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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13 | import argparse |
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14 | import logging |
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15 | from numpy import pi, log, exp, sin, cos |
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16 | |
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17 | # Baroclinic instability test based on Ullrich et al. 2015, QJRMS |
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18 | |
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19 | parser = argparse.ArgumentParser() |
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20 | |
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21 | parser.add_argument("--mpi_ni", type=int, default=1, |
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22 | help="number of x processors") |
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23 | parser.add_argument("--mpi_nj", type=int, default=1, |
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24 | help="number of y processors") |
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25 | parser.add_argument("--T", type=float, default=3600., |
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26 | help="Length of time slice in seconds") |
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27 | parser.add_argument("--N", type=int, default=48, |
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28 | help="Number of time slices") |
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29 | parser.add_argument("--log",type=str,default='DEBUG',choices=('DEBUG', 'INFO', 'WARNING', 'ERROR', 'CRITICAL'), |
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30 | help="Set verbosity level of logging") |
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31 | parser.add_argument("--Davies_N1", type=int, default=3) |
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32 | parser.add_argument("--Davies_N2", type=int, default=3) |
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33 | parser.add_argument("--llm", type=int, default=50) |
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34 | parser.add_argument("--nx", type=int, default=200) |
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35 | parser.add_argument("--ny", type=int, default=30) |
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36 | parser.add_argument("--dt", type=float, default=360., help='Time step in seconds') |
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37 | parser.add_argument("--hydrostatic", action='store_true') |
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38 | parser.add_argument("--betaplane", action='store_true') |
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39 | |
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40 | args = parser.parse_args() |
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41 | |
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42 | |
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43 | def baroclinic_3D(Lx,nx,Ly,ny,llm,ztop=25000.): |
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44 | Rd = 287.0 # Gas constant for dryy air (j kg^-1 K^-1) |
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45 | T0 = 288.0 # Reference temperature (K) |
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46 | lap = 0.005 # Lapse rate (K m^-1) |
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47 | b = 2. # Non dimensional vertical width parameter |
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48 | u0 = 35. # Reference zonal wind speed (m s^-1) |
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49 | a = 6.371229e6 # Radius of the Earth (m) |
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50 | ptop = 2000. |
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51 | y0 = .5*Ly |
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52 | Cpd = 1004.5 |
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53 | p0 = 1e5 |
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54 | up = 1. # amplitude (m/s) |
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55 | xc,yc,lp = 0.,Ly/2.,600000. |
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56 | |
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57 | omega = 7.292e-5 # Angular velocity of the Earth (s^-1) |
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58 | phi0 = 45.*np.pi/180.0 # Reference latitude North pi/4 (deg) |
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59 | f0 = 2*omega*np.sin(phi0) |
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60 | beta0 = 2*omega*np.cos(phi0)/a if args.betaplane else 0. |
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61 | fb = f0 - beta0*y0 |
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62 | |
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63 | def Phi_xy(y): |
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64 | fc = y*y - (Ly*y/pi)*sin(2*pi*y/Ly) |
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65 | fd = Ly*Ly/(2*pi*pi)*cos(2*pi*y/Ly) |
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66 | 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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67 | |
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68 | 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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69 | def ulon(x,y,eta): |
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70 | u = -u0*(sin(pi*y/Ly)**2)*log(eta)*(eta**(-log(eta)/(b*b))) |
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71 | # u = u + up*exp(-(((x-xc)**2+(y-yc)**2)/lp**2)) |
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72 | return u |
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73 | |
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74 | def tmean(eta) : return T0*eta**(Rd*lap/g) |
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75 | 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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76 | def p(eta): return p0*eta # eta = p/p_s |
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77 | |
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78 | def eta(alpha) : return (1.-(lap*ztop*alpha/T0))**(g/(Rd*lap)) # roughly equispaced levels |
