def dq_hyperbolic(self,state):
r"""
Compute dq/dt * (delta t) for the hyperbolic hyperbolic system.
Note that the capa array, if present, should be located in the aux
variable.
Indexing works like this (here num_ghost=2 as an example)::
0 1 2 3 4 mx+num_ghost-2 mx+num_ghost mx+num_ghost+2
| mx+num_ghost-1 | mx+num_ghost+1
| | | | | ... | | | | |
0 1 | 2 3 mx+num_ghost-2 |mx+num_ghost
mx+num_ghost-1 mx+num_ghost+1
The top indices represent the values that are located on the grid
cell boundaries such as waves, s and other Riemann problem values,
the bottom for the cell centered values such as q. In particular
the ith grid cell boundary has the following related information::
i-1 i i+1
| | |
| i-1 | i |
| | |
Again, grid cell boundary quantities are at the top, cell centered
values are in the cell.
"""
import numpy as np
self._apply_q_bcs(state)
if state.num_aux > 0:
self._apply_aux_bcs(state)
q = self.qbc
grid = state.grid
mx = grid.num_cells[0]
ixy=1
if self.kernel_language=='Fortran':
rp1 = self.rp.rp1._cpointer
dq,cfl=self.fmod.flux1(q,self.auxbc,self.dt,state.t,ixy,mx,self.num_ghost,mx,rp1)
elif self.kernel_language=='Python':
dtdx = np.zeros( (mx+2*self.num_ghost) ,order='F')
dq = np.zeros( (state.num_eqn,mx+2*self.num_ghost) ,order='F')
# Find local value for dt/dx
if state.index_capa>=0:
dtdx = self.dt / (grid.delta[0] * state.aux[state.index_capa,:])
else:
dtdx += self.dt/grid.delta[0]
aux=self.auxbc
if aux.shape[0]>0:
aux_l=aux[:,:-1]
aux_r=aux[:,1: ]
else:
aux_l = None
aux_r = None
#Reconstruct (wave reconstruction uses a Riemann solve)
if self.lim_type==-1: #1st-order Godunov
ql=q; qr=q
elif self.lim_type==0: #Unlimited reconstruction
raise NotImplementedError('Unlimited reconstruction not implemented')
elif self.lim_type==1: #TVD Reconstruction
raise NotImplementedError('TVD reconstruction not implemented')
elif self.lim_type==2: #WENO Reconstruction
if self.char_decomp==0: #No characteristic decomposition
ql,qr=recon.weno(5,q)
elif self.char_decomp==1: #Wave-based reconstruction
q_l=q[:,:-1]
q_r=q[:,1: ]
wave,s,amdq,apdq = self.rp(q_l,q_r,aux_l,aux_r,state.problem_data)
ql,qr=recon.weno5_wave(q,wave,s)
elif self.char_decomp==2: #Characteristic-wise reconstruction
raise NotImplementedError
# Solve Riemann problem at each interface
q_l=qr[:,:-1]
q_r=ql[:,1: ]
wave,s,amdq,apdq = self.rp(q_l,q_r,aux_l,aux_r,state.problem_data)
# Loop limits for local portion of grid
# THIS WON'T WORK IN PARALLEL!
LL = self.num_ghost - 1
UL = grid.num_cells[0] + self.num_ghost + 1
# Compute maximum wave speed
cfl = 0.0
for mw in xrange(self.num_waves):
smax1 = np.max( dtdx[LL :UL] *s[mw,LL-1:UL-1])
smax2 = np.max(-dtdx[LL-1:UL-1]*s[mw,LL-1:UL-1])
cfl = max(cfl,smax1,smax2)
#Find total fluctuation within each cell
wave,s,amdq2,apdq2 = self.rp(ql,qr,aux,aux,state.problem_data)
# Compute dq
for m in xrange(state.num_eqn):
dq[m,LL:UL] = -dtdx[LL:UL]*(amdq[m,LL:UL] + apdq[m,LL-1:UL-1] \
+ apdq2[m,LL:UL] + amdq2[m,LL:UL])
else:
raise Exception('Unrecognized value of solver.kernel_language.')
self.cfl.update_global_max(cfl)
return dq[:,self.num_ghost:-self.num_ghost]
def dq_hyperbolic(self,state):
r"""
Compute dq/dt * (delta t) for the hyperbolic hyperbolic system.
