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TimeStepping.pyx
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TimeStepping.pyx
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#!python
#cython: boundscheck=False
#cython: wraparound=False
#cython: initializedcheck=False
#cython: cdivision=True
cimport ParallelMPI as ParallelMPI
cimport PrognosticVariables as PrognosticVariables
cimport DiagnosticVariables as DiagnosticVariables
cimport Grid as Grid
cimport Restart
cimport mpi4py.libmpi as mpi
import numpy as np
cimport numpy as np
from libc.math cimport fmin, fmax, fabs
cdef class TimeStepping:
def __init__(self):
return
cpdef initialize(self,namelist,PrognosticVariables.PrognosticVariables PV, ParallelMPI.ParallelMPI Pa):
#Get the time stepping potions from the name list
try:
self.ts_type = namelist['time_stepping']['ts_type']
except:
Pa.root_print('ts_type not given in namelist')
Pa.root_print('Killing simulation now')
Pa.kill()
try:
self.dt = namelist['time_stepping']['dt_initial']
except:
Pa.root_print('dt_initial (initial time step) not given in namelist so taking defualt value dt_initail = 1.0')
self.dt = 1.0
try:
self.dt_max = namelist['time_stepping']['dt_max']
except:
Pa.root_print('dt_max (maximum permissible time step) not given in namelist so taking default value dt_max =10.0')
self.dt_max = 10.0
try:
self.t = namelist['time_stepping']['t']
except:
Pa.root_print('t (initial time) not given in namelist so taking default value t = 0')
self.t = 0.0
try:
self.cfl_limit = namelist['time_stepping']['cfl_limit']
except:
Pa.root_print('cfl_limit (maximum permissible cfl number) not given in namelist so taking default value cfl_max=0.7')
self.cfl_limit = 0.7
try:
self.t_max = namelist['time_stepping']['t_max']
except:
Pa.root_print('t_max (time at end of simulation) not given in name list! Killing Simulation Now')
Pa.kill()
#Now initialize the correct time stepping routine
if self.ts_type == 2:
self.initialize_second(PV)
elif self.ts_type == 3:
self.initialize_third(PV)
elif self.ts_type == 4:
self.initialize_fourth(PV)
else:
Pa.root_print('Invalid ts_type: ' + str(self.ts_type))
Pa.root_print('Killing simulation now')
Pa.kill()
return
cpdef update(self, Grid.Grid Gr, PrognosticVariables.PrognosticVariables PV, ParallelMPI.ParallelMPI Pa):
if self.ts_type == 2:
self.update_second(Gr,PV)
elif self.ts_type == 3:
self.update_third(Gr,PV)
elif self.ts_type == 4:
self.update_fourth(Gr,PV)
else:
Pa.root_print('Time stepping option not found ts_type = ' + str(self.ts_type))
Pa.root_print('Killing Simulation Now!')
Pa.kill()
return
cpdef adjust_timestep(self,Grid.Grid Gr, PrognosticVariables.PrognosticVariables PV, DiagnosticVariables.DiagnosticVariables DV, ParallelMPI.ParallelMPI Pa):
#Compute the CFL number and diffusive stability criterion
if self.rk_step == self.n_rk_steps - 1:
self.compute_cfl_max(Gr, PV,DV, Pa)
self.dt = self.cfl_time_step()
#Diffusive limiting not yet implemented
if self.t + self.dt > self.t_max:
self.dt = self.t_max - self.t
if self.dt < 0.0:
Pa.root_print('dt = '+ str(self.dt)+ " killing simulation!")
Pa.kill()
return
cpdef update_second(self, Grid.Grid Gr, PrognosticVariables.PrognosticVariables PV):
cdef:
Py_ssize_t i
with nogil:
if self.rk_step == 0:
for i in xrange(Gr.dims.npg*PV.nv):
self.value_copies[0,i] = PV.values[i]
PV.values[i] += PV.tendencies[i]*self.dt
PV.tendencies[i] = 0.0
else:
for i in xrange(Gr.dims.npg*PV.nv):
PV.values[i] = 0.5 * (self.value_copies[0,i] + PV.values[i] + PV.tendencies[i] * self.dt)
PV.tendencies[i] = 0.0
self.t += self.dt
return
cpdef update_third(self, Grid.Grid Gr, PrognosticVariables.PrognosticVariables PV):
cdef:
Py_ssize_t i
with nogil:
if self.rk_step == 0:
for i in xrange(Gr.dims.npg*PV.nv):
self.value_copies[0,i] = PV.values[i]
PV.values[i] += PV.tendencies[i]*self.dt
PV.tendencies[i] = 0.0
elif self.rk_step == 1:
for i in xrange(Gr.dims.npg*PV.nv):
PV.values[i] = 0.75 * self.value_copies[0,i] + 0.25*(PV.values[i] + PV.tendencies[i]*self.dt)
PV.tendencies[i] = 0.0
else:
