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annotate +scheme/Utux2d.m @ 1023:defc9d0cc1f2 feature/advectionRV

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Remove incorrect assertion of the number of BC:s
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 07 Jan 2019 12:06:49 +0100
parents 234c1c02ea39
children ac80bedc8df7
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
950
cab047de7f5d Rename *2D schemes to *2d
Jonatan Werpers <jonatan@werpers.com>
parents: 948
diff changeset
1 classdef Utux2d < scheme.Scheme
591
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
2 properties
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
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3 m % Number of points in each direction, possibly a vector
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
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4 h % Grid spacing
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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5 grid % Grid
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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6 order % Order accuracy for the approximation
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
7 v0 % Initial data
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
8
591
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
9 a % Wave speed a = [a1, a2];
743
f4595f14d696 Change schemes to work for special coefficients.
Martin Almquist <malmquist@stanford.edu>
parents: 666
diff changeset
10 % Can either be a constant vector or a cell array of function handles.
591
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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11
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
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12 H % Discrete norm
595
2a2f34778ded Make Utux2D work
Martin Almquist <malmquist@stanford.edu>
parents: 591
diff changeset
13 H_x, H_y % Norms in the x and y directions
2a2f34778ded Make Utux2D work
Martin Almquist <malmquist@stanford.edu>
parents: 591
diff changeset
14 Hi, Hx, Hy, Hxi, Hyi % Kroneckered norms
591
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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15
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
16 % Derivatives
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
17 Dx, Dy
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
18
1019
f029b97dbc72 Support upwind opSet in Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
diff changeset
19 % Dissipation Operators
f029b97dbc72 Support upwind opSet in Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
diff changeset
20 DissOpx, DissOpy
f029b97dbc72 Support upwind opSet in Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
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21
591
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
22 % Boundary operators
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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23 e_w, e_e, e_s, e_n
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
24
591
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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25 D % Total discrete operator
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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26 end
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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27
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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28
905
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Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
29 methods
1021
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1019
diff changeset
30 function obj = Utux2d(g ,order, opSet, a, fluxSplitting)
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
31
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Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
32 default_arg('a',1/sqrt(2)*[1, 1]);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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33 default_arg('opSet',@sbp.D2Standard);
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cc61dde120cd Add upwind dissipation to the operator inside Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1019
diff changeset
34 default_arg('fluxSplitting',[]);
743
f4595f14d696 Change schemes to work for special coefficients.
Martin Almquist <malmquist@stanford.edu>
parents: 666
diff changeset
35
948
3dd7f87c9a1b Use assertType(...) instead of assert(isa(...))
Jonatan Werpers <jonatan@werpers.com>
parents: 942
diff changeset
36 assertType(g, 'grid.Cartesian');
743
f4595f14d696 Change schemes to work for special coefficients.
Martin Almquist <malmquist@stanford.edu>
parents: 666
diff changeset
37 if iscell(a)
f4595f14d696 Change schemes to work for special coefficients.
Martin Almquist <malmquist@stanford.edu>
parents: 666
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38 a1 = grid.evalOn(g, a{1});
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Martin Almquist <malmquist@stanford.edu>
parents: 666
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39 a2 = grid.evalOn(g, a{2});
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Martin Almquist <malmquist@stanford.edu>
parents: 666
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40 a = {spdiag(a1), spdiag(a2)};
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Martin Almquist <malmquist@stanford.edu>
parents: 666
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41 else
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Martin Almquist <malmquist@stanford.edu>
parents: 666
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42 a = {a(1), a(2)};
f4595f14d696 Change schemes to work for special coefficients.
