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annotate +scheme/Burgers1D.m @ 834:f1f0bf087e1c feature/burgers1d

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Add support for artificial viscosity - Add option to use upwind operators for discretizing the scheme - Add option to use dissipation operators constructed from undivided differences when discretizing with narrow stencil operators
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 13 Sep 2018 14:21:47 +0200
parents 9f4c45a2d271
children 9e4e0576ca0f
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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814
3a5e635a93fd Add scheme for 1D Burgers equation
Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
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1 classdef Burgers1D < scheme.Scheme
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2 properties
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3 grid % Physical grid
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4 order % Order accuracy for the approximation
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5
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6 params
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7
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8 D % Non-stabalized scheme operator
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9 H % Discrete norm
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10 Hi % Norm inverse
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11 e_l
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12 e_r
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13 d_l
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14 d_r
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15 end
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16
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17 methods
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18 function obj = Burgers1D(grid, pde_form, operator_type, order, dissipation, params)
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19 assert(grid.D == 1);
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20 assert(grid.size() == length(params.eps));
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21 m = grid.size();
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22 lim = grid.lim{1}; % Ugly, and only applicable for cartesian grids.
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23 default_arg('pde_form','skew-symmetric');
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24 default_arg('operator_type','narrow');
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25 default_arg('dissipation','on');
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26
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27 switch operator_type
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28 case 'narrow'
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29 ops = sbp.D4Variable(m, lim, order);
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30 D1 = ops.D1;
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31 D2 = ops.D2;
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32 DissipationOp = -1*sbp.dissipationOperator(m, order, ops.HI);
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33 d_l = ops.d1_l';
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34 d_r = ops.d1_r';
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35 case 'upwind'
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36 ops = sbp.D1Upwind(m, lim, order);
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37 D1 = (ops.Dp + ops.Dm)/2;
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38 %D2eps = @(eps) ops.Dp*diag(eps)*ops.Dm;
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39 %D2eps = @(eps) ops.Dm*diag(eps)*ops.Dp;
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40 D2 = @(eps) (ops.Dp*diag(eps)*ops.Dm + ops.Dm*diag(eps)*ops.Dp)/2;
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41 DissipationOp = (ops.Dp-ops.Dm)/2;
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42 d_l = D1;
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43 d_r = D1;
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44 otherwise
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45 error('Other operator types not yet supported', operator_type);
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46 end
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47
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48 %% TODO: Figure out how to evaluate viscosity as viscosity(v,t) here instead of parametrizing D on the viscosity.
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49 switch pde_form
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50 case 'skew-symmetric'
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51 if (strcmp(dissipation,'on'))
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52 D = @(v, viscosity) - 1/3*D1*v.^2 + (-1/3*v.*D1 + D2(params.eps + viscosity) + max(abs(v))*DissipationOp)*v;
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53 else
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54 D = @(v, viscosity) - 1/3*D1*v.^2 + (-1/3*v.*D1 + D2(params.eps + viscosity))*v;
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55 end
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56 case 'conservative'
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57 if (strcmp(dissipation,'on'))
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58 D = @(v, viscosity) -1/2*D1*v.^2 + (D2(params.eps + viscosity) + max(abs(v))*DissipationOp)*v;
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59 else
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60 D = @(v, viscosity) -1/2*D1*v.^2 + D2(params.eps + viscosity)*v;
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61 end
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62 end
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63
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64 obj.grid = grid;
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65 obj.order = order;
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66 obj.params = params;
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67
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68 obj.D = D;
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69 obj.H = ops.H;
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70 obj.Hi = ops.HI;
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71 obj.e_l = ops.e_l;
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72 obj.e_r = ops.e_r;
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73 obj.d_l = d_l;
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74 obj.d_r = d_r;
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75 end
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76
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77 % Closure functions return the opertors applied to the own doamin to close the boundary
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78 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other domain.
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79 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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80 % type is a string specifying the type of boundary condition if there are several.
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81 % data is a function returning the data that should be applied at the boundary.
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82 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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83 % neighbour_boundary is a string specifying which boundary to interface to.
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84 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
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85 default_arg('type','robin');
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86 default_arg('data',0);
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87 [e, s, d] = obj.get_boundary_ops(boundary);
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88 switch type
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89 % Stable robin-like boundary conditions ((u+-abs(u))*u/3 - eps*u_x)) with +- at left/right boundary
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90 case {'R','robin'}
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91 p = s*obj.Hi*e;
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92 closure = @(v, viscosity) p*(e'*((v-s*abs(v))/3)*(e'*v) - e'*((obj.params.eps + viscosity).*d*v));
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93 switch class(data)
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94 case 'double'
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95 penalty = s*p*data;
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96 case 'function_handle'
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97 penalty = @(t) s*p*data(t);
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98 otherwise
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99 error('Wierd data argument!')
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100 end
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101 % Unknown, boundary condition
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102 otherwise
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103 error('No such boundary condition: type = %s',type);
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104 end
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105 end
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106
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107 % Ruturns the boundary ops and sign for the boundary specified by the string boundary.
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108 % The right boundary is considered the positive boundary
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109 function [e, s, d] = get_boundary_ops(obj,boundary)
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110 switch boundary
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111 case 'l'
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112 e = obj.e_l;
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113 s = -1;
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114 d = obj.d_l;
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115 case 'r'
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116 e = obj.e_r;
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117 s = 1;
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118 d = obj.d_r;
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119 otherwise
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120 error('No such boundary: boundary = %s',boundary);
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121 end
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122 end
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123
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124 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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125 error('An interface function does not exist yet');
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126 end
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127
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128 function N = size(obj)
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129 N = obj.grid.m;
814
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130 end
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131 end
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132 end