for i in xrange(Gr.dims.npg*PV.nv):
PV.values[i] = (1.0/3.0) * self.value_copies[0,i] + (2.0/3.0)*(PV.values[i] + PV.tendencies[i]*self.dt)
PV.tendencies[i] = 0.0
self.t += self.dt
return
cpdef update_fourth(self, Grid.Grid Gr, PrognosticVariables.PrognosticVariables PV):
cdef:
Py_ssize_t i
with nogil:
if self.rk_step == 0:
for i in xrange(Gr.dims.npg*PV.nv):
self.value_copies[0,i] = PV.values[i]
PV.values[i] += 0.391752226571890 * PV.tendencies[i]*self.dt
PV.tendencies[i] = 0.0
elif self.rk_step == 1:
for i in xrange(Gr.dims.npg*PV.nv):
PV.values[i] = (0.444370493651235*self.value_copies[0,i] + 0.555629506348765*PV.values[i]
+ 0.368410593050371*PV.tendencies[i]*self.dt )
PV.tendencies[i] = 0.0
elif self.rk_step == 2:
for i in xrange(Gr.dims.npg*PV.nv):
self.value_copies[1,i] = PV.values[i]
PV.values[i] = (0.620101851488403*self.value_copies[0,i] + 0.379898148511597*PV.values[i]
+ 0.251891774271694*PV.tendencies[i]*self.dt)
PV.tendencies[i] = 0.0
elif self.rk_step == 3:
for i in xrange(Gr.dims.npg*PV.nv):
self.value_copies[2,i] = PV.values[i]
self.tendency_copies[0,i] = PV.tendencies[i]
PV.values[i] = (0.178079954393132*self.value_copies[0,i] + 0.821920045606868*PV.values[i]
+ 0.544974750228521*PV.tendencies[i]*self.dt)
PV.tendencies[i] = 0.0
else:
for i in xrange(Gr.dims.npg*PV.nv):
PV.values[i] = (0.517231671970585*self.value_copies[1,i]
+ 0.096059710526147*self.value_copies[2,i] +0.063692468666290*self.tendency_copies[0,i]*self.dt
+ 0.386708617503269*PV.values[i] + 0.226007483236906*PV.tendencies[i]*self.dt)
PV.tendencies[i] = 0.0
self.t += self.dt
return
cdef void initialize_second(self,PrognosticVariables.PrognosticVariables PV):
self.rk_step = 0
self.n_rk_steps = 2
#Initialize storage
self.value_copies = np.zeros((1,PV.values.shape[0]),dtype=np.double,order='c')
self.tendency_copies = None
return
cdef void initialize_third(self,PrognosticVariables.PrognosticVariables PV):
self.rk_step = 0
self.n_rk_steps = 3
#Initialize storage
self.value_copies = np.zeros((1,PV.values.shape[0]),dtype=np.double,order='c')
self.tendency_copies = None
return
cdef void initialize_fourth(self,PrognosticVariables.PrognosticVariables PV):
self.rk_step = 0
self.n_rk_steps = 5
#Initialize storage
self.value_copies = np.zeros((3,PV.values.shape[0]),dtype=np.double,order='c')
self.tendency_copies = np.zeros((1,PV.values.shape[0]),dtype=np.double,order='c')
return
cdef void compute_cfl_max(self,Grid.Grid Gr, PrognosticVariables.PrognosticVariables PV,DiagnosticVariables.DiagnosticVariables DV, ParallelMPI.ParallelMPI Pa):
cdef:
double cfl_max_local = -9999.0
double [3] dxi = Gr.dims.dxi
Py_ssize_t u_shift = PV.get_varshift(Gr,'u')
Py_ssize_t v_shift = PV.get_varshift(Gr,'v')
Py_ssize_t w_shift = PV.get_varshift(Gr,'w')
Py_ssize_t imin = Gr.dims.gw
Py_ssize_t jmin = Gr.dims.gw
Py_ssize_t kmin = Gr.dims.gw
Py_ssize_t imax = Gr.dims.nlg[0] - Gr.dims.gw
Py_ssize_t jmax = Gr.dims.nlg[1] - Gr.dims.gw
Py_ssize_t kmax = Gr.dims.nlg[2] - Gr.dims.gw
Py_ssize_t istride = Gr.dims.nlg[1] * Gr.dims.nlg[2]
Py_ssize_t jstride = Gr.dims.nlg[2]
Py_ssize_t i,j,k, ijk, ishift, jshift
double w
Py_ssize_t isedv
with nogil:
for i in xrange(imin,imax):
ishift = i * istride
for j in xrange(jmin,jmax):
jshift = j * jstride
for k in xrange(kmin,kmax):
ijk = ishift + jshift + k
w = fabs(PV.values[w_shift+ijk])
for isedv in xrange(DV.nsedv):
w = fmax(fabs( DV.values[DV.sedv_index[isedv]*Gr.dims.npg + ijk ] + PV.values[w_shift+ijk]), w)
cfl_max_local = fmax(cfl_max_local, self.dt * (fabs(PV.values[u_shift + ijk])*dxi[0] + fabs(PV.values[v_shift+ijk])*dxi[1] + w*dxi[2]))
mpi.MPI_Allreduce(&cfl_max_local,&self.cfl_max,1,
mpi.MPI_DOUBLE,mpi.MPI_MAX,Pa.comm_world)
self.cfl_max += 1e-11
if self.cfl_max < 0.0:
Pa.root_print('CFL_MAX = '+ str(self.cfl_max)+ " killing simulation!")
Pa.kill()
return
cdef inline double cfl_time_step(self):
return fmin(self.dt_max,self.cfl_limit/(self.cfl_max/self.dt))
cpdef restart(self, Restart.Restart Re):
Re.restart_data['TS'] = {}
Re.restart_data['TS']['t'] = self.t
Re.restart_data['TS']['dt'] = self.dt
return