def frontogenesis_timestep(N, days, tstepsize, Heun=None):
tf = 60 * 60 * 24 * days #final time
#initialise parameters from SG Eady model
H = 1.e4
L = 1.e6
g = 10.
f = 1.e-4
theta0 = 300.
#create new directory to store results
if Heun:
newdir = "/scratchcomp04/cvr12/Results_" + str(days) + "D_" + str(
N) + "N_" + str(int(tstepsize)) + "_heun"
else:
newdir = "/scratchcomp04/cvr12/Results_" + str(days) + "D_" + str(
N) + "N_" + str(int(tstepsize)) + "_euler"
os.mkdir(newdir)
#initialise source density with periodic BCs in x
bbox = np.array([-L, 0., L, H])
Xdens = pdx.sample_rectangle(bbox)
f0 = np.ones(4) / (2 * H * L)
rho = np.zeros(Xdens.shape[0])
T = ma.delaunay_2(Xdens, rho)
dens = pdx.Periodic_density_in_x(Xdens, f0, T, bbox)
#initialise points in geostrophic space
[Y, thetap] = initialise_points(N, bbox, RegularMesh=True)
Y = dens.to_fundamental_domain(Y)
if Heun:
#timestep using Heun's Method
[Y, w, t] = heun_sg(Y,
dens,
tf,
bbox,
newdir,
h=tstepsize,
add_data=True)
t.tofile(newdir + '/time.txt', sep=" ", format="%s")
else:
#timestep using forward euler scheme
[Y, w, t] = forward_euler_sg(Y,
dens,
tf,
bbox,
newdir,
h=tstepsize,
add_data=True)
t.tofile(newdir + '/time.txt', sep=" ", format="%s")
return ('complete results ' + str(days) + 'D_' + str(N) + 'N_' +
str(int(tstepsize)))
#os.mkdir(imgdir)
#create triangulation with random vertices - fix for miscolouring
#of pixels on diagonal as suggested by Q.MERIGOT
Tdomain = np.array([[-L, 0.], [-L, H], [L, H], [L, 0.]])
Tpoints = np.random.rand(20, 2)
Tpoints[:, 0] = Tpoints[:, 0] * 2 * L - L
Tpoints[:, 1] = Tpoints[:, 1] * H
Tri = np.vstack((Tdomain, Tpoints))
#initialise periodic density
bbox = np.array([-L, 0., L, H])
T = ma.delaunay_2(Tri)
f0 = np.ones(24) / 2 / L / H
dens = pdx.Periodic_density_in_x(Tri, f0, T, bbox)
M = int(np.ceil((60 * 60 * 24 * days) / tstepsize))
n = 0
count = 0
while n <= M:
#retrieve results from file and reshape,points
Y = np.fromfile(resultsdir + '/points_results_' + str(int(tstepsize)) +
'/points_' + str(int(n)) + '.txt',
sep=" ")
l = int(Y.size / 2)
Y = Y.reshape((l, 2))
#weights
w = np.fromfile(resultsdir + '/weights_results_' + str(int(tstepsize)) +
'/weights_' + str(int(n)) + '.txt',
import periodic_densities as pdx import MongeAmpere as ma import matplotlib.pyplot as plt import matplotlib.tri as tri from PIL import Image N = 10000 L = 1.e6 H = 1.e4 bbox = np.array([-L, 0., L, H]) Xdens = pdx.sample_rectangle(bbox) f0 = np.ones(4) / (2 * L * H) rho = np.zeros(Xdens.shape[0]) T = ma.delaunay_2(Xdens, rho) dens = pdx.Periodic_density_in_x(Xdens, f0, T, bbox) Y = np.random.rand(N, 2) xY[:, 0] = Y[:, 0] * 2 * L - L Y[:, 1] *= H #print(Y) print(Y.shape) nu = np.ones(Y[:, 0].size) nu = (dens.mass() / np.sum(nu)) * nu w = ma.optimal_transport_2(dens, Y, nu, verbose=True) #C = Y[:,1].reshape((N,1)) #print(C) Nsq = 2.5e-5
def validity_analysis_results(N, days, tstepsize, t0=0., Heun=None):
#initialise parameters
H = 1.e4
L = 1.e6
g = 10.
