-
Notifications
You must be signed in to change notification settings - Fork 4
/
RK3DG.f90
211 lines (147 loc) · 7.29 KB
/
RK3DG.f90
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
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
subroutine RK3DG(Pol,PolValue,PolDx,PolDy,Poledge,Q,hx,hy,dt,Nx,Ny,dim,dimpol,diagpol,lambdai,lambdaj,weight)
integer i,j,Nx,Ny,dim,dimpol,quad
parameter(quad = 4)
real Pol(Nx,Ny,dimpol,dim),PolValue(quad,quad,dimpol,dim),PolDx(quad,quad,dimpol,dim),PolDy(quad,quad,dimpol,dim)
real Poledge(4,quad,dimpol,dim),Q(Nx,Ny,dim),diagpol(Nx,Ny,dimpol,dim),Polone(Nx,Ny,dimpol,dim),Poltwo(Nx,Ny,dimpol,dim)
real LPol(Nx,Ny,dimpol,dim),lambdai(quad),lambdaj(quad),weight(quad)
call Lh(Pol,LPol,PolValue,PolDx,PolDy,Poledge,Q,hx,hy,dt,Nx,Ny,dim,dimpol,diagpol,lambdai,lambdaj,weight)
Polone = Pol + dt*LPol
call Lh(Polone,LPol,PolValue,PolDx,PolDy,Poledge,Q,hx,hy,dt,Nx,Ny,dim,dimpol,diagpol,lambdai,lambdaj,weight)
Poltwo = 0.75d0*Pol + 0.25d0*Polone + 0.25d0*dt*LPol
call Lh(Poltwo,LPol,PolValue,PolDx,PolDy,Poledge,Q,hx,hy,dt,Nx,Ny,dim,dimpol,diagpol,lambdai,lambdaj,weight)
Pol = (1d0/3d0)*Pol + (2d0/3d0)*Poltwo + (2d0/3d0)*dt*LPol
call Pol_to_Q(Pol,Q,Nx,Ny,dimpol,dim)
end subroutine RK3DG
subroutine Lh(Pol,DPol,PolValue,PolDx,PolDy,Poledge,Q,hx,hy,dt,Nx,Ny,dim,dimpol,diagpol,lambdai,lambdaj,weight)
integer i,j,Nx,Ny,dim,dimpol,quad,i1,j1,d1
parameter(quad = 4)
real Pol(Nx,Ny,dimpol,dim),PolValue(quad,quad,dimpol,dim),PolDx(quad,quad,dimpol,dim),PolDy(quad,quad,dimpol,dim)
real Poledge(4,quad,dimpol,dim),Q(Nx,Ny,dim),diagpol(Nx,Ny,dimpol,dim),DPol(Nx,Ny,dimpol,dim),alphax,alphay,alphatest
real PolR(Nx,Ny,dimpol,dim),PolL(Nx,Ny,dimpol,dim),PolU(Nx,Ny,dimpol,dim),PolD(Nx,Ny,dimpol,dim)
real u,v,p,rho,gamma
real IV(dim),IR(dim),IL(dim),IU(dim),ID(dim),lambdai(quad),lambdaj(quad),weight(quad),fu(dim,2)
real uint(dim),uext(dim),hLF(dim),fuint(dim),fuext(dim),hx1,hy1
integer :: boundconditionX = 1
integer :: boundconditionY = 1
call Pol_to_Q(Pol,Q,Nx,Ny,dimpol,dim)
gamma = 1.4d0
alphax = 1e-3
alphay = 1e-3
hx1 = 0.5d0*hx
hy1 = 0.5d0*hy
! 计算alphax,alphay，使用全局LF通量
do i = 1,Nx
do j = 1,Ny
rho = Q(i,j,1)
u = Q(i,j,2)/Q(i,j,1)
v = Q(i,j,3)/Q(i,j,1)
p = (gamma - 1)*(Q(i,j,4) - 0.5d0*rho*(u**2 + v**2))
call max_wavespeed(alphatest,rho,u,v,p,gamma,1)
