[761] | 1 | from dynamico import unstructured as unst |
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| 2 | from dynamico import dyn |
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| 3 | from dynamico import time_step |
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| 4 | from dynamico import DCMIP |
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| 5 | from dynamico import meshes |
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| 6 | from dynamico import xios |
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| 7 | from dynamico import precision as prec |
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| 8 | from dynamico.meshes import Cartesian_mesh as Mesh |
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| 9 | |
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| 10 | import math as math |
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| 11 | import numpy as np |
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| 12 | import time |
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[764] | 13 | import argparse |
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[761] | 14 | from numpy import pi, log, exp, sin, cos |
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| 15 | |
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| 16 | # Baroclinic instability test based on Ullrich et al. 2015, QJRMS |
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| 17 | |
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[764] | 18 | parser = argparse.ArgumentParser() |
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| 19 | |
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[771] | 20 | parser.add_argument("--mpi_ni", type=int, default=1, |
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[764] | 21 | help="number of x processors") |
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[771] | 22 | parser.add_argument("--mpi_nj", type=int, default=1, |
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[764] | 23 | help="number of y processors") |
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[769] | 24 | parser.add_argument("--T", type=float, default=5., |
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| 25 | help="Length of time slice in seconds") |
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[771] | 26 | parser.add_argument("--Davies_N1", type=int, default=5) |
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| 27 | parser.add_argument("--Davies_N2", type=int, default=5) |
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[769] | 28 | |
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[771] | 29 | |
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[764] | 30 | args = parser.parse_args() |
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| 31 | |
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| 32 | |
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[761] | 33 | def baroclinic_3D(Lx,nx,Ly,ny,llm,ztop=25000.): |
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| 34 | Rd = 287.0 # Gas constant for dryy air (j kg^-1 K^-1) |
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| 35 | T0 = 288.0 # Reference temperature (K) |
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| 36 | lap = 0.005 # Lapse rate (K m^-1) |
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| 37 | b = 2. # Non dimensional vertical width parameter |
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| 38 | u0 = 35. # Reference zonal wind speed (m s^-1) |
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| 39 | a = 6.371229e6 # Radius of the Earth (m) |
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| 40 | ptop = 2000. |
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| 41 | y0 = Ly*0.5 |
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| 42 | Cpd = 1004.5 |
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| 43 | p0 = 1e5 |
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| 44 | |
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| 45 | omega = 7.292e-5 # Angular velocity of the Earth (s^-1) |
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[771] | 46 | phi0 = 90.*np.pi/180.0 # Reference latitude North pi/4 (deg) |
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[761] | 47 | f0 = 2*omega*np.sin(phi0) |
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| 48 | beta0 = 2*omega*np.cos(phi0)/a |
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| 49 | fb = 2*omega*np.sin(phi0) - y0*2*omega*np.cos(phi0)/a |
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| 50 | |
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[769] | 51 | def Phi_xy(y): |
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[761] | 52 | fc = y*y - (Ly*y/pi)*sin(2*pi*y/Ly) |
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| 53 | fd = Ly*Ly/(2*pi*pi)*cos(2*pi*y/Ly) |
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| 54 | return .5*u0*( fb*(y-y0-Ly/(2*pi)*sin(2*pi*y/Ly)) + .5*beta0*(fc-fd-(Ly*Ly/3.)- Ly*Ly/(2*pi*pi)) ) |
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| 55 | |
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[769] | 56 | def Phi_xyeta(y,eta): return T0*g/lap*(1-eta**(Rd*lap/g)) + Phi_xy(y)*log(eta)*exp(-((log(eta)/b)**2)) |
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[761] | 57 | def ulon(x,y,eta): return -u0*(sin(pi*y/Ly)**2)*log(eta)*(eta**(-log(eta)/b/b)) |
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| 58 | def tmean(eta) : return T0*eta**(Rd*lap/g) |
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[769] | 59 | def T(y,eta) : return tmean(eta)+(Phi_xy(y)/Rd)*(((2/(b*b))*(log(eta))**2)-1)*exp(-((0.5*log(eta))**2)) |
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[761] | 60 | def p(eta): return p0*eta # eta = p/p_s |
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| 61 | |
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| 62 | def eta(alpha) : return (1-(lap*ztop*alpha/(T0)))**(g/(Rd*lap)) # roughly equispaced levels |
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| 63 | |
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| 64 | filename = 'cart_%03d_%03d.nc'%(nx,ny) |