f = 1.e-4
theta0 = 300
C = 3e-6
if Heun:
print('heun')
datadir = "/scratchcomp04/cvr12/Results_" + str(days) + "D_" + str(
N) + "N_" + str(int(tstepsize)) + "_heun/data"
resultdir = "/scratchcomp04/cvr12/Results_" + str(days) + "D_" + str(
N) + "N_" + str(int(tstepsize)) + "_heun"
else:
print('euler')
datadir = "/scratchcomp04/cvr12/Results_" + str(days) + "D_" + str(
N) + "N_" + str(int(tstepsize)) + "_euler/data"
resultdir = "/scratchcomp04/cvr12/Results_" + str(days) + "D_" + str(
N) + "N_" + str(int(tstepsize)) + "_euler"
os.mkdir(datadir)
#set up uniform density for domain Gamma
bbox = np.array([-L, 0., L, H])
Xdens = pdx.sample_rectangle(bbox)
f0 = np.ones(4) / 2 / L / H
rho = np.zeros(Xdens.shape[0])
T = ma.delaunay_2(Xdens, rho)
dens = pdx.Periodic_density_in_x(Xdens, f0, T, bbox)
#set final time(t), step size (h) and total number of time steps(N)
tf = 60 * 60 * 24 * days
h = tstepsize
N = int(np.ceil((tf - t0) / h))
#initialise arrays to store data values
KEmean = np.zeros(N + 1)
energy = np.zeros(N + 1)
vgmax = np.zeros(N + 1)
PE = np.zeros(N + 1)
KE = np.zeros(N + 1)
rmsv = np.zeros(N + 1)
w = np.fromfile(resultdir + '/weights_results_' + str(int(h)) +
'/weights_0.txt',
sep=" ")
ke = np.zeros((int(w.size), 2))
vg = np.zeros((int(w.size), 2))
t = np.array([t0 + n * h for n in range(N + 1)])
for n in range(0, N + 1):
Y = np.fromfile(resultdir + '/points_results_' + str(int(h)) +
'/points_' + str(n) + '.txt',
sep=" ")
w = np.fromfile(resultdir + '/weights_results_' + str(int(h)) +
'/weights_' + str(n) + '.txt',
sep=" ")
l = int(w.size)
Y = Y.reshape((l, 2))
#calculate centroids and mass of cells
[Yc, m] = dens.lloyd(Y, w)
mtile = np.tile(m, (2, 1)).T
#calculate second moments to find KE and maximum of vg
[m1, I] = dens.moments(Y, w)
#find kinetic energy, maximum value of vg and total energy
ke[:, 0] = 0.5 * f * f * (m * Y[:, 0]**2 - 2 * Y[:, 0] * m1[:, 0] +
I[:, 0])
vg[:, 0] = f * (Y[:, 0] - Yc[:, 0])
#map back to fundamental domain
ke = dens.to_fundamental_domain(ke)
vg = dens.to_fundamental_domain(vg)
E = ke[:,
0] - f * f * Y[:, 1] * m1[:, 1] + 0.5 * f * f * H * Y[:, 1] * m
pe = -f * f * Y[:, 1] * m1[:, 1] + 0.5 * f * f * H * Y[:, 1] * m
energy[n] = np.sum(E)
KE[n] = np.sum(ke[:, 0])
KEmean[n] = np.sum(ke[:, 0]) * float(l)
rmsv[n] = np.sqrt(KEmean[n])
PE[n] = np.sum(pe)
vgmax[n] = np.amax(vg[:, 0])
energy.tofile(datadir + '/energy.txt', sep=" ", format="%s")
KEmean.tofile(datadir + '/KEmean.txt', sep=" ", format="%s")
vgmax.tofile(datadir + '/vgmax.txt', sep=" ", format="%s")
t.tofile(datadir + '/time.txt', sep=" ", format="%s")
PE.tofile(datadir + '/PE.txt', sep=" ", format="%s")
KE.tofile(datadir + '/KE.txt', sep=" ", format="%s")
rmsv.tofile(datadir + '/rmsv.txt', sep=" ", format="%s")
return ('complete results ' + str(days) + 'D_' + str(N) + 'N_' +
str(int(tstepsize)))
def validity_analysis_results(N, days, tstepsize, t0 = 0., Heun = None):
#initialise parameters
H = 1.e4
L = 1.e6
g = 10.
