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annotate +scheme/Burgers1D.m @ 815:fae41958af4f feature/burgers1d

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Add support for artificial viscosity to the 1d burgers scheme. - Add support for artificial viscosity by parametrizing the discretization operator and boundary closure on the viscosity. - Add a time stepper which evaluates and updates the residual viscosity of the solution.
author Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
date Thu, 06 Sep 2018 12:43:51 +0200
parents 3a5e635a93fd
children d0934d1143b7
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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 m % Number of points in each direction, possibly a vector
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4 h % Grid spacing
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5 x % Grid
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6 order % Order accuracy for the approximation
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7 params
814
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8
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9 D % Non-stabalized scheme operator
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10 M % Derivative norm
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11 H % Discrete norm
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12 Hi % Norm inverse
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13 e_l
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14 e_r
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15 d_l
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16 d_r
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17 end
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18
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19 methods
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20 function obj = Burgers1D(pde_form, operator_type, order, m, lim, params)
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21 [x, h] = util.get_grid(lim{:},m);
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22 default_arg('pde_form','skew-symmetric');
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23 default_arg('operator_type','narrow');
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24
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25 switch operator_type
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26 case 'narrow'
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27 ops = sbp.D2Variable(m, lim, order);
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28 D1 = ops.D1;
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29 D2 = ops.D2;
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30 otherwise
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31 error('Other operator types not yet supported', operator_type);
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32 end
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33
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34 switch pde_form
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35 case 'skew-symmetric'
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36 D = @(v, viscosity) -1/3*v.*D1*v - 1/3*D1*v.^2 + D2(obj.params.eps + viscosity)*v;
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37 case 'conservative'
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38 D = @(v, viscosity) -1/2*D1*v.^2 + D2(obj.params.eps + viscosity)*v;
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39 end
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40
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41 obj.m = m;
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42 obj.h = h;
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43 obj.order = order;
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44 obj.x = x;
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45 obj.params = params;
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46
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47 %% TODO: Figure out how to evaluate viscosity as viscosity(v,t) here instead of parametrizing D on the viscosity.
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48 obj.D = D;
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49 obj.M = ops.M;
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50 obj.H = ops.H;
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51 obj.Hi = ops.HI;
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52 obj.e_l = ops.e_l;
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53 obj.e_r = ops.e_r;
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54 obj.d_l = ops.d1_l;
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55 obj.d_r = ops.d1_r;
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56 end
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57
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58 % Closure functions return the opertors applied to the own doamin to close the boundary
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59 % 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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60 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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61 % type is a string specifying the type of boundary condition if there are several.
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62 % data is a function returning the data that should be applied at the boundary.
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63 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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64 % neighbour_boundary is a string specifying which boundary to interface to.
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65 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
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66 default_arg('type','robin');
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67 default_arg('data',0);
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68 [e, s, d] = obj.get_boundary_ops(boundary);
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69 switch type
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70 % Stable robin-like boundary conditions ((u+-abs(u))*u/3 - eps*u_x)) with +- at left/right boundary
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71 case {'R','robin'}
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72 p = s*obj.Hi*e;
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73 closure = @(v, viscosity) p*(e'*((v-s*abs(v))/3)*(e'*v) - e'*(obj.params.eps + viscosity)*d'*v);
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74 switch class(data)
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75 case 'double'
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76 penalty = s*p*data;
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77 case 'function_handle'
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78 penalty = @(t) s*p*data(t);
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79 otherwise
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80 error('Wierd data argument!')
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81 end
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82 % Unknown, boundary condition
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83 otherwise
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84 error('No such boundary condition: type = %s',type);
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85 end
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86 end
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87
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88 % Ruturns the boundary ops and sign for the boundary specified by the string boundary.
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89 % The right boundary is considered the positive boundary
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90 function [e, s, d] = get_boundary_ops(obj,boundary)
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91 switch boundary
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92 case 'l'
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93 e = obj.e_l;
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94 s = -1;
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95 d = obj.d_l;
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96 case 'r'
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97 e = obj.e_r;
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98 s = 1;
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99 d = obj.d_r;
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100 otherwise
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101 error('No such boundary: boundary = %s',boundary);
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102 end
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103 end
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104
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105 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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106 error('An interface function does not exist yet');
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107 end
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108
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109 function N = size(obj)
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110 N = obj.m;
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111 end
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112
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113 end
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114 end