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ftle_cuda.py
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import os
import sys
import glob
import gc
from concurrent.futures import ThreadPoolExecutor as Executor
from typing import Callable, Tuple, List
import h5py
import time
import numpy as np
from numba import cuda, uint32, uint64, float32, float64, njit, prange
from numba.cuda.libdevice import fast_log2f, fmaf_rn, fast_fdividef, fsqrt_rn, fminf, fmaxf, fast_logf, floorf, float2uint_rn, int2float_rn, float2int_rn
from math import sqrt, log2, ceil, floor
from scipy.spatial import KDTree
from progressbar import ProgressBar
from pyevtk.hl import pointsToVTK, gridToVTK
from mpi4py import MPI
THREADS_PER_BLOCK = 64
MAX_THREADS_PER_SM = 2048
SM_COUNT = 80
BLOCKS_PER_GRID = (MAX_THREADS_PER_SM // THREADS_PER_BLOCK) * SM_COUNT
THREADS_PER_BLOCK_3D = (2, 2, 32)
BLOCKS_PER_GRID_3D = (16, 16, 7)
REAL_NP = np.float32
REAL_CP = float32
CUDA_INT = uint64
FAST_MATH = True
def master_print(msg):
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
if rank == 0:
print(msg)
sys.stdout.flush()
def get_my_gpu_id():
ngpus = len(cuda.gpus)
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
return rank % ngpus
def select_gpu():
return cuda.select_device(get_my_gpu_id())
select_gpu()
def read_UVW(filename, gen_2d=False):
if not gen_2d:
with h5py.File(filename, "r", driver='mpio', comm=MPI.COMM_WORLD) as f:
data = f["dataset"]
Nx, Ny, _, Nz = data.shape
U = cuda.pinned_array((Nx, Ny, Nz), dtype=REAL_NP)
V = cuda.pinned_array((Nx, Ny, Nz), dtype=REAL_NP)
W = cuda.pinned_array((Nx, Ny, Nz), dtype=REAL_NP)
data.read_direct(U, np.s_[:, :, 1, :], np.s_[:, :, :])
data.read_direct(V, np.s_[:, :, 2, :], np.s_[:, :, :])
data.read_direct(W, np.s_[:, :, 3, :], np.s_[:, :, :])
else:
#with h5py.File(filename, "r", driver='mpio', comm=MPI.COMM_WORLD) as f:
with h5py.File(filename, "r") as f:
data = f["dataset"]
#with data.collective:
Nx, Ny, _, Nz = data.shape
U = data.astype(REAL_NP)[:, :, 1, Nz//2].reshape((Nx, Ny, 1))
V = data.astype(REAL_NP)[:, :, 2, Nz//2].reshape((Nx, Ny, 1))
W = np.zeros_like(U)
return U, V, W
@cuda.jit(fastmath=FAST_MATH)
def interp_UVW_flat(U0, V0, W0, U1, V1, W1, Un, Vn, Wn, dt, fraction=0.1, N=0):
global_id = cuda.grid(1)
gridDim = cuda.gridsize(1)
tm = REAL_CP(dt / 2.)
t_target = REAL_CP(fraction * N * dt)
dt_inv = REAL_CP(1./dt)
N = U0.shape[0]
for ii in range(global_id, N, gridDim):
Um = REAL_CP(REAL_CP(0.5) * (U0[ii] + U1[ii]))
Vm = REAL_CP(REAL_CP(0.5) * (V0[ii] + V1[ii]))
Wm = REAL_CP(REAL_CP(0.5) * (W0[ii] + W1[ii]))
dUdt = REAL_CP((U1[ii] - U0[ii]) * dt_inv)
dVdt = REAL_CP((V1[ii] - V0[ii]) * dt_inv)
dWdt = REAL_CP((W1[ii] - W0[ii]) * dt_inv)
deltaT = REAL_CP((t_target - tm))
Un[ii] = REAL_CP(Um + dUdt * deltaT)
Vn[ii] = REAL_CP(Vm + dVdt * deltaT)
Wn[ii] = REAL_CP(Wm + dWdt * deltaT)
@cuda.jit(fastmath=FAST_MATH)
def interp_UVW(U0, V0, W0, U1, V1, W1, Un, Vn, Wn, dt, fraction=0.1, N=0):
global_idx, global_idy, global_idz = cuda.grid(3)
gridDimX, gridDimY, gridDimZ = cuda.gridsize(3)
tm = REAL_CP(dt / 2.)
