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annotate +scheme/Utux2d.m @ 1037:2d7ba44340d0 feature/burgers1d

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Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 18 Jan 2019 09:02:02 +0100
parents 8a9393084b30
children 433c89bf19e0
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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950
cab047de7f5d Rename *2D schemes to *2d
Jonatan Werpers <jonatan@werpers.com>
parents: 948
diff changeset
1 classdef Utux2d < scheme.Scheme
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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2 properties
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Martin Almquist <martin.almquist@it.uu.se>
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3 m % Number of points in each direction, possibly a vector
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Martin Almquist <martin.almquist@it.uu.se>
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4 h % Grid spacing
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Martin Almquist <martin.almquist@it.uu.se>
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5 grid % Grid
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Martin Almquist <martin.almquist@it.uu.se>
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6 order % Order accuracy for the approximation
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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7
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Martin Almquist <martin.almquist@it.uu.se>
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8 a % Wave speed a = [a1, a2];
743
f4595f14d696 Change schemes to work for special coefficients.
Martin Almquist <malmquist@stanford.edu>
parents: 666
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9 % Can either be a constant vector or a cell array of function handles.
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10
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11 H % Discrete norm
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Martin Almquist <malmquist@stanford.edu>
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12 H_x, H_y % Norms in the x and y directions
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Martin Almquist <malmquist@stanford.edu>
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13 Hi, Hx, Hy, Hxi, Hyi % Kroneckered norms
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14
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15 % Derivatives
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Martin Almquist <martin.almquist@it.uu.se>
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16 Dx, Dy
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17
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18 % Boundary operators
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Martin Almquist <martin.almquist@it.uu.se>
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19 e_w, e_e, e_s, e_n
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20
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21 D % Total discrete operator
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22 end
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Martin Almquist <martin.almquist@it.uu.se>
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23
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24
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25 methods
1036
8a9393084b30 Change argument order to the "correct" order, i.e providing diffOp specific parameters before the opSet.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1025
diff changeset
26 function obj = Utux2d(g ,order, a, fluxSplitting, opSet)
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27
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28 default_arg('a',1/sqrt(2)*[1, 1]);
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29 default_arg('opSet',@sbp.D2Standard);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1019
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30 default_arg('fluxSplitting',[]);
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Martin Almquist <malmquist@stanford.edu>
parents: 666
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31
948
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Jonatan Werpers <jonatan@werpers.com>
parents: 942
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32 assertType(g, 'grid.Cartesian');
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Martin Almquist <malmquist@stanford.edu>
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33 if iscell(a)
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Martin Almquist <malmquist@stanford.edu>
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34 a1 = grid.evalOn(g, a{1});
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Martin Almquist <malmquist@stanford.edu>
parents: 666
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35 a2 = grid.evalOn(g, a{2});
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Martin Almquist <malmquist@stanford.edu>
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36 a = {spdiag(a1), spdiag(a2)};
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Martin Almquist <malmquist@stanford.edu>
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37 else
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Martin Almquist <malmquist@stanford.edu>
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38 a = {a(1), a(2)};
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39 end
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40
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41 m = g.size();
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42 m_x = m(1);
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43 m_y = m(2);
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44 m_tot = g.N();
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45
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46 xlim = {g.x{1}(1), g.x{1}(end)};
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47 ylim = {g.x{2}(1), g.x{2}(end)};
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48 obj.grid = g;
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49
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50 % Operator sets
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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51 ops_x = opSet(m_x, xlim, order);
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52 ops_y = opSet(m_y, ylim, order);
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Martin Almquist <martin.almquist@it.uu.se>
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53 Ix = speye(m_x);
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54 Iy = speye(m_y);
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55
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56 % Norms
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57 Hx = ops_x.H;
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58 Hy = ops_y.H;
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59 Hxi = ops_x.HI;
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60 Hyi = ops_y.HI;
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61
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62 obj.H_x = Hx;
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63 obj.H_y = Hy;
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64 obj.H = kron(Hx,Hy);
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65 obj.Hi = kron(Hxi,Hyi);
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66 obj.Hx = kron(Hx,Iy);
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67 obj.Hy = kron(Ix,Hy);
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68 obj.Hxi = kron(Hxi,Iy);
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69 obj.Hyi = kron(Ix,Hyi);