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79 | def coriolis(x,y): return f0+beta0*y # here y is 0 at domain center |
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80 | |
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81 | filename = 'cart_%03d_%03d.nc'%(nx,ny) |
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82 | logging.info('Reading Cartesian mesh ...') |
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83 | meshfile = meshes.DYNAMICO_Format(filename) |
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84 | pmesh = meshes.Unstructured_PMesh(comm,meshfile) |
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85 | pmesh.partition_curvilinear(args.mpi_ni,args.mpi_nj) |
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86 | nqdyn, radius = 1, None |
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87 | mesh = meshes.Local_Mesh(pmesh, llm, nqdyn, radius, coriolis) |
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88 | |
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89 | alpha_k = (np.arange(llm) +.5)/llm |
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90 | alpha_l = (np.arange(llm+1)+ 0.)/llm |
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91 | x_ik, alpha_ik = np.meshgrid(mesh.lon_i, alpha_k, indexing='ij') |
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92 | y_ik, alpha_ik = np.meshgrid(mesh.lat_i+y0, alpha_k, indexing='ij') |
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93 | x_il, alpha_il = np.meshgrid(mesh.lon_i, alpha_l, indexing='ij') |
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94 | y_il, alpha_il = np.meshgrid(mesh.lat_i+y0, alpha_l, indexing='ij') |
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95 | x_ek, alpha_ek = np.meshgrid(mesh.lon_e, alpha_k, indexing='ij') |
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96 | y_ek, alpha_ek = np.meshgrid(mesh.lat_e+y0, alpha_k, indexing='ij') |
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97 | |
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98 | print('ztop(ptop) according to Eq. 7:', T0/lap*(1.-(ptop/p0)**(Rd*lap/g))) |
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99 | print(np.shape(alpha_k),np.shape(alpha_l)) |
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100 | thermo = dyn.Ideal_perfect(Cpd, Rd, p0, T0) |
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101 | |
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102 | eta_il = eta(alpha_il) |
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103 | eta_ik = eta(alpha_ik) |
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104 | eta_ek = eta(alpha_ek) |
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105 | print('min max eta_il', np.min(eta_il),np.max(eta_il)) |
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106 | |
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107 | Phi_il = Phi_xyeta(y_il, eta_il) |
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108 | Phi_ik = Phi_xyeta(y_ik, eta_ik) |
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109 | p_ik, p_il = p(eta_ik), p(eta_il) |
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110 | T_ik = T(y_ik, eta_ik) #ik full level(40), il(41) |
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111 | |
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112 | gas = thermo.set_pT(p_ik,T_ik) |
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113 | mass_ik = mesh.field_mass() |
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114 | for l in range(llm): |
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115 | mass_ik[:,l]=(Phi_il[:,l+1]-Phi_il[:,l])/(g*gas.v[:,l]) |
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116 | # mass_ik[:,l]=(p_il[:,l]-p_il[:,l+1])/g |
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117 | Sik, Wil = gas.s*mass_ik, mesh.field_w() |
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118 | |
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119 | u_ek = mesh.ucov3D(ulon(x_ek, y_ek, eta_ek), 0.*eta_ek) |
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120 | |
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121 | print('ztop (m) = ', Phi_il[0,-1]/g, ztop) |
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122 | ptop = p(eta(1.)) |
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123 | print( 'ptop (Pa) = ', gas.p[0,-1], ptop) |
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124 | |
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125 | params=dyn.Struct() |
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126 | params.ptop=ptop |
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127 | params.dx=dx |
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128 | params.dx_g0=dx/g |
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129 | params.g = g |
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130 | |
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131 | # define parameters for lower BC |
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132 | pbot = p(eta_il[:,0]) |
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133 | print( 'min p, T :', pbot.min(), tmean(pbot/p0)) |
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134 | gas_bot = thermo.set_pT(pbot, tmean(pbot/p0)) |
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135 | params.pbot = gas_bot.p |
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136 | params.rho_bot = 1e6/gas_bot.v |
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137 | |
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138 | return thermo, mesh, params, prec.asnum([mass_ik,Sik,u_ek,Phi_il,Wil]), gas |
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139 | |
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140 | def diagnose(Phi,S,m,W): |
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141 | s=S/m |
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142 | for l in range(llm): |
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143 | v[:,l]=(Phi[:,l+1]-Phi[:,l])/(g*m[:,l]) |
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144 | w[:,l]=.5*params.g*(W[:,l+1]+W[:,l])/m[:,l] |
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145 | z[:,l]=.5*(Phi[:,l+1]+Phi[:,l])/params.g |