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| 65 | print 'Reading Cartesian mesh ...' |
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[771] | 66 | def coriolis(x,y): return f0+beta0*(y+.5*Ly) |
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[761] | 67 | meshfile = meshes.DYNAMICO_Format(filename) |
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| 68 | pmesh = meshes.Unstructured_PMesh(comm,meshfile) |
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[763] | 69 | pmesh.partition_curvilinear(args.mpi_ni,args.mpi_nj) |
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[769] | 70 | nqdyn, radius = 1, None |
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[761] | 71 | mesh = meshes.Local_Mesh(pmesh, llm, nqdyn, radius, coriolis) |
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| 72 | |
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[769] | 73 | |
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[761] | 74 | alpha_k = (np.arange(llm) +.5)/llm |
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| 75 | alpha_l = (np.arange(llm+1)+ 0.)/llm |
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| 76 | x_ik, alpha_ik = np.meshgrid(mesh.lon_i, alpha_k, indexing='ij') |
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| 77 | y_ik, alpha_ik = np.meshgrid(mesh.lat_i, alpha_k, indexing='ij') |
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| 78 | x_il, alpha_il = np.meshgrid(mesh.lon_i, alpha_l, indexing='ij') |
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| 79 | y_il, alpha_il = np.meshgrid(mesh.lat_i, alpha_l, indexing='ij') |
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| 80 | x_ek, alpha_ek = np.meshgrid(mesh.lon_e, alpha_k, indexing='ij') |
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| 81 | y_ek, alpha_ek = np.meshgrid(mesh.lat_e, alpha_k, indexing='ij') |
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| 82 | |
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| 83 | print('----------------') |
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| 84 | print 'ztop(ptop) according to Eq. 7:', T0/lap*(1.-(ptop/p0)**(Rd*lap/g)) |
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| 85 | print(np.shape(alpha_k),np.shape(alpha_l)) |
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| 86 | thermo = dyn.Ideal_perfect(Cpd, Rd, p0, T0) |
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| 87 | |
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| 88 | eta_il = eta(alpha_il) |
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| 89 | eta_ik = eta(alpha_ik) |
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| 90 | eta_ek = eta(alpha_ek) |
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| 91 | print('min max eta_il', np.min(eta_il),np.max(eta_il)) |
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| 92 | |
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[769] | 93 | Phi_il = Phi_xyeta(y_il, eta_il) |
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| 94 | Phi_ik = Phi_xyeta(y_ik, eta_ik) |
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[761] | 95 | p_ik = p(eta_ik) |
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[769] | 96 | T_ik = T(y_ik, eta_ik) #ik full level(40), il(41) |
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[761] | 97 | |
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| 98 | gas = thermo.set_pT(p_ik,T_ik) |
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| 99 | mass_ik = mesh.field_mass() |
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| 100 | for l in range(llm): |
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| 101 | mass_ik[:,l]=(Phi_il[:,l+1]-Phi_il[:,l])/(g*gas.v[:,l]) |
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| 102 | Sik, ujk, Wil = gas.s*mass_ik, mesh.field_u(), mesh.field_w() |
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| 103 | |
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| 104 | u_ek = mesh.ucov3D(ulon(x_ek, y_ek, eta_ek), 0.*eta_ek) |
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| 105 | |
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| 106 | print 'ztop (m) = ', Phi_il[0,-1]/g, ztop |
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| 107 | ptop = p(eta(1.)) |
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| 108 | print 'ptop (Pa) = ', gas.p[0,-1], ptop |
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| 109 | |
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| 110 | params=dyn.Struct() |
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| 111 | params.ptop=ptop |
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| 112 | params.dx=dx |
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| 113 | params.dx_g0=dx/g |
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| 114 | params.g = g |
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| 115 | |
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| 116 | # define parameters for lower BC |
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| 117 | pbot = p(eta_il[:,0]) |
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| 118 | print 'min p, T :', pbot.min(), tmean(pbot/p0) |
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| 119 | gas_bot = thermo.set_pT(pbot, tmean(pbot/p0)) |
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| 120 | params.pbot = gas_bot.p |
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| 121 | params.rho_bot = 1e6/gas_bot.v |
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| 122 | |
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| 123 | return thermo, mesh, params, prec.asnum([mass_ik,Sik,ujk,Phi_il,Wil]), gas |
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| 124 | |
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[769] | 125 | def diagnose(Phi,S,m,W): |
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| 126 | s=S/m ; s=.5*(s+abs(s)) |
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| 127 | for l in range(llm): |
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| 128 | v[:,l]=(Phi[:,l+1]-Phi[:,l])/(g*m[:,l]) |
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| 129 | w[:,l]=.5*params.g*(W[:,l+1]+W[:,l])/m[:,l] |