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70
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71 % Derivatives
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
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72 if (isequal(opSet,@sbp.D1Upwind))
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
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73 Dx = (ops_x.Dp + ops_x.Dm)/2;
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74 Dy = (ops_y.Dp + ops_y.Dm)/2;
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75 obj.Dx = kron(Dx,Iy);
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parents: 1022
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76 obj.Dy = kron(Ix,Dy);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 950
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77 DissOpx = (ops_x.Dm - ops_x.Dp)/2;
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78 DissOpy = (ops_y.Dm - ops_y.Dp)/2;
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79 DissOpx = kron(DissOpx,Iy);
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80 DissOpy = kron(Ix,DissOpy);
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81
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82 obj.D = -(a{1}*obj.Dx + a{2}*obj.Dy + fluxSplitting{1}*DissOpx + fluxSplitting{2}*DissOpy);
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83 else
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84 Dx = ops_x.D1;
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85 Dy = ops_y.D1;
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86 obj.Dx = kron(Dx,Iy);
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87 obj.Dy = kron(Ix,Dy);
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88
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89 obj.D = -(a{1}*obj.Dx + a{2}*obj.Dy);
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90 end
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91
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92 % Boundary operators
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93 obj.e_w = kr(ops_x.e_l, Iy);
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94 obj.e_e = kr(ops_x.e_r, Iy);
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95 obj.e_s = kr(Ix, ops_y.e_l);
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96 obj.e_n = kr(Ix, ops_y.e_r);
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97
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98 obj.m = m;
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99 obj.h = [ops_x.h ops_y.h];
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100 obj.order = order;
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101 obj.a = a;
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102 end
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103 % Closure functions return the opertors applied to the own domain to close the boundary
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104 % 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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105 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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106 % type is a string specifying the type of boundary condition if there are several. %TBD Remove type here? Only dirichlet applicable?
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107 % data is a function returning the data that should be applied at the boundary.
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108 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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109 % neighbour_boundary is a string specifying which boundary to interface to.
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110 function [closure, penalty] = boundary_condition(obj,boundary,type)
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111 default_arg('type','dirichlet');
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112 sigma_left = -1; % Scalar penalty parameter for left boundaries (West/South)
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113 sigma_right = 1; % Scalar penalty parameter for right boundaries (East/North)
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114 switch boundary
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115 % Can only specify boundary condition where there is inflow
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116 % Extract the postivie resp. negative part of a, for the left
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117 % resp. right boundaries, and set other values of a to zero.
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118 % Then the closure will effectively only contribute to inflow boundaries
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119 case {'w','W','west','West'}
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120 a_inflow = obj.a{1};
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121 a_inflow(a_inflow < 0) = 0;
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122 tau = sigma_left*a_inflow*obj.e_w*obj.H_y;
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123 closure = obj.Hi*tau*obj.e_w';
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124 case {'e','E','east','East'}
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125 a_inflow = obj.a{1};
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126 a_inflow(a_inflow > 0) = 0;
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127 tau = sigma_right*a_inflow*obj.e_e*obj.H_y;
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128 closure = obj.Hi*tau*obj.e_e';
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129 case {'s','S','south','South'}
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130 a_inflow = obj.a{2};
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parents: 1022
diff changeset
131 a_inflow(a_inflow < 0) = 0;
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diff changeset
132 tau = sigma_left*a_inflow*obj.e_s*obj.H_x;
591
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
133 closure = obj.Hi*tau*obj.e_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
diff changeset
134 case {'n','N','north','North'}
1025
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parents: 1022
diff changeset
135 a_inflow = obj.a{2};
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1022
diff changeset
136 a_inflow(a_inflow > 0) = 0;
ac80bedc8df7 Clean up of Utux2d
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1022
diff changeset
137 tau = sigma_right*a_inflow*obj.e_n*obj.H_x;
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
138 closure = obj.Hi*tau*obj.e_n';
905
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parents: 743
diff changeset
139 end
591
39554f2de783 Add Utux2D scheme
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parents:
diff changeset
140 penalty = -obj.Hi*tau;
914
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parents: 910
diff changeset
141 end
905
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parents: 743
diff changeset
142
942
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143 % type Struct that specifies the interface coupling.
914
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144 % Fields:
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145 % -- couplingType String, type of interface coupling
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146 % % Default: 'upwind'. Other: 'centered'
942
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147 % -- interpolation: type of interpolation, default 'none'
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diff changeset
148 % -- interpolationDamping: damping on upstream and downstream sides, when using interpolation.
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149 % Default {0,0} gives zero damping.