f = 1.e-4
theta0 = 300
C = 3e-6
if Heun:
print('heun')
datadir = "Results_"+str(days)+"D_"+str(N)+"N_"+str(int(tstepsize))+"_heun/data"
resultdir = "Results_"+str(days)+"D_"+str(N)+"N_"+str(int(tstepsize))+"_heun"
plotsdir = "Results_"+str(days)+"D_"+str(N)+"N_"+str(int(tstepsize))+"_heun/plots"
else:
print('euler')
datadir = "Results_"+str(days)+"D_"+str(N)+"N_"+str(int(tstepsize))+"_euler/data"
resultdir = "Results_"+str(days)+"D_"+str(N)+"N_"+str(int(tstepsize))+"_euler"
plotsdir = "Results_"+str(days)+"D_"+str(N)+"N_"+str(int(tstepsize))+"_euler/plots"
os.mkdir(datadir)
os.mkdir(plotsdir)
#set up uniform density for domain Gamma
bbox = np.array([-L, 0., L, H])
Xdens = pdx.sample_rectangle(bbox)
f0 = np.ones(4)/2/L/H
rho = np.zeros(Xdens.shape[0])
T = ma.delaunay_2(Xdens,rho)
dens = pdx.Periodic_density_in_x(Xdens,f0,T,bbox)
#set up plotting uniform density for domain Gamma
bbox = np.array([-L, 0., L, H])
Xdens = pdx.sample_rectangle(bbox)
npts = 100
Xrnd = 2*L*(np.random.rand(npts)-0.5)
Zrnd = H*np.random.rand(npts)
Xdens = np.concatenate((Xdens, np.array((Xrnd, Zrnd)).T))
f0 = np.ones(npts+4)/2/L/H
rho = np.zeros(Xdens.shape[0])
T = ma.delaunay_2(Xdens,rho)
pdens = pdx.Periodic_density_in_x(Xdens,f0,T,bbox)
#set final time(t), step size (h) and total number of time steps(N)
tf = 60*60*24*days
h = tstepsize
N = int(np.ceil((tf-t0)/h))
#initialise arrays to store data values
KEmean = np.zeros(N+1)
energy = np.zeros(N+1)
vgmax = np.zeros(N+1)
PE = np.zeros(N+1)
KE = np.zeros(N+1)
rmsv = np.zeros(N+1)
w = np.fromfile(resultdir+'/weights_results_'+str(int(h))+'/weights_0.txt', sep = " ")
ke = np.zeros((int(w.size),2))
vg = np.zeros((int(w.size),2))
t = np.array([t0 + n*h for n in range(N+1)])
Ndump = 100
for n in range(0,N+1, Ndump):
print(n,N)
try:
Y = np.fromfile(resultdir+'/points_results_'+str(int(h))+'/points_'+str(n)+'.txt', sep = " ")
w = np.fromfile(resultdir+'/weights_results_'+str(int(h))+'/weights_'+str(n)+'.txt', sep = " ")
l = int(w.size)
Y = Y.reshape((l,2))
except IOError:
break
#Plots
C = Y[:,1].reshape((l,1))
print(C.shape, w.shape)
img = periodic_laguerre_diagram_to_image(pdens,Y,w,C,bbox,100,100)
plt.pcolor(img)
plt.savefig(plotsdir+'/c_'+str(n)+'.jpg')
plt.clf()
plt.plot(Y[:,0], Y[:,1], '.')
plt.savefig(plotsdir+'/Y_'+str(n)+'.jpg')
plt.clf()
#calculate centroids and mass of cells
[Yc, m] = dens.lloyd(Y, w)
mtile = np.tile(m,(2,1)).T
#calculate second moments to find KE and maximum of vg
[m1, I] = dens.moments(Y, w)
#find kinetic energy, maximum value of vg and total energy
ke[:,0] = 0.5*f*f*(m*Y[:,0]**2 - 2*Y[:,0]*m1[:,0] + I[:,0])
vg[:,0] = f*(Y[:,0] - Yc[:,0])
#map back to fundamental domain
ke = dens.to_fundamental_domain(ke)
vg = dens.to_fundamental_domain(vg)
E = ke[:,0] - f*f*Y[:,1]*m1[:,1] + 0.5*f*f*H*Y[:,1]*m
pe = - f*f*Y[:,1]*m1[:,1] + 0.5*f*f*H*Y[:,1]*m
energy[n] = np.sum(E)
KE[n] = np.sum(ke[:,0])
KEmean[n] = np.sum(ke[:,0])*float(l)
rmsv[n] = np.sqrt(KEmean[n])
PE[n] = np.sum(pe)
vgmax[n] = np.amax(vg[:,0])
energy.tofile(datadir+'/energy.txt',sep = " ",format = "%s")
KEmean.tofile(datadir+'/KEmean.txt',sep = " ",format = "%s")
vgmax.tofile(datadir+'/vgmax.txt',sep = " ",format = "%s")
t.tofile(datadir+'/time.txt',sep = " ",format = "%s")
PE.tofile(datadir+'/PE.txt',sep = " ",format = "%s")
KE.tofile(datadir+'/KE.txt',sep = " ",format = "%s")
rmsv.tofile(datadir+'/rmsv.txt',sep = " ",format = "%s")
return('complete results '+str(days)+'D_'+str(N)+'N_'+str(int(tstepsize)))