;
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
42 case 'upwind+'
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
43 ops = sbp.D1Upwind(m, lim, order);
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
44 D1 = (ops.Dp + ops.Dm)/2;
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
45 D2 = @(eps) ops.Dm*spdiag(eps)*ops.Dp;
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
46 if (strcmp(dissipation,'on'))
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
47 DissipationOp = (ops.Dp-ops.Dm)/2;
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
48 end
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
49 d_l = ops.e_l'*ops.Dp;
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
50 d_r = ops.e_r'*ops.Dp;
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
51 case 'upwind+-'
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
52 ops = sbp.D1Upwind(m, lim, order);
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
53 D1 = (ops.Dp + ops.Dm)/2;
fbb8be3177c8 Fix bug in SAT terms for upwind operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 851
diff changeset
54 D2 = @(eps) (ops.Dp*spdiag(eps)*ops.Dm + ops.Dm*spdiag(eps)*ops.Dp)/2;
844
9e4e0576ca0f Only compute dissipation operator when requested
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 834
diff changeset
55 if (strcmp(dissipation,'on'))
9e4e0576ca0f Only compute dissipation operator when requested
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 834
diff changeset
56 DissipationOp = (ops.Dp-ops.Dm)/2;
9e4e0576ca0f Only compute dissipation operator when requested
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 834
diff changeset
57 end
851
ab2e5a24ddde - Fix bug when constructing closure for narrow stencils
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 848
diff changeset
58 d_l = ops.e_l'*D1;
ab2e5a24ddde - Fix bug when constructing closure for narrow stencils
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 848
diff changeset
59 d_r = ops.e_r'*D1;
815
fae41958af4f Add support for artificial viscosity to the 1d burgers scheme.
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
diff changeset
60 otherwise
fae41958af4f Add support for artificial viscosity to the 1d burgers scheme.
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
diff changeset
61 error('Other operator types not yet supported', operator_type);
fae41958af4f Add support for artificial viscosity to the 1d burgers scheme.
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
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62 end
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
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63
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
diff changeset
64 switch pde_form
fae41958af4f Add support for artificial viscosity to the 1d burgers scheme.
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
diff changeset
65 case 'skew-symmetric'
834
f1f0bf087e1c Add support for artificial viscosity
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
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66 if (strcmp(dissipation,'on'))
f1f0bf087e1c Add support for artificial viscosity
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
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67 D = @(v, viscosity) - 1/3*D1*v.^2 + (-1/3*v.*D1 + D2(params.eps + viscosity) + max(abs(v))*DissipationOp)*v;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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68 else
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
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69 D = @(v, viscosity) - 1/3*D1*v.^2 + (-1/3*v.*D1 + D2(params.eps + viscosity))*v;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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70 end
815
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
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diff changeset
71 case 'conservative'
834
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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72 if (strcmp(dissipation,'on'))
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
diff changeset
73 D = @(v, viscosity) -1/2*D1*v.^2 + (D2(params.eps + viscosity) + max(abs(v))*DissipationOp)*v;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
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74 else
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
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75 D = @(v, viscosity) -1/2*D1*v.^2 + D2(params.eps + viscosity)*v;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
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76 end
853
cda996e64925 Minor renaming and clean up
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 852
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77 otherwise
cda996e64925 Minor renaming and clean up
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 852
diff changeset
78 error('Not supported', pde_form);
815
fae41958af4f Add support for artificial viscosity to the 1d burgers scheme.
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
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79 end
814
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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80
832
5573913a0949 Merged with default, and updated +scheme/Burgers1D accordingly
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 831
diff changeset
81 obj.grid = grid;
814
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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82 obj.order = order;
815
fae41958af4f Add support for artificial viscosity to the 1d burgers scheme.
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
diff changeset
83 obj.params = params;
814
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parents:
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84
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fae41958af4f Add support for artificial viscosity to the 1d burgers scheme.
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
diff changeset
85 obj.D = D;
814
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
86 obj.H = ops.H;
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
87 obj.Hi = ops.HI;
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
88 obj.e_l = ops.e_l;
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
89 obj.e_r = ops.e_r;
834
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
diff changeset
90 obj.d_l = d_l;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
diff changeset
91 obj.d_r = d_r;
814
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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92 end
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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93
853
cda996e64925 Minor renaming and clean up
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 852
diff changeset
94 % Closure functions return the operators applied to the own doamin to close the boundary
cda996e64925 Minor renaming and clean up
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 852
diff changeset
95 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other domain.
814
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
96 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
97 % type is a string specifying the type of boundary condition if there are several.
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
98 % data is a function returning the data that should be applied at the boundary.
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
99 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
100 default_arg('type','robin');
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
101 default_arg('data',0);
853
cda996e64925 Minor renaming and clean up
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 852
diff changeset
102 [e, d, i_b, s] = obj.get_boundary_ops(boundary);
814
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
103 switch type
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
104 % Stable robin-like boundary conditions ((u+-abs(u))*u/3 - eps*u_x)) with +- at left/right boundary
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
105 case {'R','robin'}
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
106 p = s*obj.Hi*e;
851
ab2e5a24ddde - Fix bug when constructing closure for narrow stencils
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 848
diff changeset
107 closure = @(v, viscosity) p*(((v(i_b)-s*abs(v(i_b)))/3)*(v(i_b)) - ((obj.params.eps(i_b) + viscosity(i_b))*d*v));
814
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
108 switch class(data)
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
109 case 'double'
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
110 penalty = s*p*data;
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
111 case 'function_handle'
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
112 penalty = @(t) s*p*data(t);
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
113 otherwise
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
114 error('Wierd data argument!')
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
115 end
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
116 otherwise
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
117 error('No such boundary condition: type = %s',type);
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118 end
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119 end
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120
853
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diff changeset
121 % Ruturns the boundary ops, boundary index and sign for the boundary specified by the string boundary.
814
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122 % The right boundary is considered the positive boundary
853
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123 function [e, d, i_b, s] = get_boundary_ops(obj,boundary)
814
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124 switch boundary
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125 case 'l'
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126 e = obj.e_l;
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127 d = obj.d_l;
848
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128 i_b = 1;
853
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129 s = -1;
814
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130 case 'r'
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131 e = obj.e_r;
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132 d = obj.d_r;
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133 i_b = length(e);
853
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parents: 852
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134 s = 1;
814
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135 otherwise
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136 error('No such boundary: boundary = %s',boundary);
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137 end
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138 end
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139
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140 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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141 error('An interface function does not exist yet');
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142 end
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parents:
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143
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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144 function N = size(obj)
832
5573913a0949 Merged with default, and updated +scheme/Burgers1D accordingly
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 831
diff changeset
145 N = obj.grid.m;
814
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146 end
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147 end
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148 end