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diff changeset
150 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
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151
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diff changeset
152 defaultType.couplingType = 'upwind';
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
153 defaultType.interpolation = 'none';
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Martin Almquist <malmquist@stanford.edu>
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154 defaultType.interpolationDamping = {0,0};
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
155 default_struct('type', defaultType);
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156
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
157 switch type.interpolation
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Martin Almquist <malmquist@stanford.edu>
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158 case {'none', ''}
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
159 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
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diff changeset
160 case {'op','OP'}
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diff changeset
161 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
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diff changeset
162 otherwise
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163 error('Unknown type of interpolation: %s ', type.interpolation);
914
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164 end
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diff changeset
165 end
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166
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diff changeset
167 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
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168 couplingType = type.couplingType;
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169
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170 % Get neighbour boundary operator
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171 switch neighbour_boundary
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diff changeset
172 case {'e','E','east','East'}
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173 e_neighbour = neighbour_scheme.e_e;
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174 case {'w','W','west','West'}
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175 e_neighbour = neighbour_scheme.e_w;
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diff changeset
176 case {'n','N','north','North'}
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177 e_neighbour = neighbour_scheme.e_n;
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178 case {'s','S','south','South'}
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179 e_neighbour = neighbour_scheme.e_s;
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180 end
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181
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182 switch couplingType
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183
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184 % Upwind coupling (energy dissipation)
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185 case 'upwind'
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186 sigma_ds = -1; %"Downstream" penalty
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187 sigma_us = 0; %"Upstream" penalty
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188
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189 % Energy-preserving coupling (no energy dissipation)
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190 case 'centered'
605
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191 sigma_ds = -1/2; %"Downstream" penalty
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192 sigma_us = 1/2; %"Upstream" penalty
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193
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194 otherwise
942
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195 error(['Interface coupling type ' couplingType ' is not available.'])
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196 end
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197
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198 switch boundary
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199 case {'w','W','west','West'}
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diff changeset
200 tau = sigma_ds*obj.a{1}*obj.e_w*obj.H_y;
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201 closure = obj.Hi*tau*obj.e_w';
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diff changeset
202 penalty = -obj.Hi*tau*e_neighbour';
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diff changeset
203 case {'e','E','east','East'}
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diff changeset
204 tau = sigma_us*obj.a{1}*obj.e_e*obj.H_y;
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diff changeset
205 closure = obj.Hi*tau*obj.e_e';
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diff changeset
206 penalty = -obj.Hi*tau*e_neighbour';
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diff changeset
207 case {'s','S','south','South'}
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diff changeset
208 tau = sigma_ds*obj.a{2}*obj.e_s*obj.H_x;
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diff changeset
209 closure = obj.Hi*tau*obj.e_s';
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diff changeset
210 penalty = -obj.Hi*tau*e_neighbour';
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diff changeset
211 case {'n','N','north','North'}
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diff changeset
212 tau = sigma_us*obj.a{2}*obj.e_n*obj.H_x;
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diff changeset
213 closure = obj.Hi*tau*obj.e_n';
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diff changeset
214 penalty = -obj.Hi*tau*e_neighbour';
605
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diff changeset
215 end
610
b7b3c11fab4d Add interpolation to scheme
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diff changeset
216
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diff changeset
217 end
610
b7b3c11fab4d Add interpolation to scheme
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diff changeset
218
942
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diff changeset
219 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
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220
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diff changeset
221 % User can request special interpolation operators by specifying type.interpOpSet
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diff changeset
222 default_field(type, 'interpOpSet', @sbp.InterpOpsOP);
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diff changeset
223
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diff changeset
224 interpOpSet = type.interpOpSet;
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diff changeset
225 couplingType = type.couplingType;
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226 interpolationDamping = type.interpolationDamping;
610
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diff changeset
227
914
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228 % Get neighbour boundary operator
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229 switch neighbour_boundary
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diff changeset
230 case {'e','E','east','East'}
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diff changeset
231 e_neighbour = neighbour_scheme.e_e;
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diff changeset
232 case {'w','W','west','West'}
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diff changeset
233 e_neighbour = neighbour_scheme.e_w;
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diff changeset
234 case {'n','N','north','North'}
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diff changeset
235 e_neighbour = neighbour_scheme.e_n;
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diff changeset
236 case {'s','S','south','South'}
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diff changeset
237 e_neighbour = neighbour_scheme.e_s;
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
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diff changeset
238 end
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239
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diff changeset
240 switch couplingType
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241
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diff changeset
242 % Upwind coupling (energy dissipation)
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diff changeset
243 case 'upwind'
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diff changeset
244 sigma_ds = -1; %"Downstream" penalty
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diff changeset
245 sigma_us = 0; %"Upstream" penalty
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diff changeset
246
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
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diff changeset
247 % Energy-preserving coupling (no energy dissipation)
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diff changeset
248 case 'centered'
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diff changeset
249 sigma_ds = -1/2; %"Downstream" penalty
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diff changeset
250 sigma_us = 1/2; %"Upstream" penalty
666
2d85f17a8aec Add possibility for damping terms at interpolation interface.