Martin Almquist <malmquist@stanford.edu>
parents: 666
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43 end
905
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Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
44
591
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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45 m = g.size();
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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46 m_x = m(1);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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47 m_y = m(2);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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48 m_tot = g.N();
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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49
595
2a2f34778ded Make Utux2D work
Martin Almquist <malmquist@stanford.edu>
parents: 591
diff changeset
50 xlim = {g.x{1}(1), g.x{1}(end)};
2a2f34778ded Make Utux2D work
Martin Almquist <malmquist@stanford.edu>
parents: 591
diff changeset
51 ylim = {g.x{2}(1), g.x{2}(end)};
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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52 obj.grid = g;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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53
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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54 % Operator sets
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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55 ops_x = opSet(m_x, xlim, order);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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56 ops_y = opSet(m_y, ylim, order);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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57 Ix = speye(m_x);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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58 Iy = speye(m_y);
905
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parents: 743
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59
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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60 % Norms
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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61 Hx = ops_x.H;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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62 Hy = ops_y.H;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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63 Hxi = ops_x.HI;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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64 Hyi = ops_y.HI;
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
65
595
2a2f34778ded Make Utux2D work
Martin Almquist <malmquist@stanford.edu>
parents: 591
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66 obj.H_x = Hx;
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Martin Almquist <malmquist@stanford.edu>
parents: 591
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67 obj.H_y = Hy;
591
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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68 obj.H = kron(Hx,Hy);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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69 obj.Hi = kron(Hxi,Hyi);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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70 obj.Hx = kron(Hx,Iy);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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71 obj.Hy = kron(Ix,Hy);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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72 obj.Hxi = kron(Hxi,Iy);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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73 obj.Hyi = kron(Ix,Hyi);
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
74
591
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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75 % Derivatives
1019
f029b97dbc72 Support upwind opSet in Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
diff changeset
76 if (isequal(opSet,@sbp.D1Upwind))
f029b97dbc72 Support upwind opSet in Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
diff changeset
77 Dx = (ops_x.Dp + ops_x.Dm)/2;
f029b97dbc72 Support upwind opSet in Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
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78 Dy = (ops_y.Dp + ops_y.Dm)/2;
f029b97dbc72 Support upwind opSet in Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
diff changeset
79 DissOpx = (ops_x.Dm - ops_x.Dp)/2;
f029b97dbc72 Support upwind opSet in Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
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80 DissOpy = (ops_y.Dm - ops_y.Dp)/2;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
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81 obj.Dx = kron(Dx,Iy);
f029b97dbc72 Support upwind opSet in Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
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82 obj.Dy = kron(Ix,Dy);
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parents: 950
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83 obj.DissOpx = kron(DissOpx,Iy);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
diff changeset
84 obj.DissOpy = kron(Ix,DissOpy);
f029b97dbc72 Support upwind opSet in Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
diff changeset
85 else
f029b97dbc72 Support upwind opSet in Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
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86 Dx = ops_x.D1;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
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87 Dy = ops_y.D1;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
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88 obj.Dx = kron(Dx,Iy);
f029b97dbc72 Support upwind opSet in Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
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89 obj.Dy = kron(Ix,Dy);
f029b97dbc72 Support upwind opSet in Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
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90 end
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 743
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91
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Martin Almquist <martin.almquist@it.uu.se>
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92 % Boundary operators
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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93 obj.e_w = kr(ops_x.e_l, Iy);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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94 obj.e_e = kr(ops_x.e_r, Iy);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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95 obj.e_s = kr(Ix, ops_y.e_l);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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96 obj.e_n = kr(Ix, ops_y.e_r);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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97
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Martin Almquist <martin.almquist@it.uu.se>
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98 obj.m = m;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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99 obj.h = [ops_x.h ops_y.h];
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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100 obj.order = order;
595
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Martin Almquist <malmquist@stanford.edu>
parents: 591
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101 obj.a = a;
1021
cc61dde120cd Add upwind dissipation to the operator inside Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1019
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102
cc61dde120cd Add upwind dissipation to the operator inside Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1019
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103 if (isequal(opSet,@sbp.D1Upwind))
cc61dde120cd Add upwind dissipation to the operator inside Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1019
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104 obj.D = -(a{1}*obj.Dx + a{2}*obj.Dy + fluxSplitting{1}*obj.DissOpx + fluxSplitting{2}*obj.DissOpy);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1019
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105 else
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1019
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106 obj.D = -(a{1}*obj.Dx + a{2}*obj.Dy);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1019
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107 end
591
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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108 end
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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109 % Closure functions return the opertors applied to the own domain to close the boundary
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Martin Almquist <martin.almquist@it.uu.se>
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110 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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111 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
1022
234c1c02ea39 Add dirichlet bc for north and south boundary and handle cases where the wave speed changes in sign.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1021
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112 % type is a string specifying the type of boundary condition if there are several. %TBD Remove type here? Only dirichlet applicable?