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146 | gas = thermo.set_vs(v,s) |
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147 | return gas, w, z |
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148 | |
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149 | def grad(mesh, s_ik): |
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150 | llm=s_ik.shape[1] |
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151 | edge_num, left, right = mesh.edge_num, mesh.left, mesh.right |
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152 | grad_ek = prec.zeros((edge_num, llm)) |
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153 | for e in range(edge_num): |
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154 | left_e = left[e]-1 # Fortran => Python indexing |
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155 | right_e = right[e]-1 # Fortran => Python indexing |
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156 | grad_ek[e,:] = s_ik[right_e,:]-s_ik[left_e,:] |
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157 | return grad_ek |
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158 | |
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159 | def div(mesh, u_ek): |
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160 | llm=u_ek.shape[1] |
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161 | primal_num, primal_deg, primal_edge = mesh.primal_num, mesh.primal_deg, mesh.primal_edge |
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162 | primal_ne, le_de, Ai = mesh.primal_ne, mesh.le_de, mesh.Ai |
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163 | div_ik = prec.zeros((primal_num, llm)) |
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164 | for i in range(primal_num): |
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165 | div_i = 0. |
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166 | for iedge in range(primal_deg[i]): |
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167 | e = primal_edge[i,iedge]-1 # Fortran => Python indexing |
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168 | div_i = div_i + u_ek[e,:]*primal_ne[i,iedge]*le_de[e] |
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169 | div_ik[i,:] = div_i / Ai[i] |
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170 | return div_ik |
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171 | |
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172 | def curl(mesh, u_ek): |
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173 | llm=u_ek.shape[1] |
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174 | dual_num, dual_deg, dual_edge, dual_ne, Av = mesh.dual_num, mesh.dual_deg, mesh.dual_edge, mesh.dual_ne, mesh.Av |
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175 | curl_vk = prec.zeros((dual_num, llm)) |
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176 | for v in range(dual_num): |
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177 | curl_v = 0. |
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178 | for iedge in range(dual_deg[v]): |
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179 | e = dual_edge[v,iedge]-1 # Fortran => Python indexing |
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180 | curl_v = curl_v + u_ek[e,:]*dual_ne[v,iedge] |
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181 | curl_vk[v,:] = curl_v / Av[v] |
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182 | return curl_vk |
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183 | |
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184 | class Davies: |
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185 | def __init__(self,N1,N2,x_i,y_i,x_e,y_e): |
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186 | self.N1, self.N2 = N1, N2 |
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187 | self.beta_i = self.mask(x_i,y_i) |
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188 | self.beta_e = self.mask(x_e,y_e) |
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189 | self.x_e,self.y_e = x_e,y_e |
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190 | def mask0(self,c,c0,delta): # 1D building block for Davies relaxation |
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191 | N1, N2 = self.N1, self.N2 |
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192 | m = np.zeros(c.size) |
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193 | c1,c2 = c0-N1*delta, c0-(N1+N2)*delta |
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194 | for i in range(c.size): |
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195 | ci=c[i] |
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196 | m[i] = (1.+np.cos((ci-c2)*np.pi/(N2*delta)))/2.0 |
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197 | if ci < c2 : m[i]=1. |
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198 | if ci > c1 : m[i]=0. |
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199 | return m |
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200 | def relax(self, llm, step, flow): |
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201 | beta_i, beta_e = self.beta_i, self.beta_e |
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202 | m,S,u,Phi,W=flow |
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203 | for l in range(llm): |
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204 | step.mass[:,l] = beta_i*step.mass[:,l] + (1.-beta_i)*m[:,l] |
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205 | step.theta_rhodz[:,l] = beta_i*step.theta_rhodz[:,l] + (1.-beta_i)*S[:,l] |
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206 | step.u[:,l] = beta_e*step.u[:,l] + (1.-beta_e)*u[:,l] |
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207 | for l in range(llm+1): |
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208 | step.geopot[:,l] = beta_i*step.geopot[:,l] + (1.-beta_i)*Phi[:,l] |
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209 | step.W[:,l] = beta_i*step.W[:,l] + (1.-beta_i)*W[:,l] |
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210 | |
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211 | class myDavies(Davies): |
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212 | def mask(self,x,y): |
