def RK3evolve(y,CFL,nstep,rho0,s,RKopt, param=0.0,param0 =0.0,verb = False,time0=None, ru00=[], rv00=[], t00=[]):
""" This functions evolve rhou00,T00 and updates rhov00 using drho,
reproduces 00 mode evolution of loma
(time,y,rhou00,rhov00,T00,timev,dwv) = evolve(my,CFL,nstep,deltaT,RKopt,time0,y,ru00,rv00,t00)
"""
if verb == True:
print "Running Runge-Kutta evolution..."
#RKNEW
if RKopt == 1: #RK 3
xi = [0 ,-17.0/60.0, -5.0/12.0]
gamma = [8./15., 5./12., 3./4. ]
beta = [gamma[0]-param0, param, (param*(gamma[0]*gamma[2]+gamma[1]*gamma[2]+xi[1]*gamma[2]+gamma[0]*xi[2])-gamma[0]*gamma[1]*gamma[2]+gamma[0]*gamma[1]*xi[2])/(param-gamma[0]*gamma[1])]
alpha = [param0, gamma[1]+xi[1]-param, gamma[2]+xi[2]-beta[2] ]
#beta = [8./15., 17/15., 1/6. ]
if verb == True:
print "using RK3 with Low Storage"
print alpha, beta, gamma,xi
elif RKopt == 2:
alpha = [0, -1., 1/6. ]
gamma = [8./15., 5./12., 3./4. ]
beta = [8./15., param, (1-gamma[0]+param*gamma[0])/(param*gamma[0])]
#beta = [8./15., 17/15., 1/6. ]
xi = [0.0 ,-17.0/60.0, -5.0/12.0]
#ibeta = [15./4., 15., 6.0 ]
if verb == True:
print "Using RK3 new option (not Spalart)"
else:
#NOTE THAT RKopt==3 gives EXPLICIT RK3
#RKspalart
gamma = [8./15, 5./12., 3./4. ]
xi = [0.0 , -17./60.0, -5.0/12.0]
alpha = [29./96., -3./40., 1./6. ]
beta = [37./160., 5./24., 1./6. ]
ibeta = [160./37., 24./5.0, 6.0 ]
if verb == True:
print "Using RK3 Spalart, EXP-IMP"
#------------Physics -------------------------#
ire = 1./160. #inverse of Reynolds
ipe = 1./(160.*0.7) #inverse of Peclet
my = len(y)
L = y[-1]
#---------------------------------------------#
#Initialization of variables (arrays)
if RKopt == 3 and verb==True:
print "using RK3 Spalart..."
time=0.0
dw=zeros(nstep)
timev = zeros(nstep)
T00last = zeros(my)
T00last1 = zeros(my)
drho = zeros(my)
drhodt = zeros(my)
drholast = zeros(my)
intdrho = zeros(my)
DT00 = zeros(my)
if time0 is None:
(rhou00,rhov00,T00) = geninit(y,rho0,s)
else: #restarting
print "Restarting from previous run..."
rhou00 = ru00
rhov00 = rv00
T00 = t00
time = time0
[prem1,prem3,dt11,dt12,dt21,dt22,fmap]= compact.derivadas(y,my)
rhotop = 1.0/T00[-1]
rhobot = 1.0/T00[0]
DU = (rhou00*T00).max()-(rhou00*T00).min()
#density ratio
sratio = s
if verb == True:
print "density ratio = %s" % sratio
#Start RHS
rhs1=zeros([my,3]) #RHS rhou00
rhs4=zeros([my,3]) #RHS T00
Dtvisc = min(diff(y))**2./(2.*ire)
#Start istep
if RKopt==2: #Update using N(rho) directly (NOT low-storage)
for istep in range(nstep):
#Obtain timestep
Dt = max(1./Dtvisc,max(rhov00*T00)/min(diff(y)))
Dt = CFL/Dt
if istep==0 and verb == True:
# Dt = 0.01*Dtvisc #first step is important
print "Initial Dt = %s" % Dt
for rkstep in range(3):
#For each rkstep
#Define the RHS's
rhs1[:,rkstep] = -compact.deryr(rhou00*rhov00*T00,dt12,prem1,fmap,my) +ire *compact.deryyr(rhou00*T00,dt22,prem3,my)
rhs4[:,rkstep] = -rhov00*T00*compact.deryr(T00,dt12,prem1,fmap,my) + ipe*T00*compact.deryyr(T00,dt22,prem3,my)
#Define Dt*RKparameters
dtxi = Dt* xi[rkstep]
dtgamma = Dt* gamma[rkstep]
dtbeta = Dt* beta[rkstep]
T00last = T00 #Save T00 before evolution
#Explicit Evolution:
if rkstep == 0: #First rkstep
rhou00 = rhou00 + dtgamma*rhs1[:,rkstep] #Evolve rhou00
DT00 = dtgamma*rhs4[:,rkstep] #Save the increment of T00
T00 = T00 + dtgamma*rhs4[:,rkstep]
drhodt = -rhs4[:,rkstep]/T00last**2.0 #First substep
else:
rhou00 = rhou00[:] + dtgamma*rhs1[:,rkstep] + dtxi*rhs1[:,rkstep-1]
DT00 = dtgamma*rhs4[:,rkstep] + dtxi*rhs4[:,rkstep-1]
T00 = T00 + dtgamma*rhs4[:,rkstep] + dtxi*rhs4[:,rkstep-1]
drhodt=(1.0-xi[rkstep]/beta[rkstep])*(-rhs4[:,rkstep]/T00**2.)+xi[rkstep]/beta[rkstep]*(-rhs4[:,rkstep-1]/T00last**2.)
