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annotate +scheme/Utux.m @ 1198:2924b3a9b921 feature/d2_compatible

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Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
author Martin Almquist <malmquist@stanford.edu>
date Fri, 16 Aug 2019 14:30:28 -0700
parents 0c504a21432d
children 433c89bf19e0
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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 H % Discrete norm
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9 D
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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 v0
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16 end
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19 methods
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20 function obj = Utux(g, order, opSet)
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21 default_arg('opSet',@sbp.D2Standard);
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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 obj.D1 = ops.D1;
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31 obj.grid = g;
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33 obj.H = ops.H;
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34 obj.Hi = ops.HI;
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36 obj.e_l = ops.e_l;
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37 obj.e_r = ops.e_r;
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38 obj.D = -obj.D1;
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39
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40 obj.m = m;
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41 obj.h = ops.h;
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42 obj.order = order;
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43
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44 end
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45 % Closure functions return the opertors applied to the own doamin to close the boundary
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46 % 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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47 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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48 % type is a string specifying the type of boundary condition if there are several.
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49 % data is a function returning the data that should be applied at the boundary.
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50 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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51 % neighbour_boundary is a string specifying which boundary to interface to.
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52 function [closure, penalty] = boundary_condition(obj,boundary,type)
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53 default_arg('type','dirichlet');
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54 tau =-1*obj.e_l;
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55 closure = obj.Hi*tau*obj.e_l';
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56 penalty = -obj.Hi*tau;
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58 end
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59
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60 function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type)
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61 switch boundary
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62 % Upwind coupling
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63 case {'l','left'}
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64 tau = -1*obj.e_l;
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65 closure = obj.Hi*tau*obj.e_l';
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66 penalty = -obj.Hi*tau*neighbour_scheme.e_r';
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67 case {'r','right'}
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68 tau = 0*obj.e_r;
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69 closure = obj.Hi*tau*obj.e_r';
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70 penalty = -obj.Hi*tau*neighbour_scheme.e_l';
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71 end
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73 end
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75 % Returns the boundary operator op for the boundary specified by the string boundary.
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76 % op -- string
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77 % boundary -- string
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78 function o = getBoundaryOperator(obj, op, boundary)
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79 assertIsMember(op, {'e'})
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80 assertIsMember(boundary, {'l', 'r'})
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81
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82 o = obj.([op, '_', boundary]);
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83 end
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85 % Returns square boundary quadrature matrix, of dimension
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86 % corresponding to the number of boundary points
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87 %
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88 % boundary -- string
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89 % Note: for 1d diffOps, the boundary quadrature is the scalar 1.
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90 function H_b = getBoundaryQuadrature(obj, boundary)
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91 assertIsMember(boundary, {'l', 'r'})
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92
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93 H_b = 1;
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94 end
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95
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96 function N = size(obj)
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97 N = obj.m;
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98 end
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99
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100 end
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101 end