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213 | logging.debug('davies dy = %f' % dy) |
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214 | return self.mask0(y,.5*Ly,dy)*self.mask0(-y,.5*Ly,dy) |
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215 | |
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216 | |
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217 | |
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218 | with xios.Client() as client: # setup XIOS which creates the DYNAMICO communicator |
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219 | comm = client.comm |
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220 | mpi_rank, mpi_size = comm.Get_rank(), comm.Get_size() |
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221 | |
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222 | #-------------Logging verbosity configuration--------------------------- |
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223 | myloglevel = args.log |
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224 | myloglevel = getattr(logging, myloglevel.upper()) |
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225 | logging.basicConfig(filename='out.log',filemode='w',level=myloglevel, |
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226 | format='%(processName)s:%(name)s:%(filename)s:%(module)s:%(funcName)s:%(lineno)d:%(levelname)s:%(message)s' ) |
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227 | |
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228 | logging.debug('%d/%d starting'%(mpi_rank,mpi_size)) |
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229 | |
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230 | g, Lx, Ly = 9.81, 4e7, 6e6 |
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231 | nx, ny, llm = args.nx, args.ny, args.llm |
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232 | dx,dy = Lx/nx,Ly/ny |
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233 | |
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234 | unst.setvar('g',g) |
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235 | |
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236 | thermo, mesh, params, flow0, gas0 = baroclinic_3D(Lx,nx,Ly,ny,llm) |
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237 | |
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238 | mass_bl,mass_dak,mass_dbk = meshes.compute_hybrid_coefs(flow0[0]) |
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239 | print( 'Type of mass_bl, mass_dak, mass_dbk : ', [x.dtype for x in mass_bl, mass_dak, mass_dbk]) |
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240 | unst.ker.dynamico_init_hybrid(mass_bl,mass_dak,mass_dbk) |
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241 | |
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242 | T = args.T |
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243 | dt = args.dt |
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244 | dz = flow0[3].max()/(params.g*llm) |
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245 | nt = int(math.ceil(T/dt)) |
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246 | dt = T/nt |
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247 | logging.info( 'Time step : %d x %g = %g s' % (nt,dt,nt*dt)) |
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248 | |
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249 | dt=0. # FIXME |
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250 | |
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251 | caldyn_thermo, caldyn_eta = unst.thermo_entropy, unst.eta_mass |
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252 | |
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253 | if False: # time stepping in Python |
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254 | caldyn = unst.Caldyn_NH(caldyn_thermo,caldyn_eta, mesh,thermo,params,params.g) |
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255 | scheme = time_step.ARK2(caldyn.bwd_fast_slow, dt) |
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256 | def next_flow(m,S,u,Phi,W): |
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257 | return scheme.advance((m,S,u,Phi,W),nt) |
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258 | |
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259 | else: # time stepping in Fortran |
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260 | scheme = time_step.ARK2(None, dt) |
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261 | if args.hydrostatic: |
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262 | caldyn_step = unst.caldyn_step_HPE(mesh,scheme,1, caldyn_thermo,caldyn_eta,thermo,params,params.g) |
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263 | else: |
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264 | caldyn_step = unst.caldyn_step_NH(mesh,scheme,1, caldyn_thermo,caldyn_eta,thermo,params,params.g) |
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265 | davies = myDavies(args.Davies_N1, args.Davies_N2, mesh.lon_i, mesh.lat_i, mesh.lon_e,mesh.lat_e) |
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266 | print('mask min/max :', davies.beta_i.min(), davies.beta_i.max() ) |
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267 | logging.debug('mask min/max :') |
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268 | logging.debug(davies.beta_i.min()) |
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269 | logging.debug(davies.beta_i.max()) |
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270 | def next_flow(m,S,u,Phi,W): |
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271 | # junk,fast,slow = caldyn.bwd_fast_slow(flow, 0.) |
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272 | caldyn_step.mass[:,:], caldyn_step.theta_rhodz[:,:], caldyn_step.u[:,:] = m,S,u |
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273 | caldyn_step.geopot[:,:], caldyn_step.W[:,:] = Phi,W |
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274 | kappa = dx**4/43200. |
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275 | for i in range(nt): |
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276 | caldyn_step.next() |
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277 | davies.relax(llm, caldyn_step, flow0) |