t_target = REAL_CP(fraction * N * dt)
dt_inv = REAL_CP(1./dt)
Nx, Ny, Nz = U0.shape
for ii in range(global_idx, Nx, gridDimX):
for jj in range(global_idy, Ny, gridDimY):
for kk in range(global_idz, Nz, gridDimZ):
Um = REAL_CP(REAL_CP(0.5) * (U0[ii, jj, kk] + U1[ii, jj, kk]))
Vm = REAL_CP(REAL_CP(0.5) * (V0[ii, jj, kk] + V1[ii, jj, kk]))
Wm = REAL_CP(REAL_CP(0.5) * (W0[ii, jj, kk] + W1[ii, jj, kk]))
dUdt = REAL_CP((U1[ii, jj, kk] - U0[ii, jj, kk]) * dt_inv)
dVdt = REAL_CP((V1[ii, jj, kk] - V0[ii, jj, kk]) * dt_inv)
dWdt = REAL_CP((W1[ii, jj, kk] - W0[ii, jj, kk]) * dt_inv)
deltaT = REAL_CP((t_target - tm))
Un[ii, jj, kk] = REAL_CP(Um + dUdt * deltaT)
Vn[ii, jj, kk] = REAL_CP(Vm + dVdt * deltaT)
Wn[ii, jj, kk] = REAL_CP(Wm + dWdt * deltaT)
@cuda.jit(fastmath=FAST_MATH, device = True, inline = True)
def max_cube(Uc):
U000 = Uc[0,0,0]
U100 = Uc[1,0,0]
U010 = Uc[0,1,0]
U001 = Uc[0,0,1]
U110 = Uc[1,1,0]
U011 = Uc[0,1,1]
U101 = Uc[1,0,1]
U111 = Uc[1,1,1]
return max(U000, U100, U010, U001, U110, U011, U101, U111)
@cuda.jit(fastmath=FAST_MATH, device = True, inline = True)
def min_cube(Uc):
U000 = Uc[0,0,0]
U100 = Uc[1,0,0]
U010 = Uc[0,1,0]
U001 = Uc[0,0,1]
U110 = Uc[1,1,0]
U011 = Uc[0,1,1]
U101 = Uc[1,0,1]
U111 = Uc[1,1,1]
return min(U000, U100, U010, U001, U110, U011, U101, U111)
@cuda.jit(fastmath=FAST_MATH, device = True, inline = True)
def minmax_cube(Uc):
U000 = Uc[0,0,0]
U100 = Uc[1,0,0]
U010 = Uc[0,1,0]
U001 = Uc[0,0,1]
U110 = Uc[1,1,0]
U011 = Uc[0,1,1]
U101 = Uc[1,0,1]
U111 = Uc[1,1,1]
mini = min(U000, U100, U010, U001, U110, U011, U101, U111)
maxi = max(U000, U100, U010, U001, U110, U011, U101, U111)
return mini, maxi
@cuda.jit(fastmath=FAST_MATH, device = True, inline = True)
def clip(v, minimum, maximum):
return max(min(maximum, v), minimum)
@cuda.jit(fastmath=FAST_MATH, device = True, inline = True)
def inner_trilinear_interpolate(Uc, dx, dy, dz):
dxdy = dx * dy
dxdz = dx * dz
dydz = dy * dz
dxdydz = dx * dy * dz
mini, maxi = minmax_cube(Uc)
U000 = Uc[0,0,0]
U100 = Uc[1,0,0]
U010 = Uc[0,1,0]
U001 = Uc[0,0,1]
U110 = Uc[1,1,0]
U011 = Uc[0,1,1]
U101 = Uc[1,0,1]
U111 = Uc[1,1,1]
c0u = (U000)
c1u = (U100 - U000)
c2u = (U010 - U000)
c3u = (U001 - U000)
c4u = (U110 - U010 - U100 + U000)
c5u = (U011 - U001 - U010 + U000)
c6u = (U101 - U001 - U100 + U000)
c7u = (U111 - U011 - U101 - U110 + U100 + U001 + U010 - U000)
return clip(c0u + c1u * dx + c2u * dy + c3u * dz + c4u * dxdy + c5u * dydz + c6u * dxdz + c7u * dxdydz, mini, maxi) # 80
@cuda.jit(fastmath=FAST_MATH, device = True)
def gpu_nns(x, y, z, xp, yp, zp, coarse_levels):
Nx, Ny, Nz = x.shape
COARSE_FACTOR = ((2)**coarse_levels)
