-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathconvDiffPU.m
123 lines (91 loc) · 2.27 KB
/
convDiffPU.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
%% convDiffPU.m
% Version 1.0
% Modified on 17th March 2017
% A function to solve the 1-D source-free convection diffusion equation using the
% pure upwind finite volume approximation. This is a sub-function of
% the convectionDiffusion code and does the actual computation.
%
% Inputs:
% x : (vector) grid of node locations along with the boundary points
% phiBound : (vector) property of interest at the boundary points.
% F : (scalar) a product of rho and u.
% gamma : (scalar) diffusion coefficient
%
% Outputs:
% phi : (vector) value of the quantity of interest at the nodes
%%
function phi = convDiffPU(x, phiBound, F, gamma)
N = length(x) - 2;
phiA = phiBound(1);
phiB = phiBound(2);
dx = diff(x);
ndx = length(dx);
D = gamma./dx;
mainD = zeros(1,N);
subD = zeros(1,N-1);
superD = zeros(1,N-1);
RHSmat = zeros(1,N);
aW = zeros(1,N);
aE = zeros(1,N);
aP = zeros(1,N);
if(F>=0)
%For intermediate nodes aPtP = aWtW + aEtE
for i=2:1:(N-1)
aW(i) = D(i)+F;
aE(i) = D(i+1);
aP(i) = aE(i) + aW(i);
end
%For node 1 the descretised equation is a1t1 = aWWtWW + aELtE + Su
aW(1) = 0;
aE(1) = D(2);
SuA = (D(1) + F)*phiA;
Sp = -(D(1) + F);
aP(1) = aW(1) + aE(1) - Sp;
%For node N the descretised equation is aNtN = aWRtW + aEEtEE + Su
aW(N) = D(ndx-1) + F;
aE(N) = 0;
SuB = D(ndx)*phiB;
Sp = -D(ndx);
aP(N) = aW(N) + aE(N) - Sp;
else
%For intermediate nodes aPtP = aWtW + aEtE
for i=2:1:(N-1)
aW(i) = D(i);
aE(i) = D(i+1)-F;
aP(i) = aE(i) + aW(i);
end
%For node 1 the descretised equation is a1t1 = aWWtWW + aELtE + Su
aW(1) = 0;
aE(1) = D(2)-F;
SuA = D(1)*phiA;
Sp = -D(1);
aP(1) = aW(1) + aE(1) - Sp;
%For node N the descretised equation is aNtN = aWRtW + aEEtEE + Su
aW(N) = D(ndx-1);
aE(N) = 0;
SuB = (D(ndx)-F)*phiB;
Sp = -(D(ndx)-F);
aP(N) = aW(N) + aE(N) - Sp;
end
%For the NXN Matrix the leading diagonal terms
mainD(1) = aP(1);
mainD(N) = aP(N);
for i = 2:1:N-1
mainD(i) = aP(i);
end
%For the NXN Matrix the sub diagonal terms
for i = 1:1:N-1
subD(i) = -aW(i+1);
end
%For the NXN Matrix the Super diagonal terms
for i = 1:1:N-1
superD(i) = -aE(i);
end
RHSmat(1) = SuA;
RHSmat(N) = SuB;
for i = 2:1:N-1
RHSmat(i) = 0;
end
phi = tdma(mainD, subD, superD, RHSmat);
phi = cat(2,phiBound(1),phi,phiBound(2));
end