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annotate +scheme/Burgers1D.m @ 814:3a5e635a93fd feature/burgers1d

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Add scheme for 1D Burgers equation - Add scheme for discretizing the 1D burgers equation, with spatially variable coefficients.
author Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
date Mon, 03 Sep 2018 14:50:27 +0200
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children fae41958af4f
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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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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
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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
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
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8 D % Non-stabalized scheme operator
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9 M % Derivative norm
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10 H % Discrete norm
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
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11 Hi % Norm inverse
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12 e_l
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13 e_r
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14 d_l
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15 d_r
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16 params % Parameters for the coefficient matrices
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17 end
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18
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19 methods
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Vidar Stiernstrom <vidar.stiernstrom@it.uu.se>
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20 function obj = Burgers1D(m, order, xlim, params)
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21 [x, h] = util.get_grid(xlim{:},m);
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22 ops = sbp.D2Variable(m, xlim, order);
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23
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24 obj.m = m;
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25 obj.h = h;
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26 obj.order = order;
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27 obj.x = x;
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28
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29 D1 = ops.D1;
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30 obj.D = @(v)(-1/3*v.*D1*v - 1/3*D1*v.^2 + ops.D2(params.eps)*v);
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31 obj.M = ops.M;
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32 obj.H = ops.H;
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33 obj.Hi = ops.HI;
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34 obj.e_l = ops.e_l;
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35 obj.e_r = ops.e_r;
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36 obj.d_l = ops.d1_l;
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37 obj.d_r = ops.d1_r;
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38 obj.params = params;
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39 end
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40
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41 % Closure functions return the opertors applied to the own doamin to close the boundary
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42 % 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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43 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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44 % type is a string specifying the type of boundary condition if there are several.
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45 % data is a function returning the data that should be applied at the boundary.
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46 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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47 % neighbour_boundary is a string specifying which boundary to interface to.
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48 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
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49 default_arg('type','robin');
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50 default_arg('data',0);
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51 [e, s, d] = obj.get_boundary_ops(boundary);
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52 switch type
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53 % Stable robin-like boundary conditions ((u+-abs(u))*u/3 - eps*u_x)) with +- at left/right boundary
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54 case {'R','robin'}
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55 p = s*obj.Hi*e;
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56 closure = @(v) p*(e'*((v-s*abs(v))/3)*(e'*v) - e'*obj.params.eps*d'*v);
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57 switch class(data)
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58 case 'double'
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59 penalty = s*p*data;
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60 case 'function_handle'
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61 penalty = @(t) s*p*data(t);
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62 otherwise
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63 error('Wierd data argument!')
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64 end
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65 % Unknown, boundary condition
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66 otherwise
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67 error('No such boundary condition: type = %s',type);
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68 end
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69 end
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70
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71 % Ruturns the boundary ops and sign for the boundary specified by the string boundary.
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72 % The right boundary is considered the positive boundary
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73 function [e, s, d] = get_boundary_ops(obj,boundary)
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74 switch boundary
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75 case 'l'
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76 e = obj.e_l;
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77 s = -1;
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78 d = obj.d_l;
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79 case 'r'
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80 e = obj.e_r;
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81 s = 1;
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82 d = obj.d_r;
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83 otherwise
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84 error('No such boundary: boundary = %s',boundary);
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85 end
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86 end
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87
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88 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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89 error('An interface function does not exist yet');
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90 end
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91
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92 function N = size(obj)
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93 N = obj.m;
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94 end
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95
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96 end
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97 end