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| 130 | z[:,l]=.5*(Phi[:,l+1]+Phi[:,l])/params.g |
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| 131 | gas = thermo.set_vs(v,s) |
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| 132 | return gas, w, z |
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| 133 | |
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[771] | 134 | class Davies: |
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| 135 | def __init__(self,N1,N2,x_i,y_i,x_e,y_e): |
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| 136 | self.N1, self.N2 = N1, N2 |
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| 137 | self.beta_i = self.mask(x_i,y_i) |
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| 138 | self.beta_e = self.mask(x_e,y_e) |
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| 139 | def mask0(self,c,c0,delta): # 1D building block for Davies relaxation |
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| 140 | N1, N2 = self.N1, self.N2 |
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| 141 | N3=N1+N2 |
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| 142 | m = np.zeros(c.size) |
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| 143 | |
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| 144 | for i in range(c.size): |
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| 145 | ci=c[i] |
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| 146 | m[i] = (1.+np.cos((ci-c0+N3*delta)*np.pi/(N2*delta)))/2.0 |
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| 147 | if ci < c0-N3*delta : m[i]=1. |
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| 148 | if ci > c0-N1*delta : m[i]=0. |
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| 149 | return m |
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| 150 | def relax(self, llm, step, flow): |
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| 151 | beta_i, beta_e = self.beta_i, self.beta_e |
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| 152 | m,S,u,Phi,W=flow |
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| 153 | for l in range(llm): |
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| 154 | step.mass[:,l] = beta_i*step.mass[:,l] + (1.-beta_i)*m[:,l] |
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| 155 | step.theta_rhodz[:,l] = beta_i*step.theta_rhodz[:,l] + (1.-beta_i)*S[:,l] |
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| 156 | step.u[:,l] = beta_e*step.u[:,l] + (1.-beta_e)*u[:,l] |
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| 157 | for l in range(llm+1): |
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| 158 | step.geopot[:,l] = beta_i*step.geopot[:,l] + (1.-beta_i)*Phi[:,l] |
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| 159 | step.W[:,l] = beta_i*step.W[:,l] + (1.-beta_i)*W[:,l] |
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| 160 | |
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| 161 | |
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| 162 | class myDavies(Davies): |
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| 163 | def mask(self,x,y): |
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| 164 | # return self.mask0(y,Ly,dy) |
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| 165 | return self.mask0(y,-.5*Ly,dy)*self.mask0(-y,-.5*Ly,dy) |
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| 166 | |
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[763] | 167 | with xios.Client() as client: # setup XIOS which creates the DYNAMICO communicator |
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| 168 | comm = client.comm |
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| 169 | mpi_rank, mpi_size = comm.Get_rank(), comm.Get_size() |
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| 170 | print '%d/%d starting'%(mpi_rank,mpi_size) |
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[761] | 171 | |
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[763] | 172 | g, Lx, Ly = 9.81, 4e7, 6e6 |
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[769] | 173 | nx, ny, llm = 200, 30, 25 |
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[763] | 174 | dx,dy=Lx/nx,Ly/ny |
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[761] | 175 | |
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[763] | 176 | unst.setvar('g',g) |
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[761] | 177 | |
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[763] | 178 | thermo, mesh, params, flow0, gas0 = baroclinic_3D(Lx,nx,Ly,ny,llm) |
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[761] | 179 | |
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[769] | 180 | mass_bl,mass_dak,mass_dbk = meshes.compute_hybrid_coefs(flow0[0]) |
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| 181 | print 'Type of mass_bl, mass_dak, mass_dbk : ', [x.dtype for x in mass_bl, mass_dak, mass_dbk] |
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| 182 | unst.ker.dynamico_init_hybrid(mass_bl,mass_dak,mass_dbk) |
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[761] | 183 | |
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[769] | 184 | T=3600. |
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| 185 | dt=360. |
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| 186 | dz = flow0[3].max()/(params.g*llm) |
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| 187 | nt = int(math.ceil(T/dt)) |
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| 188 | dt = T/nt |
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| 189 | print 'Time step : %d x %g = %g s' % (nt,dt,nt*dt) |
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| 190 | |
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| 191 | caldyn_thermo, caldyn_eta = unst.thermo_entropy, unst.eta_mass |
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| 192 | |
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| 193 | if False: # time stepping in Python |
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| 194 | caldyn = unst.Caldyn_NH(caldyn_thermo,caldyn_eta, mesh,thermo,params,params.g) |
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| 195 | scheme = time_step.ARK2(caldyn.bwd_fast_slow, dt) |
