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annotate +scheme/Burgers1d.m @ 1196:f6c571d8f22f feature/rv

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Add option to discretize Burgers1d using quasi-linear form
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 07 Aug 2019 13:28:21 +0200
parents 635386c073b9
children 433c89bf19e0
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
1034
2676ad79f994 Rename Burgers1D to Burgers1d
Vidar Stiernström <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 grid % Grid
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6 order % Order accuracy for the approximation
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7
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8 H % Discrete norm
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9 D
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5573913a0949 Merged with default, and updated +scheme/Burgers1D accordingly
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10
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11 D1
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12 Hi
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13 e_l
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14 e_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(g, order, pde_form, fluxSplitting, opSet)
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19 default_arg('opSet',@sbp.D2Standard);
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20 default_arg('fluxSplitting',@(v)max(abs(v)));
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21 assertType(g, 'grid.Cartesian');
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22
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23 m = g.size();
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24 xl = g.getBoundary('l');
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25 xr = g.getBoundary('r');
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26 xlim = {xl, xr};
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27
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28 ops = opSet(m, xlim, order);
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29
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30 if (isequal(opSet, @sbp.D1Upwind))
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31 obj.D1 = (ops.Dp + ops.Dm)/2;
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32 DissOp = (ops.Dm - ops.Dp)/2;
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33 switch pde_form
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34 case 'quasi-linear'
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35 obj.D = @(v) -((spdiag(v)*obj.D1 + fluxSplitting(v)*DissOp)*v);
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36 case 'skew-symmetric'
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37 obj.D = @(v) -(1/3*obj.D1*(v.*v) + (1/3*spdiag(v)*obj.D1 + fluxSplitting(v)*DissOp)*v);
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38 case 'conservative'
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39 obj.D = @(v) -(1/2*obj.D1*(v.*v) + fluxSplitting(v)*DissOp*v);
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40 end
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41 else
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42 obj.D1 = ops.D1;
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43 switch pde_form
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44 case 'quasi-linear'
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45 obj.D = @(v) -(spdiag(v)*obj.D1*v);
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46 case 'skew-symmetric'
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47 obj.D = @(v) -(1/3*obj.D1*(v.*v) + 1/3*spdiag(v)*obj.D1*v);
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48 case 'conservative'
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49 obj.D = @(v) -1/2*obj.D1*(v.*v);
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50 end
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51 end
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52 obj.grid = g;
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53
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54 obj.H = ops.H;
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55 obj.Hi = ops.HI;
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56
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57 obj.e_l = ops.e_l;
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58 obj.e_r = ops.e_r;
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59
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60 obj.m = m;
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61 obj.h = ops.h;
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62 obj.order = order;
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63 end
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64
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65 % Closure functions return the operators applied to the own doamin to close the boundary
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66 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other domain.
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67 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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68 % type is a string specifying the type of boundary condition if there are several.
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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 [e, index, s] = obj.get_boundary_ops(boundary);
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72 switch type
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73 % Stable dirchlet-like boundary conditions (u+-abs(u))*u/3
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74 % with +- at left/right boundaries
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75 case {'D', 'd', 'dirichlet', 'Dirichlet'}
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76 % tau = s*e;
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77 % closure = @(v) obj.Hi*tau*(((v(index)-s*abs(v(index)))/3)*v(index));
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78 % penalty = -obj.Hi*tau;
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79
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80 magnitude = 2/3;
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81 tau = @(v) s*magnitude*obj.Hi*e*(v(index)-s*abs(v(index)))/2;
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82 closure = @(v) tau(v)*v(index);
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83 penalty = @(v) -tau(v);
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84 otherwise
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85 error('No such boundary condition: type = %s',type);
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86 end
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87 end
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88
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89 % Returns the boundary ops, boundary index and sign for the boundary specified by the string boundary.
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90 % The right boundary is considered the positive boundary
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91 function [e, index, s] = get_boundary_ops(obj,boundary)
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92 switch boundary
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93 case {'l','L','left','Left'}
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94 e = obj.e_l;
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95 index = 1;
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96 s = -1;
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97 case {'r','R','right','Right'}
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98 e = obj.e_r;
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99 index = length(e);
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100 s = 1;
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101 otherwise
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102 error('No such boundary: boundary = %s',boundary);
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103 end
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104 end
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105
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106 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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107 error('An interface function does not exist yet');
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108 end
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109
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110 function N = size(obj)
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111 N = obj.grid.m;
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112 end
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113 end
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114 end