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parents: 610
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251
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252 otherwise
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253 error(['Interface coupling type ' couplingType ' is not available.'])
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254 end
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255
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256 int_damp_us = interpolationDamping{1};
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257 int_damp_ds = interpolationDamping{2};
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258
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259 % u denotes the solution in the own domain
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260 % v denotes the solution in the neighbour domain
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261 % Find the number of grid points along the interface
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262 switch boundary
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263 case {'w','e'}
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264 m_u = obj.m(2);
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265 case {'s','n'}
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266 m_u = obj.m(1);
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267 end
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268 m_v = size(e_neighbour, 2);
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269
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270 % Build interpolation operators
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271 intOps = interpOpSet(m_u, m_v, obj.order, neighbour_scheme.order);
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272 Iu2v = intOps.Iu2v;
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273 Iv2u = intOps.Iv2u;
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274
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275 I_local2neighbour_ds = intOps.Iu2v.bad;
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276 I_local2neighbour_us = intOps.Iu2v.good;
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277 I_neighbour2local_ds = intOps.Iv2u.good;
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278 I_neighbour2local_us = intOps.Iv2u.bad;
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279
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280 I_back_forth_us = I_neighbour2local_us*I_local2neighbour_us;
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281 I_back_forth_ds = I_neighbour2local_ds*I_local2neighbour_ds;
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282
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283
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284 switch boundary
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285 case {'w','W','west','West'}
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286 tau = sigma_ds*obj.a{1}*obj.e_w*obj.H_y;
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287 closure = obj.Hi*tau*obj.e_w';
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288 penalty = -obj.Hi*tau*I_neighbour2local_ds*e_neighbour';
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289
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290 beta = int_damp_ds*obj.a{1}...
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291 *obj.e_w*obj.H_y;
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292 closure = closure + obj.Hi*beta*I_back_forth_ds*obj.e_w' - obj.Hi*beta*obj.e_w';
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293 case {'e','E','east','East'}
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294 tau = sigma_us*obj.a{1}*obj.e_e*obj.H_y;
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295 closure = obj.Hi*tau*obj.e_e';
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296 penalty = -obj.Hi*tau*I_neighbour2local_us*e_neighbour';
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297
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298 beta = int_damp_us*obj.a{1}...
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299 *obj.e_e*obj.H_y;
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300 closure = closure + obj.Hi*beta*I_back_forth_us*obj.e_e' - obj.Hi*beta*obj.e_e';
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301 case {'s','S','south','South'}
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302 tau = sigma_ds*obj.a{2}*obj.e_s*obj.H_x;
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303 closure = obj.Hi*tau*obj.e_s';
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304 penalty = -obj.Hi*tau*I_neighbour2local_ds*e_neighbour';
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305
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306 beta = int_damp_ds*obj.a{2}...
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307 *obj.e_s*obj.H_x;
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308 closure = closure + obj.Hi*beta*I_back_forth_ds*obj.e_s' - obj.Hi*beta*obj.e_s';
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309 case {'n','N','north','North'}
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310 tau = sigma_us*obj.a{2}*obj.e_n*obj.H_x;
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311 closure = obj.Hi*tau*obj.e_n';
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312 penalty = -obj.Hi*tau*I_neighbour2local_us*e_neighbour';
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313
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314 beta = int_damp_us*obj.a{2}...
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315 *obj.e_n*obj.H_x;
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316 closure = closure + obj.Hi*beta*I_back_forth_us*obj.e_n' - obj.Hi*beta*obj.e_n';
591
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317 end
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318
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319
591
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320 end
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321
591
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322 function N = size(obj)
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323 N = obj.m;
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324 end
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325
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326 end
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327
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328 methods(Static)
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329 % Calculates the matrices needed for the inteface coupling between boundary bound_u of scheme schm_u
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330 % and bound_v of scheme schm_v.
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331 % [uu, uv, vv, vu] = inteface_coupling(A,'r',B,'l')
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diff changeset
332 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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333 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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parents:
diff changeset
334 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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335 end
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336 end
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337 end