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comparison +scheme/Utux.m @ 270:d755816aa0fa

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added a u_t+u_x=0 scheme
author Ylva Rydin <ylva.rydin@telia.com>
date Fri, 09 Sep 2016 16:47:53 +0200
parents
children d32f674bcbe5
comparison
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251:6a5e94bb5e13 270:d755816aa0fa
1 classdef Utux < scheme.Scheme
2 properties
3 m % Number of points in each direction, possibly a vector
4 h % Grid spacing
5 x % Grid
6 order % Order accuracy for the approximation
7
8 H % Discrete norm
9 M % Derivative norm
10 D
11
12 D1
13 Hi
14 e_l
15 e_r
16 v0
17 end
18
19
20 methods
21 function obj = Utux(m,xlim,order)
22 default_arg('a',1);
23 [x, h] = util.get_grid(xlim{:},m);
24 ops = sbp.Ordinary(m,h,order);
25
26 obj.D1 = sparse(ops.derivatives.D1);
27 obj.H = sparse(ops.norms.H);
28 obj.Hi = sparse(ops.norms.HI);
29 obj.M = sparse(ops.norms.M);
30 obj.e_l = sparse(ops.boundary.e_1);
31 obj.e_r = sparse(ops.boundary.e_m);
32 obj.D=obj.D1;
33
34 obj.m = m;
35 obj.h = h;
36 obj.order = order;
37 obj.x = x;
38
39 end
40 % Closure functions return the opertors applied to the own doamin to close the boundary
41 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
42 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
43 % type is a string specifying the type of boundary condition if there are several.
44 % data is a function returning the data that should be applied at the boundary.
45 % neighbour_scheme is an instance of Scheme that should be interfaced to.
46 % neighbour_boundary is a string specifying which boundary to interface to.
47 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
48 default_arg('type','neumann');
49 default_arg('data',0);
50 tau = -1*obj.e_l;
51 closure = obj.Hi*tau*obj.e_l';
52 penalty = 0*obj.e_l;
53
54 end
55
56 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
57 error('An interface function does not exist yet');
58 end
59
60 function N = size(obj)
61 N = obj.m;
62 end
63
64 end
65
66 methods(Static)
67 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
68 % and bound_v of scheme schm_v.
69 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
70 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
71 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
72 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
73 end
74 end
75 end