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278 | m,S = caldyn_step.mass, caldyn_step.theta_rhodz |
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279 | s = S/m |
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280 | laps = mesh.field_mass() |
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281 | bilaps = mesh.field_mass() |
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282 | unst.ker.dynamico_scalar_laplacian(s,laps) |
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283 | unst.ker.dynamico_scalar_laplacian(laps,bilaps) |
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284 | # grads = grad(mesh,s) |
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285 | # laps = div(mesh,grads) |
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286 | # gradlaps = grad(mesh,laps) # bilaplacian |
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287 | # bilaps = div(mesh,gradlaps) |
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288 | caldyn_step.theta_rhodz[:] = S - dt*kappa*bilaps*m # Euler step |
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289 | return (caldyn_step.mass.copy(), caldyn_step.theta_rhodz.copy(), caldyn_step.u.copy(), |
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290 | caldyn_step.geopot.copy(), caldyn_step.W.copy()) |
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291 | |
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292 | m,S,u,Phi,W = flow0 |
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293 | if caldyn_thermo == unst.thermo_theta: |
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294 | s=S/m |
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295 | theta = thermo.T0*np.exp(s/thermo.Cpd) |
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296 | S=m*theta |
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297 | title_format = 'Potential temperature at t=%g s (K)' |
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298 | else: |
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299 | title_format = 'Specific entropy at t=%g s (J/K/kg)' |
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300 | |
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301 | w=mesh.field_mass() |
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302 | z=mesh.field_mass() |
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303 | |
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304 | #T, nslice, dt = 3600., 1, 3600. |
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305 | Nslice = args.N |
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306 | |
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307 | with xios.Context_Curvilinear(mesh,1, 24*3600) as context: |
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308 | # now XIOS knows about the mesh and we can write to disk |
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309 | v = mesh.field_mass() # specific volume (diagnosed) |
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310 | |
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311 | for i in range(Nslice): |
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312 | context.update_calendar(i+1) |
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313 | |
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314 | # Diagnose quantities of interest from prognostic variables m,S,u,Phi,W |
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315 | gas, w, z = diagnose(Phi,S,m,W) |
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316 | ps = caldyn_step.ps |
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317 | curl_vk = curl(mesh, u) |
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318 | du_fast, du_slow = caldyn_step.du_fast[0,:,:], caldyn_step.du_slow[0,:,:] |
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319 | div_fast, div_slow = div(mesh,du_fast), div(mesh,du_slow) |
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320 | # write to disk |
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321 | context.send_field_primal('ps', ps) |
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322 | context.send_field_primal('temp', gas.T) |
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323 | context.send_field_primal('p', gas.p) |
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324 | context.send_field_primal('theta', gas.s) |
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325 | context.send_field_primal('uz', w) |
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326 | context.send_field_primal('z', z) |
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327 | context.send_field_primal('div_fast', div_fast) |
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328 | context.send_field_primal('div_slow', div_slow) |
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329 | print curl_vk.size |
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330 | context.send_field_dual('curl', curl_vk) |
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331 | |
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332 | print( 'ptop, model top (m) :', unst.getvar('ptop'), Phi.max()/unst.getvar('g')) |
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333 | |
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334 | time1, elapsed1 =time.time(), unst.getvar('elapsed') |
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335 | m,S,u,Phi,W = next_flow(m,S,u,Phi,W) |
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336 | time2, elapsed2 =time.time(), unst.getvar('elapsed') |
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337 | factor = 1000./nt |
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338 | print( 'ms per full time step : ', factor*(time2-time1), factor*(elapsed2-elapsed1)) |
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339 | factor = 1e9/(4*nt*nx*ny*llm) |
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340 | print( 'nanosec per gridpoint per full time step : ', factor*(time2-time1), factor*(elapsed2-elapsed1)) |
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341 | |
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342 | logging.info('************DONE************') |
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