#Option 1, not sure about value of v00 at boundaries:
rhov00 = trapz(drhodt,y)/(sratio+1.)-cumtrapz(drhodt,y,initial=0.0)
#Option 2, we know this should be zero
#rhov00 = -cumtrapz(drhodt,y,initial=0.0) #v00(-Ly) = 0.0
time += Dt
dw[istep]=DU/(abs(compact.deryr(rhou00*T00,dt12,prem1,fmap,my))).max()
timev[istep]=time
if isNaN(dw[istep]):
print 'NaN found in this simulation!'
return time,rhou00,rhov00, T00,timev,dw
#print "istep = %s, rkstep = %s" % (istep, rkstep)
elif RKopt==1: #Low Storage RK3
for istep in range(nstep):
#Obtain timestep
Dt = 1./Dtvisc
#Dt = max(1./Dtvisc,max(rhov00*T00)/min(diff(y)))
Dt = CFL/Dt
if istep==0 and verb == True:
# Dt = 0.01*Dtvisc #first step is important
print "Initial Dt = %s" % Dt
for rkstep in range(3):
#For each rkstep
#Define the RHS's
rhs1[:,rkstep] = -compact.deryr(rhou00*rhov00*T00,dt12,prem1,fmap,my) +ire *compact.deryyr(rhou00*T00,dt22,prem3,my)
rhs4[:,rkstep] = -rhov00*T00*compact.deryr(T00,dt12,prem1,fmap,my) + ipe*T00*compact.deryyr(T00,dt22,prem3,my)
#Define Dt*RKparameters
dtxi = Dt* xi[rkstep]
dtgamma = Dt* gamma[rkstep]
dtbeta = Dt* beta[rkstep]
T00last = T00
if rkstep == 0: #First rkstep
rhou00 = rhou00 + dtgamma*rhs1[:,rkstep] #Evolve rhou00
DT00 = dtgamma*rhs4[:,rkstep] #Save the increment of T00
T00 = T00 + DT00
drhodt = -DT00/(beta[rkstep]*Dt*T00last*T00)-alpha[rkstep]/beta[rkstep]*drhodt
#drhodt = -rhs4[:,rkstep]/T00last**2.
else:
rhou00 = rhou00[:] + dtgamma*rhs1[:,rkstep] + dtxi*rhs1[:,rkstep-1]
DT00 = dtgamma*rhs4[:,rkstep] + dtxi*rhs4[:,rkstep-1]
T00 = T00 + DT00
drhodt = -DT00/(beta[rkstep]*Dt*T00last*T00)-alpha[rkstep]/beta[rkstep]*drhodt
rhov00= compact.inty8(drhodt,fmap,dt11,dt12,prem1,my)
M = rhov00[-1]-rhov00[0]
rhov00 = -(rhov00 - rhov00[0]) + M*rhobot/(rhotop+rhobot)
#rhov00 = trapz(drhodt,y)/(sratio+1.)-cumtrapz(drhodt,y,initial=0.0)
#istep loop
time += Dt
dw[istep]=DU/(abs(compact.deryr(rhou00*T00,dt12,prem1,fmap,my))).max()
timev[istep]=time
if isNaN(dw[istep]):
print 'NaN found in this simulation!'