best_x = 0
best_y = 0
best_z = 0
distance = float32(1e6)
for ii in range((COARSE_FACTOR), (Nx-COARSE_FACTOR), (COARSE_FACTOR//2)):
for jj in range((COARSE_FACTOR), (Ny-COARSE_FACTOR), (COARSE_FACTOR//2)):
for kk in range((COARSE_FACTOR), (Nz-COARSE_FACTOR), (COARSE_FACTOR//2)):
current_distance = fsqrt_rn(
(x[ii,jj,kk] - xp)*(x[ii,jj,kk] - xp) +
(y[ii,jj,kk] - yp)*(y[ii,jj,kk] - yp) +
(z[ii,jj,kk] - zp)*(z[ii,jj,kk] - zp)
)
if (current_distance <= distance):
best_x = (ii)
best_y = (jj)
best_z = (kk)
distance = current_distance
while COARSE_FACTOR > (1):
for ii in range((best_x - COARSE_FACTOR), (best_x + COARSE_FACTOR), (COARSE_FACTOR//2)):
for jj in range((best_y - COARSE_FACTOR), (best_y + COARSE_FACTOR), (COARSE_FACTOR//2)):
for kk in range((best_z - COARSE_FACTOR), (best_z + COARSE_FACTOR), (COARSE_FACTOR//2)):
current_distance = fsqrt_rn(
(x[ii,jj,kk] - xp)*(x[ii,jj,kk] - xp) +
(y[ii,jj,kk] - yp)*(y[ii,jj,kk] - yp) +
(z[ii,jj,kk] - zp)*(z[ii,jj,kk] - zp)
)
if (current_distance <= distance):
best_x = (ii)
best_y = (jj)
best_z = (kk)
distance = current_distance
COARSE_FACTOR = (COARSE_FACTOR // 2)
return CUDA_INT(best_x), CUDA_INT(best_y), CUDA_INT(best_z)
@cuda.jit(fastmath=FAST_MATH)
def get_particle_velocity_with_integrated_nns(x, y, z, xp, yp, zp, U, V, W, dt):
local_idx = cuda.threadIdx.x
global_idx = cuda.grid(1)
blockDim = cuda.blockDim.x
gridDim = cuda.gridsize(1) #cuda.gridDim.x * cuda.blockDim.x
NParticles = xp.size
Nx, Ny, Nz = x.shape
SMALLEST_DIM = min(Nx, Ny, Nz)
P = 1
while (2**(P+1)) < (SMALLEST_DIM//2):
P+=1
for particle in range(global_idx, NParticles, gridDim):
xp_local = REAL_CP(xp[particle])
yp_local = REAL_CP(yp[particle])
zp_local = REAL_CP(zp[particle])
i, j, k = gpu_nns(x, y, z, xp_local, yp_local, zp_local, P)
i -= 1 * ((xp_local <= x[i,j,k]))
j -= 1 * ((yp_local <= y[i,j,k]))
k -= 1 * ((zp_local <= z[i,j,k]) and (zp_local >= z[i,j,max(0, k-1)]))
in_domain = (0 <= i) and (i < Nx - 1) and (0 <= j) and (j < Ny - 1) and (0 <= k) and (k < Nz - 1)
i = clip(i, 0, Nx - 2)
j = clip(j, 0, Ny - 2)
k = clip(k, 0, Nz - 2)
xc = (x[i:i+2, j:j+2, k:k+2])
yc = (y[i:i+2, j:j+2, k:k+2])
zc = (z[i:i+2, j:j+2, k:k+2])
minX, maxX = minmax_cube(xc)
minY, maxY = minmax_cube(yc)
minZ, maxZ = minmax_cube(zc)
dx = fast_fdividef(xp_local - minX, maxX - minX)
dy = fast_fdividef(yp_local - minY, maxY - minY)
dz = fast_fdividef(zp_local - minZ, maxZ - minZ)
Uc = (U[i:i+2, j:j+2, k:k+2])
Vc = (V[i:i+2, j:j+2, k:k+2])
Wc = (W[i:i+2, j:j+2, k:k+2])
Up = REAL_CP(inner_trilinear_interpolate(Uc, dx, dy, dz)) * REAL_CP(in_domain) + REAL_CP(not in_domain) * REAL_CP(U[i, j, k])
