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Support variable wave speed and upwind operators in Utux
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 07 Jan 2019 16:35:04 +0100
parents 6d2167719557
children 8a9393084b30
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Ylva Rydin <ylva.rydin@telia.com>
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1 classdef Utux < scheme.Scheme
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2 properties
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3 m % Number of points in each direction, possibly a vector
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4 h % Grid spacing
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5 grid % Grid
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6 order % Order accuracy for the approximation
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7
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8 a % Wave speed
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9 % Can either be a constant or function handle.
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10
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11 H % Discrete norm
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12 D
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13
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14 D1
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15 Hi
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16 e_l
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17 e_r
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18 end
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19
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20
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21 methods
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22 function obj = Utux(g, order, opSet, a, fluxSplitting)
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23 default_arg('opSet',@sbp.D2Standard);
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24 default_arg('a',1);
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25 default_arg('fluxSplitting',[]);
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26
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27 assertType(g, 'grid.Cartesian');
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28 if isa(a, 'function_handle')
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29 obj.a = spdiag(grid.evalOn(g, a));
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30 else
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31 obj.a = a;
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32 end
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33
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34 m = g.size();
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35 xl = g.getBoundary('l');
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36 xr = g.getBoundary('r');
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37 xlim = {xl, xr};
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38
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39 ops = opSet(m, xlim, order);
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40
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41 if (isequal(opSet, @sbp.D1Upwind))
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42 obj.D1 = (ops.Dp + ops.Dm)/2;
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43 DissOp = (ops.Dm - ops.Dp)/2;
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44 obj.D = -(obj.a*obj.D1 + fluxSplitting*DissOp);
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45 else
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46 obj.D1 = ops.D1;
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47 obj.D = -obj.a*obj.D1;
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48 end
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49
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4a73b2aab91f Edit scheme.Utux: Add interface function. Compatible with new grids. Works with Utux_1D_interface.
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50 obj.grid = g;
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52 obj.H = ops.H;
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53 obj.Hi = ops.HI;
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55 obj.e_l = ops.e_l;
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56 obj.e_r = ops.e_r;
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57
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58 obj.m = m;
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59 obj.h = ops.h;
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60 obj.order = order;
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61 end
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62 % Closure functions return the opertors applied to the own doamin to close the boundary
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63 % 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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64 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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65 % type is a string specifying the type of boundary condition if there are several.
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66 % data is a function returning the data that should be applied at the boundary.
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67 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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68 % neighbour_boundary is a string specifying which boundary to interface to.
573
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69 function [closure, penalty] = boundary_condition(obj,boundary,type)
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70 default_arg('type','dirichlet');
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71 sigma_left = -1; % Scalar penalty parameter for left boundary
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72 sigma_right = 1; % Scalar penalty parameter for right boundary
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73 switch boundary
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74 % Can only specify boundary condition where there is inflow
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75 % Extract the postivie resp. negative part of a, for the left
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76 % resp. right boundary, and set other values of a to zero.
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77 % Then the closure will effectively only contribute to inflow boundaries
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78 case {'l','L','left','Left'}
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79 a_inflow = obj.a;
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80 a_inflow(a_inflow < 0) = 0;
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81 tau = sigma_left*a_inflow*obj.e_l;
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82 closure = obj.Hi*tau*obj.e_l';
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83 case {'r','R','right','Right'}
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84 a_inflow = obj.a;
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85 a_inflow(a_inflow > 0) = 0;
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86 tau = sigma_right*a_inflow*obj.e_r;
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87 closure = obj.Hi*tau*obj.e_r';
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88 end
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89 penalty = -obj.Hi*tau;
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90
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91 end
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92
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93 function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type)
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94 switch boundary
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95 % Upwind coupling
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96 case {'l','left'}
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97 tau = -1*obj.a*obj.e_l;
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98 closure = obj.Hi*tau*obj.e_l';
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99 penalty = -obj.Hi*tau*neighbour_scheme.e_r';
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100 case {'r','right'}
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101 tau = 0*obj.a*obj.e_r;
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102 closure = obj.Hi*tau*obj.e_r';
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103 penalty = -obj.Hi*tau*neighbour_scheme.e_l';
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104 end
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105
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106 end
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107
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108 function N = size(obj)
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109 N = obj.m;
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110 end
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111
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112 end
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113
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114 methods(Static)
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115 % Calculates the matrices needed for the inteface coupling between boundary bound_u of scheme schm_u
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116 % and bound_v of scheme schm_v.
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117 % [uu, uv, vv, vu] = inteface_coupling(A,'r',B,'l')
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118 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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119 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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120 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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121 end
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122 end
d755816aa0fa added a u_t+u_x=0 scheme
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
123 end