if (alphatest > alphax) then
alphax = alphatest
end if
call max_wavespeed(alphatest,rho,u,v,p,gamma,2)
if (alphatest > alphay) then
alphay = alphatest
end if
end do
end do
! 赋边界条件
if (boundconditionX == 1) then ! 周期边界
PolR(1:Nx - 1,:,:,:) = Pol(2:Nx,:,:,:)
PolR(Nx,:,:,:) = Pol(1,:,:,:)
PolL(2:Nx,:,:,:) = Pol(1:Nx - 1,:,:,:)
PolL(1,:,:,:) = Pol(Nx,:,:,:)
end if
if (boundconditionY == 1) then ! 周期边界
PolU(:,1:Ny - 1,:,:) = Pol(:,2:Ny,:,:)
PolU(:,Ny,:,:) = Pol(:,1,:,:)
PolD(:,2:Ny,:,:) = Pol(:,1:Ny - 1,:,:)
PolD(:,1,:,:) = Pol(:,Ny,:,:)
end if
! 迭代
do i = 1,Nx
do j = 1,Ny
do d = 1,dimpol
! 体积分 \int_K (f(u)·▽v) dx
IV = 0
do i1 = 1,quad
do j1 = 1,quad
! 计算当前积分点上的解
uint = 0
do d1 = 1,dimpol
uint = uint + Pol(i,j,d1,:)*PolValue(i1,j1,d1,:)
end do
call f(uint,fu)
IV = IV + weight(i1)*weight(j1)*(fu(:,1)*PolDx(i1,j1,d,:) + fu(:,2)*PolDy(i1,j1,d,:))
end do
end do
IV = hx1*hy1*IV
! 面积分 \int_(partial K) (h(uint,uext,n)·v) dSx
! 右
IR = 0
do j1 = 1,quad
! 计算当前积分点上内部和外部的解
uint = 0
uext = 0
do d1 = 1,dimpol
uint = uint + Pol(i,j,d1,:)*Poledge(1,j1,d1,:)
uext = uext + PolR(i,j,d1,:)*Poledge(2,j1,d1,:)
end do
call f1(uint,fuint)
call f1(uext,fuext)
hLF = 0.5d0*(fuint + fuext - alphax*(uext - uint))
IR = IR + weight(j1)*hLF*Poledge(1,j1,d,:)
end do
IR = hx1*IR
! 左
IL = 0
do j1 = 1,quad
uint = 0
uext = 0
do d1 = 1,dimpol
uint = uint + Pol(i,j,d1,:)*Poledge(2,j1,d1,:)
uext = uext + PolL(i,j,d1,:)*Poledge(1,j1,d1,:)
end do
call f1(uint,fuint)
call f1(uext,fuext)
hLF = 0.5d0*(-(fuint + fuext) - alphax*(uext - uint))
IL = IL + weight(j1)*hLF*Poledge(2,j1,d,:)
end do
IL = hx1*IL
! 上
IU = 0
do i1 = 1,quad
uint = 0
uext = 0
do d1 = 1,dimpol
uint = uint + Pol(i,j,d1,:)*Poledge(3,i1,d1,:)
uext = uext + PolU(i,j,d1,:)*Poledge(4,i1,d1,:)
end do
call f2(uint,fuint)
call f2(uext,fuext)
hLF = 0.5d0*(fuint + fuext - alphay*(uext - uint))
IU = IU + weight(i1)*hLF*Poledge(3,i1,d,:)
end do
IU = hy1*IU
! 下
ID = 0
do i1 = 1,quad
uint = 0
uext = 0
do d1 = 1,dimpol
uint = uint + Pol(i,j,d1,:)*Poledge(4,i1,d1,:)
uext = uext + PolD(i,j,d1,:)*Poledge(3,i1,d1,:)
end do
call f2(uint,fuint)
call f2(uext,fuext)
hLF = 0.5d0*(-(fuint + fuext) - alphay*(uext - uint))
ID = ID + weight(i1)*hLF*Poledge(4,i1,d,:)
end do
ID = hy1*ID
DPol(i,j,d,:) = IV - IR - IL - IU - ID
end do
end do
end do
DPol = DPol/diagpol
end subroutine Lh