return time,rhou00,rhov00, T00,timev,dw
elif RKopt==3: #Update using N(rho) directly (NOT low-storage)
#FIRST STEP is different
timev[0] = 0.0
dw[0]=DU/(abs(compact.deryr(rhou00*T00,dt12,prem1,fmap,my))).max()
Dt = max(1./Dtvisc,max(rhov00*T00)/min(diff(y)))
Dt = CFL/Dt
print "Initial Dt = %s" % Dt
T00last = T00 #Save T00 at step n
Dtkp1 = 0.0
for rkstep in range(3):
Dtkp1 += Dt*(gamma[rkstep]+xi[rkstep])
#For each rkstep
#Define the RHS's
rhs1[:,rkstep] = -compact.deryr(rhou00*rhov00*T00,dt12,prem1,fmap,my) +ire *compact.deryyr(rhou00*T00,dt22,prem3,my)
rhs4[:,rkstep] = -rhov00*T00*compact.deryr(T00,dt12,prem1,fmap,my) + ipe*T00*compact.deryyr(T00,dt22,prem3,my)
#Define Dt*RKparameters
dtxi = Dt* xi[rkstep]
dtgamma = Dt* gamma[rkstep]
dtbeta = Dt* beta[rkstep]
#Explicit Evolution:
if rkstep == 0: #First rkstep
rhou00 = rhou00 + dtgamma*rhs1[:,rkstep] #Evolve rhou00
DT00 = dtgamma*rhs4[:,rkstep] #Save the increment of T00
T00 = T00 + dtgamma*rhs4[:,rkstep]
else:
rhou00 = rhou00[:] + dtgamma*rhs1[:,rkstep] + dtxi*rhs1[:,rkstep-1]
DT00 = dtgamma*rhs4[:,rkstep] + dtxi*rhs4[:,rkstep-1]
T00 = T00 + dtgamma*rhs4[:,rkstep] + dtxi*rhs4[:,rkstep-1]
drhodt = ((1.0/T00)-(1.00/T00last))/Dtkp1
#Option 1, not sure about value of v00 at boundaries:
rhov00 = trapz(drhodt,y)/(sratio+1.)-cumtrapz(drhodt,y,initial=0.0)
#Option 2, we know this should be zero
#rhov00 = -cumtrapz(drhodt,y,initial=0.0) #v00(-Ly) = 0.0
time += Dt
dw[istep]=DU/(abs(compact.deryr(rhou00*T00,dt12,prem1,fmap,my))).max()
timev[1]=time
#End OF FIRST STEP
#--------------------------------------------------------------#
for istep in range(1,nstep-1):
T00last1 = T00last
T00last = T00 #Save T00 before evolution
Dtkp1 = 0.0
Dt1 = Dt #PREVIOUS DT
#Obtain timestep
Dt = max(1./Dtvisc,max(rhov00*T00)/min(diff(y)))
Dt = CFL/Dt
for rkstep in range(3):
Dtkp1 += Dt*(gamma[rkstep]+xi[rkstep])
ALP = Dt1/Dtkp1
#For each rkstep
#Define the RHS's
rhs1[:,rkstep] = -compact.deryr(rhou00*rhov00*T00,dt12,prem1,fmap,my) +ire *compact.deryyr(rhou00*T00,dt22,prem3,my)
rhs4[:,rkstep] = -rhov00*T00*compact.deryr(T00,dt12,prem1,fmap,my) + ipe*T00*compact.deryyr(T00,dt22,prem3,my)
#Define Dt*RKparameters
dtxi = Dt* xi[rkstep]
dtgamma = Dt* gamma[rkstep]
dtbeta = Dt* beta[rkstep]
#Explicit Evolution:
if rkstep == 0: #First rkstep
rhou00 = rhou00 + dtgamma*rhs1[:,rkstep] #Evolve rhou00
T00 = T00 + dtgamma*rhs4[:,rkstep]
else:
rhou00 = rhou00[:] + dtgamma*rhs1[:,rkstep] + dtxi*rhs1[:,rkstep-1]
T00 = T00 + dtgamma*rhs4[:,rkstep] + dtxi*rhs4[:,rkstep-1]
drhodt = (((1.+ALP)**2.0-1.0)*(1.0/T00)-(1.0+ALP)**2.0*(1.0/T00last)+1.0/T00last1)/((1.+ALP)*Dt1)
#Option 1, not sure about value of v00 at boundaries:
rhov00 = trapz(drhodt,y)/(sratio+1.)-cumtrapz(drhodt,y,initial=0.0)
#Option 2, we know this should be zero
#rhov00 = -cumtrapz(drhodt,y,initial=0.0) #v00(-Ly) = 0.0
dw[istep]=DU/(abs(compact.deryr(rhou00*T00,dt12,prem1,fmap,my))).max()
time += Dt
timev[istep+1]=time
if isNaN(dw[istep]):
print 'NaN found in this simulation!'
return time, rhou00,rhov00, T00,timev,dw
#print "istep = %s, rkstep = %s" % (istep, rkstep)
if verb == True:
print "last Dt = %s" % Dt
print "final time = %s, dw = %s " % (timev[-1],dw[-1])
return time, rhou00,rhov00, T00,timev,dw
def lomahz(y,CFL,nstep,rho0,s,RKopt, param=0.4,param0 =-0.2,verb = False,time0=None, ru00=[], rv00=[], t00=[]):
""" This functions evolve rhou00,T00 and updates rhov00 using drho,
reproduces 00 mode evolution of loma
(time,y,rhou00,rhov00,T00,timev,dmv) = evolve(my,CFL,nstep,deltaT,RKopt,time0,y,ru00,rv00,t00)
"""
if verb == True:
print "Running Runge-Kutta evolution of LOMAHZ_1D..."