Note that the capa array, if present, should be located in the aux
variable.
Indexing works like this (here num_ghost=2 as an example)::
0 1 2 3 4 mx+num_ghost-2 mx+num_ghost mx+num_ghost+2
| mx+num_ghost-1 | mx+num_ghost+1
| | | | | ... | | | | |
0 1 | 2 3 mx+num_ghost-2 |mx+num_ghost
mx+num_ghost-1 mx+num_ghost+1
The top indices represent the values that are located on the grid
cell boundaries such as waves, s and other Riemann problem values,
the bottom for the cell centered values such as q. In particular
the ith grid cell boundary has the following related information::
i-1 i i+1
| | |
| i-1 | i |
| | |
Again, grid cell boundary quantities are at the top, cell centered
values are in the cell.
"""
import numpy as np
self._apply_bcs(state)
q = self.qbc
aux = self.auxbc
grid = state.grid
mx = grid.num_cells[0]
ixy=1
if self.kernel_language=='Fortran':
rp1 = self.rp.rp1._cpointer
if self.tfluct_solver:
tfluct1 = self.tfluct.tfluct1._cpointer
else:
tfluct1 = self.tfluct
dq,cfl=self.fmod.flux1(q,self.auxbc,self.dt,state.t,ixy,mx,self.num_ghost,mx,rp1,tfluct1)
elif self.kernel_language=='Python':
dtdx = np.zeros( (mx+2*self.num_ghost) ,order='F')
dq = np.zeros( (state.num_eqn,mx+2*self.num_ghost) ,order='F')
# Find local value for dt/dx
if state.index_capa>=0:
dtdx = self.dt / (grid.delta[0] * aux[state.index_capa,:])
else:
dtdx += self.dt/grid.delta[0]
if aux.shape[0]>0:
aux_l=aux[:,:-1]
aux_r=aux[:,1: ]
else:
aux_l = None
aux_r = None
#Reconstruct (wave reconstruction uses a Riemann solve)
if self.lim_type==-1: #1st-order Godunov
ql=q; qr=q
elif self.lim_type==0: #Unlimited reconstruction
raise NotImplementedError('Unlimited reconstruction not implemented')
elif self.lim_type==1: #TVD Reconstruction
raise NotImplementedError('TVD reconstruction not implemented')
elif self.lim_type==2: #WENO Reconstruction
if self.char_decomp==0: #No characteristic decomposition
ql,qr=recon.weno(5,q)
elif self.char_decomp==1: #Wave-based reconstruction
q_l=q[:,:-1]
q_r=q[:,1: ]
wave,s,amdq,apdq = self.rp(q_l,q_r,aux_l,aux_r,state.problem_data)
ql,qr=recon.weno5_wave(q,wave,s)
elif self.char_decomp==2: #Characteristic-wise reconstruction
raise NotImplementedError
# Solve Riemann problem at each interface
q_l=qr[:,:-1]
q_r=ql[:,1: ]
wave,s,amdq,apdq = self.rp(q_l,q_r,aux_l,aux_r,state.problem_data)
# Loop limits for local portion of grid
# THIS WON'T WORK IN PARALLEL!
LL = self.num_ghost - 1
UL = grid.num_cells[0] + self.num_ghost + 1
# Compute maximum wave speed
cfl = 0.0
for mw in range(self.num_waves):
smax1 = np.max( dtdx[LL :UL] *s[mw,LL-1:UL-1])
smax2 = np.max(-dtdx[LL-1:UL-1]*s[mw,LL-1:UL-1])
cfl = max(cfl,smax1,smax2)
#Find total fluctuation within each cell
wave,s,amdq2,apdq2 = self.rp(ql,qr,aux,aux,state.problem_data)
# Compute dq
for m in range(state.num_eqn):
dq[m,LL:UL] = -dtdx[LL:UL]*(amdq[m,LL:UL] + apdq[m,LL-1:UL-1] \
+ apdq2[m,LL:UL] + amdq2[m,LL:UL])
else:
raise Exception('Unrecognized value of solver.kernel_language.')
self.cfl.update_global_max(cfl)
return dq[:,self.num_ghost:-self.num_ghost]