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| 196 | def next_flow(m,S,u,Phi,W): |
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| 197 | return scheme.advance((m,S,u,Phi,W),nt) |
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| 198 | |
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| 199 | else: # time stepping in Fortran |
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| 200 | scheme = time_step.ARK2(None, dt) |
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[771] | 201 | caldyn_step = unst.caldyn_step_NH(mesh,scheme,1, caldyn_thermo,caldyn_eta,thermo,params,params.g) |
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| 202 | davies = myDavies(args.Davies_N1, args.Davies_N2, mesh.lon_i, mesh.lat_i, mesh.lon_e,mesh.lat_e) |
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[769] | 203 | def next_flow(m,S,u,Phi,W): |
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| 204 | # junk,fast,slow = caldyn.bwd_fast_slow(flow, 0.) |
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| 205 | caldyn_step.mass[:,:], caldyn_step.theta_rhodz[:,:], caldyn_step.u[:,:] = m,S,u |
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| 206 | caldyn_step.geopot[:,:], caldyn_step.W[:,:] = Phi,W |
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[771] | 207 | for i in range(nt): |
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| 208 | caldyn_step.next() |
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| 209 | davies.relax(llm, caldyn_step, flow0) |
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[769] | 210 | return (caldyn_step.mass.copy(), caldyn_step.theta_rhodz.copy(), caldyn_step.u.copy(), |
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[771] | 211 | caldyn_step.geopot.copy(), caldyn_step.W.copy()) |
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[769] | 212 | |
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| 213 | m,S,u,Phi,W=flow0 |
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| 214 | if caldyn_thermo == unst.thermo_theta: |
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| 215 | s=S/m |
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| 216 | theta = thermo.T0*np.exp(s/thermo.Cpd) |
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| 217 | S=m*theta |
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| 218 | title_format = 'Potential temperature at t=%g s (K)' |
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| 219 | else: |
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| 220 | title_format = 'Specific entropy at t=%g s (J/K/kg)' |
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| 221 | |
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| 222 | w=mesh.field_mass() |
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| 223 | z=mesh.field_mass() |
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| 224 | |
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| 225 | |
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| 226 | #T, nslice, dt = 3600., 1, 3600. |
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| 227 | Nslice=24 |
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| 228 | |
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| 229 | with xios.Context_Curvilinear(mesh,1, 24*3600) as context: |
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[763] | 230 | # now XIOS knows about the mesh and we can write to disk |
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[769] | 231 | v = mesh.field_mass() # specific volume (diagnosed) |
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| 232 | |
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| 233 | for i in range(Nslice): |
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[763] | 234 | context.update_calendar(i) |
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[769] | 235 | |
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| 236 | # Diagnose quantities of interest from prognostic variables m,S,u,Phi,W |
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| 237 | gas, w, z = diagnose(Phi,S,m,W) |
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| 238 | |
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| 239 | # write to disk |
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[763] | 240 | context.send_field_primal('temp', gas0.T) |
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[769] | 241 | context.send_field_primal('p', gas.p) |
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| 242 | context.send_field_primal('theta', gas.s) |
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| 243 | context.send_field_primal('uz', w) |
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| 244 | |
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| 245 | print 'ptop, model top (m) :', unst.getvar('ptop'), Phi.max()/unst.getvar('g') |
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| 246 | #if args.mpi_ni*args.mpi_nj==1: plot() |
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| 247 | |
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| 248 | time1, elapsed1 =time.time(), unst.getvar('elapsed') |
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| 249 | m,S,u,Phi,W = next_flow(m,S,u,Phi,W) |
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| 250 | time2, elapsed2 =time.time(), unst.getvar('elapsed') |
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| 251 | factor = 1000./nt |
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| 252 | print 'ms per full time step : ', factor*(time2-time1), factor*(elapsed2-elapsed1) |
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| 253 | factor = 1e9/(4*nt*nx*ny*llm) |
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| 254 | print 'nanosec per gridpoint per full time step : ', factor*(time2-time1), factor*(elapsed2-elapsed1) |
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| 255 | |
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| 256 | context.update_calendar(Nslice+1) # make sure XIOS writes last iteration |
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| 257 | print('************DONE************') |
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