-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathkernels.py
180 lines (137 loc) · 5.46 KB
/
kernels.py
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
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
# array of particles:
#[x, y, z, radius, mass, pressure, velocity, type]
from numpy import pi, power, array, linalg, sqrt
class Cubic_Spline:
def __init__(self,r=1.0,h=2.0,dim=3.0,step=1/1e6):
self.r = r
self.h = h
self.step = step
self.q = abs(r/h)
self.fac = float(1./power(h,dim))
def Kernel(self):
if self.q >= 0 and self.q < 1:
return self.fac*3/(2*pi)*(2/3-power(self.q,2)+1/2*power(self.q,3))
elif self.q >= 1 and self.q <= 2:
return self.fac/(4*pi)*power(2-self.q,3)
else:
return 0
def Gradient(self):
pts = [abs((self.r - self.step)/self.h),abs((self.r + self.step)/self.h)]
kernel_func = []
for self.q in pts:
kernel_func.append(self.Kernel())
return (kernel_func[1]-kernel_func[0])/(2*self.step)
def Laplacian(self):
pts = [abs((self.r - self.step)/(self.h)),abs((self.r)/(self.h)),abs((self.r + self.step)/(self.h))]
kernel_func = []
for self.q in pts:
kernel_func.append(self.Kernel())
return (kernel_func[0] - 2*kernel_func[1] + kernel_func[2])/(self.step**2)
class B_Spline:
def __init__(self,r=1,h=2,dim=3,step=1/1e6):
self.r = abs(r)
self.h = h
self.step = step
self.q = r/h
self.fac = 1/power(h,dim)
def Kernel(self):
self.q = abs(self.q)
if self.q >= 0 and self.q <= 1:
return self.fac/pi*(1+(3*power(self.q,3)/4)+(3*power(self.q,2)/2))
elif self.q > 1 and self.q <= 2:
return self.fac/pi*(0.25*power(2-self.q,3))
else:
return 0
def Gradient(self):
pts = [(self.r - self.step)/self.h, (self.r + self.step)/self.h]
kernel_func = []
for self.q in pts:
kernel_func.append(self.Kernel())
return (kernel_func[1]-kernel_func[0])/(2*self.step)
def Laplacian(self):
pts = [(self.r - self.step)/self.h, (self.r)/self.h, (self.r + self.step)/self.h]
kernel_func = []
for self.q in pts:
kernel_func.append(self.Kernel())
return (kernel_func[0] - 2*kernel_func[1] + kernel_func[2])/(self.step**2)
class Poly_6:
def __init__(self,r=1,h=2,step=1/1e6):
self.r = r
self.h = h
self.step = step
def Kernel(self):
if abs(self.r) >= 0 and abs(self.r) <= self.h:
return 315/(64*pi*self.h**9)*power(self.h**2-abs(self.r)**2,3)
else:
return 0
def Gradient(self,r_vector):
if abs(self.r) >= 0 and abs(self.r) <= self.h:
return -945/(32*pi*self.h**9)*r_vector*power(self.h**2-abs(self.r)**2,2)
else:
return 0
def Laplacian(self):
if abs(self.r) >= 0 and abs(self.r) <= self.h:
return -945/(32*pi*self.h**9)*(self.h**2-abs(self.r)**2)*(3*self.h**2-7*abs(self.r)**2)
else:
return 0
class Spiky: #Recommended for pressure
def __init__(self,r=1,h=2,step=1/1e6):
self.r = r
self.h = h
self.step = step
def Kernel(self):
if abs(self.r) >= 0 and abs(self.r) <= self.h:
return 15/(pi*self.h**6)*power(self.h-(abs(self.r)),3)
else:
return 0
def Gradient(self,r_vector):
if abs(self.r) >= 0 and abs(self.r) <= self.h:
return -45/(pi*self.h**6)*r_vector/self.r*power(self.h-abs(self.r),2)
else:
return array([0.,0.,0.])
def Laplacian(self):
if abs(self.r) >= 0 and abs(self.r) <= self.h:
return -90/(pi*self.h**6*abs(self.r))*(self.h-abs(self.r))*(self.h-2*abs(self.r))
else:
return 0
class Viscosity_Kernel:
def __init__(self,r=1,h=2,step=1/1e6):
self.r = r
self.h = h
self.step = step
def Kernel(self):
if abs(self.r) >= 0 and abs(self.r) <= self.h:
return 15/(2*pi*self.h**3)*(-(abs(self.r)**3/(2*self.h**3))+(abs(self.r)**2/self.h**2)+self.h/(2*abs(self.r))-1)
else:
return 0
def Gradient(self,r_vector):
if abs(self.r) >= 0 and abs(self.r) <= self.h:
return 15/(2*pi*self.h**3)*r_vector*(-3*abs(self.r)/(2*self.h**3)+2/self.h**2-self.h/(2*abs(self.r)**3))
else:
return 0
def Laplacian(self):
if abs(self.r) >= 0 and abs(self.r) <= self.h:
return 45/(pi*self.h**6)*(self.h-abs(self.r))
else:
return 0
def Kernel_Correction(neighbors,ri,h,kernel_name):
kernel_name = globals()['%s' % kernel_name]
A = array([[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0]])
for i in neighbors:
r_vector = ri - array([neighbors[i]['X'],neighbors[i]['Y'],neighbors[i]['Z']])
r = sqrt(r_vector[0]**2+r_vector[1]**2+r_vector[2]**2)
W = kernel_name(r,h).Kernel()
rx = r_vector[0]
ry = r_vector[1]
rz = r_vector[2]
Aij = array([[1,rx,ry,rz],
[rx,rx*rx,rx*ry,rx*rz],
[ry,ry*rx,ry*ry,ry*rz],
[rz,rz*rx,rz*ry,rz*rz]])
Aij = Aij * W * neighbors[i]['Mass']/neighbors[i]['Density']
A = [[A[j][k] + Aij[j][k] for k in range(len(A[0]))] for j in range(len(A))]
beta = linalg.pinv(A)*[[1],[0],[0],[0]]
return beta[0]