591
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Martin Almquist <martin.almquist@it.uu.se>
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113 % data is a function returning the data that should be applied at the boundary.
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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114 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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Martin Almquist <martin.almquist@it.uu.se>
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115 % neighbour_boundary is a string specifying which boundary to interface to.
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Martin Almquist <martin.almquist@it.uu.se>
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116 function [closure, penalty] = boundary_condition(obj,boundary,type)
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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117 default_arg('type','dirichlet');
1022
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1021
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118 sigma_left = -1; % Scalar penalty parameter for left boundaries
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1021
diff changeset
119 sigma_right = 1; % Scalar penalty parameter for right boundaries
591
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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120 switch boundary
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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121 case {'w','W','west','West'}
1022
234c1c02ea39 Add dirichlet bc for north and south boundary and handle cases where the wave speed changes in sign.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1021
diff changeset
122 % Can only specify boundary condition where there is inflow
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1021
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123 % Extract positive part of a{1}
234c1c02ea39 Add dirichlet bc for north and south boundary and handle cases where the wave speed changes in sign.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1021
diff changeset
124 a_pos = obj.a{1};
234c1c02ea39 Add dirichlet bc for north and south boundary and handle cases where the wave speed changes in sign.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1021
diff changeset
125 a_pos(a_pos < 0) = 0;
234c1c02ea39 Add dirichlet bc for north and south boundary and handle cases where the wave speed changes in sign.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1021
diff changeset
126 tau = sigma_left*a_pos*obj.e_w*obj.H_y;
591
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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127 closure = obj.Hi*tau*obj.e_w';
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parents:
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128 case {'s','S','south','South'}
1022
234c1c02ea39 Add dirichlet bc for north and south boundary and handle cases where the wave speed changes in sign.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1021
diff changeset
129 % Can only specify boundary condition where there is inflow
234c1c02ea39 Add dirichlet bc for north and south boundary and handle cases where the wave speed changes in sign.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1021
diff changeset
130 % Extract positive part of a{2}
234c1c02ea39 Add dirichlet bc for north and south boundary and handle cases where the wave speed changes in sign.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1021
diff changeset
131 a_pos = obj.a{2};
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132 a_pos(a_pos < 0) = 0;
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diff changeset
133 tau = sigma_left*a_pos*obj.e_s*obj.H_x;
591
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diff changeset
134 closure = obj.Hi*tau*obj.e_s';
1022
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diff changeset
135 case {'e','E','east','East'}
234c1c02ea39 Add dirichlet bc for north and south boundary and handle cases where the wave speed changes in sign.
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diff changeset
136 % Can only specify boundary condition where there is inflow
234c1c02ea39 Add dirichlet bc for north and south boundary and handle cases where the wave speed changes in sign.
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diff changeset
137 % Extract negative part of a{1}
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diff changeset
138 a_neg = obj.a{1};
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diff changeset
139 a_neg(a_neg > 0) = 0;
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diff changeset
140 tau = sigma_right*a_neg*obj.e_e*obj.H_y;
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diff changeset
141 closure = obj.Hi*tau*obj.e_e';
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diff changeset
142 case {'n','N','north','North'}
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parents: 1021
diff changeset
143 % Can only specify boundary condition where there is inflow
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diff changeset
144 % Extract negative part of a{2}
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diff changeset
145 a_neg = obj.a{2};
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diff changeset
146 a_neg(a_neg > 0) = 0;
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147 tau = sigma_right*a_neg*obj.e_n*obj.H_x;
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148 closure = obj.Hi*tau*obj.e_n';
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149 end
591
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150 penalty = -obj.Hi*tau;
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151 end
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152
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153 % type Struct that specifies the interface coupling.
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154 % Fields:
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155 % -- couplingType String, type of interface coupling
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156 % % Default: 'upwind'. Other: 'centered'
942
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157 % -- interpolation: type of interpolation, default 'none'
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diff changeset
158 % -- interpolationDamping: damping on upstream and downstream sides, when using interpolation.
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159 % Default {0,0} gives zero damping.
