Mercurial > repos > public > sbplib

annotate +rv/constructDiffOps.m @ 1156:8c0e2b50f018 feature/rv

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Tue, 25 Jun 2019 13:06:42 +0200
parents 3108963cc42c
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
1156
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
1 function [D_rv, D_flux, DvDt, solutionPenalties, residualPenalties] = constructDiffOps(scheme, g, schemeOrder, residualOrder, schemeParams, opSet, BCs)
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
2 %% DiffOps for solution vector
1156
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
3 [D, solutionPenalties] = constructFluxDiffOp(scheme, g, schemeOrder, schemeParams, opSet, BCs);
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
4 D2 = constructSymmetricD2Operator(g, schemeOrder, opSet);
1154
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
5 D_rv = @(v,Viscosity)(D(v) + D2(Viscosity)*v);
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
6
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
7 %% DiffOps for residual viscosity
1156
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
8 [D_flux, residualPenalties] = constructFluxDiffOp(scheme, g, residualOrder, schemeParams, opSet, BCs);
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
9 % TODO: Construct D_flux without closures when using bdfs.
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
10 % diffOp = scheme(g, residualOrder, schemeParams{:}, opSet);
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
11 % if ~isa(diffOp.D, 'function_handle')
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
12 % D_flux = @(v) diffOp.D*v;
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
13 % else
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
14 % D_flux = diffOp.D;
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
15 % end
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
16
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
17 % DiffOp for flux in residual viscosity. Due to sign conventions of the implemented schemes, we need to
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
18 % change the sign.
1037
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
19 D_flux = @(v) -D_flux(v);
1156
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
20 lim = {g.x{1}(1), g.x{1}(end)};
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
21 o = 2;
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
22 h = g.scaling();
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
23 gam = 1;
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
24 if isequal(opSet,@sbp.D1Upwind)
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
25 ops = sbp.D1Upwind(g.m(), lim, o);
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
26 Hi = ops.HI;
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
27 e_r = ops.e_r;
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
28 e_l = ops.e_l;
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
29 B = e_r*e_r' - e_l*e_l';
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
30 M = ops.Dm - Hi*B;
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
31 D2 = M*ops.Dp;
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
32 else
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
33 ops = sbp.D2Standard(g.m(), lim, o);
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
34 D2 = ops.D2;
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
35 end
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
36 D2_low = gam*h^(residualOrder)*D2;
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
37 D2_low = @(v) D2_low*v;
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
38 % DiffOp for time derivative in residual viscosity
1156
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
39 DvDt = @(v) D(v)+D2_low(v);
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
40 %DvDt = @(v) D(v);
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
41 end
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
42
1154
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
43 function [D, penalties] = constructFluxDiffOp(scheme, g, order, schemeParams, opSet, BCs)
1037
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
44 diffOp = scheme(g, order, schemeParams{:}, opSet);
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
45 [D, penalties] = addClosuresToDiffOp(diffOp, BCs);
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
46 end
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
47
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
48 function [D, penalties] = addClosuresToDiffOp(diffOp, BCs)
1037
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
49 if ~isa(diffOp.D, 'function_handle')
1146
52f59d27b40f Add missing semicolon
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1037
diff changeset
50 D = @(v) diffOp.D*v;
1037
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
51 else
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
52 D = diffOp.D;
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
53 end
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
54 penalties = cell(size(BCs));
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
55 for i = 1:size(BCs,1)
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
56 for j = 1:size(BCs,2)
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
57 [closure, penalties{i,j}] = diffOp.boundary_condition(BCs{i,j}.boundary, BCs{i,j}.type);
1037
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
58 if ~isa(closure, 'function_handle')
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
59 closure = @(v) closure*v;
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
60 end
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
61 D = @(v) D(v) + closure(v);
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
62 end
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
63 end
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
64 end
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
65
1037
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
66 function D2 = constructSymmetricD2Operator(g, order, opSet)
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
67 m = g.size();
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
68 ops = cell(g.D(),1);
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
69 I = cell(g.D(),1);
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
70 for i = 1:g.D()
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
71 lim = {g.x{i}(1), g.x{i}(end)};
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
72 ops{i} = opSet(m(i), lim, order);
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
73 I{i} = speye(m(i));
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
74 end
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
75
1037
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
76 switch g.D()
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
77 case 1
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
78 e_r = ops{1}.e_r;
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
79 e_l = ops{1}.e_l;
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
80 Hi = ops{1}.HI;
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
81 B = e_r*e_r' - e_l*e_l';
1037
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
82 if isequal(opSet,@sbp.D1Upwind)
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
83 Dm = ops{1}.Dm;
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
84 Dp = ops{1}.Dp;
1154
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
85 M = Dm - Hi*B;
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
86 D2 = @(Viscosity) M*Viscosity*Dp;
1037
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
87 else
1154
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
88 % TODO: Fix closure for D2Variable
1156
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
89 % TODO: Fix Viscosity not being vector
8c0e2b50f018 Attempt to fix oscilations when not using bdfs by adding lower-order 2nd derivative correction term to the Residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
diff changeset
90 D2 = @(Viscosity)ops{1}.D2(diag(Viscosity));
1037
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
91 end
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
92 case 2
1037
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
93 % TODO:
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
94 % Currently only implemented for upwind operators.
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
95 % Remove this part once the time-dependent D2 operator is implemented for other opSets
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
96 % or if it is decided that it should only be supported for upwind operators.
2d7ba44340d0 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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
diff changeset
97 assert(isequal(opSet,@sbp.D1Upwind))
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
98 e_e = kron(ops{1}.e_r,I{2});
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
99 e_w = kron(ops{1}.e_l,I{2});
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
100 Dm_x = kron(ops{1}.Dm,I{2});
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
101 Dp_x = kron(ops{1}.Dp,I{2});
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
102 H_x = kron(ops{1}.HI,I{2});
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
103 B_x = e_e*e_e' - e_w*e_w';
1154
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
104 M_x = Dm_x-H_x*B_x;
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
105 D2_x = @(Viscosity) M_x*Viscosity*Dp_x;
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
106
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
107 e_n = kron(I{1},ops{2}.e_r);
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
108 e_s = kron(I{1},ops{2}.e_l);
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
109 Dm_y = kron(I{1},ops{2}.Dm);
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
110 Dp_y = kron(I{1},ops{2}.Dp);
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
111 H_y = kron(I{1},ops{2}.HI);
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
112 B_y = e_n*e_n' - e_s*e_s';
1154
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
113 M_y = Dm_y-H_y*B_y;
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
114 D2_y = @(Viscosity) M_y*Viscosity*Dp_y;
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
115 D2 = @(Viscosity) D2_x(Viscosity) + D2_y(Viscosity);
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
116 otherwise
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
117 error('3D not yet implemented')
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
118 end
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
119 end