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annotate +scheme/Burgers1D.m @ 853:cda996e64925 feature/burgers1d

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Minor renaming and clean up
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 12 Oct 2018 08:41:57 +0200
parents fbb8be3177c8
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
814
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
1 classdef Burgers1D < scheme.Scheme
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
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
4 order % Order accuracy for the approximation
832
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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
3a5e635a93fd Add scheme for 1D Burgers equation
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parents:
diff changeset
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:
diff changeset
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
3a5e635a93fd Add scheme for 1D Burgers equation
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>
parents:
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
834
f1f0bf087e1c Add support for artificial viscosity
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
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
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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
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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
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31 d_l = ops.d1_l';
f1f0bf087e1c Add support for artificial viscosity
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
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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-'
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f1f0bf087e1c Add support for artificial viscosity
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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);
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
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62 end
fae41958af4f Add support for artificial viscosity to the 1d burgers scheme.
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
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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'))
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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>
parents: 833
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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>
parents: 833
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70 end
815
fae41958af4f Add support for artificial viscosity to the 1d burgers scheme.
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
diff changeset
71 case 'conservative'
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
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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
diff changeset
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);
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
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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;
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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82 obj.order = order;
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
diff changeset
83 obj.params = params;
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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84
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents: 814
diff changeset
85 obj.D = D;
814
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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;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 833
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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
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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92 end
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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
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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)
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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
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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
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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
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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'
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
110 penalty = s*p*data;
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
111 case 'function_handle'
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
112 penalty = @(t) s*p*data(t);
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
113 otherwise
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
114 error('Wierd data argument!')
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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115 end
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
116 otherwise
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
117 error('No such boundary condition: type = %s',type);
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
118 end
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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119 end
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120
853
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 852
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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parents: 852
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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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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
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125 case 'l'
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
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126 e = obj.e_l;
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127 d = obj.d_l;
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parents: 845
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128 i_b = 1;
853
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parents: 852
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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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parents: 845
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133 i_b = length(e);
853
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parents: 852
diff changeset
134 s = 1;
814
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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135 otherwise
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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136 error('No such boundary: boundary = %s',boundary);
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parents:
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137 end
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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138 end
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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139
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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140 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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141 error('An interface function does not exist yet');
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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142 end
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
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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parents:
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146 end
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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147 end
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
parents:
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148 end