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160 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
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161
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162 defaultType.couplingType = 'upwind';
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163 defaultType.interpolation = 'none';
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164 defaultType.interpolationDamping = {0,0};
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165 default_struct('type', defaultType);
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166
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167 switch type.interpolation
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168 case {'none', ''}
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169 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
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diff changeset
170 case {'op','OP'}
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171 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
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172 otherwise
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173 error('Unknown type of interpolation: %s ', type.interpolation);
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174 end
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175 end
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176
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177 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
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178 couplingType = type.couplingType;
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179
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180 % Get neighbour boundary operator
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181 switch neighbour_boundary
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182 case {'e','E','east','East'}
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183 e_neighbour = neighbour_scheme.e_e;
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184 case {'w','W','west','West'}
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185 e_neighbour = neighbour_scheme.e_w;
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186 case {'n','N','north','North'}
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187 e_neighbour = neighbour_scheme.e_n;
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188 case {'s','S','south','South'}
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189 e_neighbour = neighbour_scheme.e_s;
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190 end
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191
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192 switch couplingType
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193
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194 % Upwind coupling (energy dissipation)
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195 case 'upwind'
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196 sigma_ds = -1; %"Downstream" penalty
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197 sigma_us = 0; %"Upstream" penalty
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198
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199 % Energy-preserving coupling (no energy dissipation)
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200 case 'centered'
605
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201 sigma_ds = -1/2; %"Downstream" penalty
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202 sigma_us = 1/2; %"Upstream" penalty
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203
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204 otherwise
942
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205 error(['Interface coupling type ' couplingType ' is not available.'])
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206 end
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207
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208 switch boundary
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209 case {'w','W','west','West'}
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diff changeset
210 tau = sigma_ds*obj.a{1}*obj.e_w*obj.H_y;
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211 closure = obj.Hi*tau*obj.e_w';
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212 penalty = -obj.Hi*tau*e_neighbour';
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diff changeset
213 case {'e','E','east','East'}
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214 tau = sigma_us*obj.a{1}*obj.e_e*obj.H_y;
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215 closure = obj.Hi*tau*obj.e_e';
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diff changeset
216 penalty = -obj.Hi*tau*e_neighbour';
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diff changeset
217 case {'s','S','south','South'}
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diff changeset
218 tau = sigma_ds*obj.a{2}*obj.e_s*obj.H_x;
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diff changeset
219 closure = obj.Hi*tau*obj.e_s';
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diff changeset
220 penalty = -obj.Hi*tau*e_neighbour';
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diff changeset
221 case {'n','N','north','North'}
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diff changeset
222 tau = sigma_us*obj.a{2}*obj.e_n*obj.H_x;
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diff changeset
223 closure = obj.Hi*tau*obj.e_n';
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diff changeset
224 penalty = -obj.Hi*tau*e_neighbour';
605
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diff changeset
225 end
610
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diff changeset
226
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227 end
610
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diff changeset
228
942
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diff changeset
229 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
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230
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231 % User can request special interpolation operators by specifying type.interpOpSet
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232 default_field(type, 'interpOpSet', @sbp.InterpOpsOP);
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diff changeset
233
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diff changeset
234 interpOpSet = type.interpOpSet;
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diff changeset
235 couplingType = type.couplingType;
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236 interpolationDamping = type.interpolationDamping;
610
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diff changeset
237
914
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238 % Get neighbour boundary operator
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diff changeset
239 switch neighbour_boundary
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diff changeset
240 case {'e','E','east','East'}
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diff changeset
241 e_neighbour = neighbour_scheme.e_e;
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diff changeset
242 case {'w','W','west','West'}
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diff changeset
243 e_neighbour = neighbour_scheme.e_w;
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diff changeset
244 case {'n','N','north','North'}
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diff changeset
245 e_neighbour = neighbour_scheme.e_n;
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diff changeset
246 case {'s','S','south','South'}
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diff changeset
247 e_neighbour = neighbour_scheme.e_s;
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459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
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248 end
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249
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250 switch couplingType
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251
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252 % Upwind coupling (energy dissipation)
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253 case 'upwind'
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254 sigma_ds = -1; %"Downstream" penalty
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255 sigma_us = 0; %"Upstream" penalty
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256
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257 % Energy-preserving coupling (no energy dissipation)
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258 case 'centered'
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259 sigma_ds = -1/2; %"Downstream" penalty
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260 sigma_us = 1/2; %"Upstream" penalty
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261
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262 otherwise
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263 error(['Interface coupling type ' couplingType ' is not available.'])