#RKNEW
xi = [0 ,-17.0/60.0, -5.0/12.0]
gamma = [8./15., 5./12., 3./4. ]
beta = [gamma[0]-param0, param, (param*(gamma[0]*gamma[2]+gamma[1]*gamma[2]+xi[1]*gamma[2]+gamma[0]*xi[2])-gamma[0]*gamma[1]*gamma[2]+gamma[0]*gamma[1]*xi[2])/(param-gamma[0]*gamma[1])]
alpha = [param0, gamma[1]+xi[1]-param, gamma[2]+xi[2]-beta[2] ]
#------------Physics -------------------------#
Reynolds = 160.0;Pr=0.7
ire = 1./Reynolds #inverse of Reynolds
ipe = 1./(Reynolds*Pr) #inverse of Peclet
my = len(y)
L = y[-1]
#---------------------------------------------#
#Initialization of variables (arrays)
time=0.0
dm=zeros(nstep)
timev = zeros(nstep)
T00last = zeros(my)
T00last1 = zeros(my)
drho = zeros(my)
drhodt = zeros(my)
drholast = zeros(my)
intdrho = zeros(my)
DT00 = zeros(my)
if time0 is None:
(rhou00,rhov00,T00) = geninit(y,rho0,s)
else: #restarting
print "Restarting from previous run..."
rhou00 = ru00
rhov00 = rv00
T00 = t00
time = time0
[prem1,prem3,dt11,dt12,dt21,dt22,fmap]= compact.derivadas(y,my)
rhotop = 1.0/T00[-1]
rhobot = 1.0/T00[0]
#
#density ratio
sratio = s
if verb == True:
print "density ratio = %s" % sratio
#Start RHS
rhs1=zeros([my,3]) #RHS rhou00
rhs4=zeros([my,3]) #RHS T00
rhomin = min(rhobot,rhotop)
sigma = 0.0
Tmax = 1.0/rhomin
#Calculating viscous timestep
Dmu =Tmax**(sigma+1.0)/(Reynolds*Pr)*(1.0/np.min(diff(y))**2)
#Start istep
for istep in range(nstep):
Dc =np.max(rhov00*T00)*(1.0/np.min(diff(y)))
#Obtain timestep
Dt = CFL/(Dc+Dmu)
if istep==0 and verb == True:
# Dt = 0.01*Dtvisc #first step is important
print "Initial Dt = %s" % Dt
for rkstep in range(3):
#For each rkstep
#Define the RHS's
rhs1[:,rkstep] = -compact.deryr(rhou00*rhov00*T00,dt12,prem1,fmap,my) +ire *compact.deryyr(rhou00*T00,dt22,prem3,my)
rhs4[:,rkstep] = -rhov00*T00*compact.deryr(T00,dt12,prem1,fmap,my) + ipe*T00*compact.deryyr(T00,dt22,prem3,my)
#Define Dt*RKparameters
dtxi = Dt* xi[rkstep]
dtgamma = Dt* gamma[rkstep]
dtbeta = Dt* beta[rkstep]
#Calculations
T00last = T00
#rhou00=evolverkstep(rhou00,rhs1[:,rkstep],rhs1[:,rkstep-1],dtgamma,dtxi]
rhou00 = rhou00[:] + dtgamma*rhs1[:,rkstep] + dtxi*rhs1[:,rkstep-1]
DT00 = dtgamma*rhs4[:,rkstep] + dtxi*rhs4[:,rkstep-1]
T00 = T00 + DT00
#drhodt=-Drho/betaDt
drhodt = DT00/(beta[rkstep]*Dt*T00last*T00)
kk = compact.inty80(list(drhodt),fmap,dt11,dt12,prem1)
M = kk[-1] #flow outcome
#M = trapz(drhodt,y) #flow outcome
#drhodt = cumtrapz(drhodt,y,initial=0)-M/(1.0+sratio**(-0.5))
drhodt = kk-M/(1.0+sratio**(-0.5))
rhov00 = drhodt-alpha[rkstep]/beta[rkstep]*rhov00
#istep loop
time += Dt
dm[istep]=calcdmcomp(y,rhou00*T00,rhou00,1.0/T00)
timev[istep]=time
if isNaN(dm[istep]):
print 'NaN found in this simulation!'
return time,rhou00,rhov00, T00,timev,dm
if verb == True:
print "last Dt = %s" % Dt
print "final time = %s, dm = %s " % (timev[-1],dm[-1])
return time, rhou00,rhov00, T00,timev,dm