1 | from __future__ import print_function |
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2 | |
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3 | print('Loading DYNAMICO modules ...') |
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4 | from dynamico import unstructured as unst |
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5 | from dynamico.precision import asnum |
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6 | from dynamico.dev.meshes import MPAS_Format, Unstructured_Mesh |
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7 | from dynamico.dev.numba import jit |
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8 | from dynamico import time_step |
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9 | print('...Done') |
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10 | |
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11 | print('Loading modules ...') |
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12 | import math as math |
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13 | import matplotlib.pyplot as plt |
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14 | import numpy as np |
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15 | from numba import int32, float64 |
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16 | import numba |
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17 | import time |
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18 | |
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19 | print('...Done') |
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20 | |
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21 | grid, llm, nqdyn = 10242, 1,1 # 2562, 10242, 40962 |
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22 | Omega, radius, g = 2.*np.pi/86400., 6.4e6, 1. |
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23 | N, T, courant = 10, 10800., 0.5 # simulation length = N*T |
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24 | |
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25 | def f(lon,lat): return 2*Omega*np.sin(lat) # Coriolis parameter |
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26 | print('Reading MPAS mesh ...') |
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27 | meshfile = MPAS_Format('grids/x1.%d.grid.nc'%grid) |
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28 | mesh=Unstructured_Mesh(meshfile, llm, nqdyn, radius, f) |
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29 | print('...Done') |
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30 | lon, lat = mesh.lon_i, mesh.lat_i |
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31 | x,y,z = np.cos(lat)*np.cos(lon), np.cos(lat)*np.sin(lon), np.sin(lat) |
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32 | |
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33 | u0 = Omega*radius/12. # cf Williamson (1991), p.13 |
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34 | gh1 = radius*Omega*u0+.5*u0**2 |
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35 | print('u0=', u0) |
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36 | ulon = u0*np.cos(mesh.lat_e) |
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37 | |
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38 | dx = mesh.de.min() |
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39 | dt = courant*dx/u0 |
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40 | nt = int(math.ceil(T/dt)) |
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41 | dt = T/nt |
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42 | print(dx, dt, dt*u0/dx) |
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43 | print(T, nt) |
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44 | |
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45 | q0 = np.exp(-32.*(x+1.)**2) |
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46 | q0, u0 = asnum([q0, mesh.ucov2D(ulon,0.*ulon)]) |
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47 | |
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48 | @jit |
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49 | def upwind(mesh,u,q,flux): |
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50 | # compute upwind fluxes |
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51 | for edge in range(mesh.edge_num): |
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52 | left = mesh.left[edge]-1 |
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53 | right = mesh.right[edge]-1 |
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54 | ue = u[edge]*mesh.le_de[edge] |
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55 | if ue>0: |
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56 | flux[edge]=ue*q[left] |
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57 | else: |
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58 | flux[edge]=ue*q[right] |
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59 | |
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60 | @jit |
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61 | def advance(mesh, scheme, u, q, flux): |
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62 | scheme(mesh,u,q,flux) |
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63 | # advance by -divergence of flux |
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64 | for cell in range(mesh.primal_num): |
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65 | div=0. |
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66 | for iedge in range(mesh.primal_deg[cell]): |
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67 | edge = mesh.primal_edge[cell,iedge]-1 |
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68 | div = div + flux[edge]*mesh.primal_ne[cell,iedge] |
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69 | q[cell] = q[cell] - dt*div/mesh.Ai[cell] |
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70 | |
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71 | q = q0 |
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72 | flux = mesh.field_u() |
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73 | |
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74 | mesh_data = mesh.data() |
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75 | |
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76 | for i in range(N): |
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77 | mesh.plot_i(q) ; plt.title('q'); plt.xlim([0.,360.]) |
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78 | plt.savefig('fig_Godunov/q_%02d.png'%i) |
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79 | plt.close() |
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80 | print(i) |
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81 | start_time = time.time() |
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82 | for iter in range(100): |
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83 | advance(mesh_data, upwind, u0,q,flux) |
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84 | elapsed_time = time.time() - start_time |
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85 | print('elapsed time : %g ms/step'%(1000.*elapsed_time/iter)) |
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86 | |
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87 | print('Time spent in DYNAMICO (s) : ', unst.getvar('elapsed')) |
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