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264 end
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265
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266 int_damp_us = interpolationDamping{1};
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267 int_damp_ds = interpolationDamping{2};
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268
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269 % u denotes the solution in the own domain
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270 % v denotes the solution in the neighbour domain
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271 % Find the number of grid points along the interface
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272 switch boundary
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273 case {'w','e'}
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274 m_u = obj.m(2);
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275 case {'s','n'}
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276 m_u = obj.m(1);
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277 end
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278 m_v = size(e_neighbour, 2);
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279
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280 % Build interpolation operators
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281 intOps = interpOpSet(m_u, m_v, obj.order, neighbour_scheme.order);
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282 Iu2v = intOps.Iu2v;
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283 Iv2u = intOps.Iv2u;
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284
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285 I_local2neighbour_ds = intOps.Iu2v.bad;
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286 I_local2neighbour_us = intOps.Iu2v.good;
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287 I_neighbour2local_ds = intOps.Iv2u.good;
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288 I_neighbour2local_us = intOps.Iv2u.bad;
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289
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290 I_back_forth_us = I_neighbour2local_us*I_local2neighbour_us;
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291 I_back_forth_ds = I_neighbour2local_ds*I_local2neighbour_ds;
666
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292
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293
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294 switch boundary
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295 case {'w','W','west','West'}
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296 tau = sigma_ds*obj.a{1}*obj.e_w*obj.H_y;
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297 closure = obj.Hi*tau*obj.e_w';
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298 penalty = -obj.Hi*tau*I_neighbour2local_ds*e_neighbour';
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299
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300 beta = int_damp_ds*obj.a{1}...
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301 *obj.e_w*obj.H_y;
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302 closure = closure + obj.Hi*beta*I_back_forth_ds*obj.e_w' - obj.Hi*beta*obj.e_w';
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303 case {'e','E','east','East'}
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304 tau = sigma_us*obj.a{1}*obj.e_e*obj.H_y;
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305 closure = obj.Hi*tau*obj.e_e';
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306 penalty = -obj.Hi*tau*I_neighbour2local_us*e_neighbour';
666
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diff changeset
307
942
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308 beta = int_damp_us*obj.a{1}...
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309 *obj.e_e*obj.H_y;
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310 closure = closure + obj.Hi*beta*I_back_forth_us*obj.e_e' - obj.Hi*beta*obj.e_e';
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311 case {'s','S','south','South'}
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312 tau = sigma_ds*obj.a{2}*obj.e_s*obj.H_x;
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313 closure = obj.Hi*tau*obj.e_s';
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314 penalty = -obj.Hi*tau*I_neighbour2local_ds*e_neighbour';
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315
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316 beta = int_damp_ds*obj.a{2}...
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317 *obj.e_s*obj.H_x;
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318 closure = closure + obj.Hi*beta*I_back_forth_ds*obj.e_s' - obj.Hi*beta*obj.e_s';
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319 case {'n','N','north','North'}
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320 tau = sigma_us*obj.a{2}*obj.e_n*obj.H_x;
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diff changeset
321 closure = obj.Hi*tau*obj.e_n';
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322 penalty = -obj.Hi*tau*I_neighbour2local_us*e_neighbour';
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diff changeset
323
942
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324 beta = int_damp_us*obj.a{2}...
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325 *obj.e_n*obj.H_x;
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326 closure = closure + obj.Hi*beta*I_back_forth_us*obj.e_n' - obj.Hi*beta*obj.e_n';
591
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parents:
diff changeset
327 end
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
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328
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329
591
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330 end
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459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
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diff changeset
331
591
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parents:
diff changeset
332 function N = size(obj)
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333 N = obj.m;
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334 end
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diff changeset
335
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336 end
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parents:
diff changeset
337
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diff changeset
338 methods(Static)
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diff changeset
339 % Calculates the matrices needed for the inteface coupling between boundary bound_u of scheme schm_u
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parents:
diff changeset
340 % and bound_v of scheme schm_v.
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341 % [uu, uv, vv, vu] = inteface_coupling(A,'r',B,'l')
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parents:
diff changeset
342 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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parents:
diff changeset
343 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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parents:
diff changeset
344 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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diff changeset
345 end
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parents:
diff changeset
346 end
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parents:
diff changeset
347 end