Vp = REAL_CP(inner_trilinear_interpolate(Vc, dx, dy, dz)) * REAL_CP(in_domain) + REAL_CP(not in_domain) * REAL_CP(V[i, j, k])
Wp = REAL_CP(inner_trilinear_interpolate(Wc, dx, dy, dz)) * REAL_CP(in_domain) + REAL_CP(not in_domain) * REAL_CP(W[i, j, k])
xp[particle] = fmaf_rn(dt, Up, xp_local) #xp_local + REAL_CP(dt * Up)
yp[particle] = fmaf_rn(dt, Vp, yp_local) #yp_local + REAL_CP(dt * Vp)
zp[particle] = fmaf_rn(dt, Wp, zp_local) #zp_local + REAL_CP(dt * Wp)
def update_particle_velocity(
point: Tuple[np.ndarray, np.ndarray, np.ndarray],
x: np.ndarray,
y: np.ndarray,
z: np.ndarray,
U: np.ndarray,
V: np.ndarray,
W: np.ndarray,
is_2d: bool = False,
stream: cuda.stream = cuda.default_stream(),
dt: float = None,
):
xtarget, ytarget, ztarget = point
get_particle_velocity_with_integrated_nns[BLOCKS_PER_GRID, THREADS_PER_BLOCK](
x,
y,
z,
xtarget,
ytarget,
ztarget,
U,
V,
W,
REAL_CP(dt)
)
stream.synchronize()
return
@cuda.jit(fastmath=FAST_MATH)
def step_particles_euler(
Up, Vp, Wp, xp, yp, zp, dt, maxz=0.0, minz=0.0
):
global_idx = cuda.grid(1)
gridDim = cuda.gridsize(1) #cuda.gridDim.x * cuda.blockDim.x
NParticles = xp.size
for particle in range(global_idx, NParticles, gridDim):
xp[particle] = REAL_CP(dt * Up[particle] + xp[particle])
yp[particle] = REAL_CP(dt * Vp[particle] + yp[particle])
zp[particle] = REAL_CP(dt * Wp[particle] + zp[particle])
def particle_first_step(
U: np.ndarray,
V: np.ndarray,
W: np.ndarray,
x: np.ndarray,
y: np.ndarray,
z: np.ndarray,
dt: float,
mask: List[int],
step_particles: Callable,
is_2d: bool,
newx: np.ndarray,
newy: np.ndarray,
newz: np.ndarray,
stream: cuda.stream = cuda.default_stream()
):
with stream.auto_synchronize():
N = len(mask) - 1
xp = cuda.to_device(np.ascontiguousarray(newx.reshape((-1,))[mask[0]:mask[-1]]), stream)
yp = cuda.to_device(np.ascontiguousarray(newy.reshape((-1,))[mask[0]:mask[-1]]), stream)
zp = cuda.to_device(np.ascontiguousarray(newz.reshape((-1,))[mask[0]:mask[-1]]), stream)
update_particle_velocity(
(xp, yp, zp), x, y, z, U, V, W, is_2d, stream, dt
)
#step_particles_euler[BLOCKS_PER_GRID, THREADS_PER_BLOCK, stream](Up, Vp, Wp, xp, yp, zp, dt, maxz, minz)
return xp, yp, zp
def particle_update_velocities(
U: np.ndarray,
V: np.ndarray,
W: np.ndarray,
x: np.ndarray,
y: np.ndarray,
z: np.ndarray,
dt: float,
xp: np.ndarray,
yp: np.ndarray,
zp: np.ndarray,
step_particles: Callable,
is_2d: bool = False,
stream: cuda.stream = cuda.default_stream()
):
N = xp.size
with stream.auto_synchronize():
update_particle_velocity(
(xp, yp, zp), x, y, z, U, V, W, is_2d, stream, dt
)
#step_particles_euler[BLOCKS_PER_GRID, THREADS_PER_BLOCK, stream](Up, Vp, Wp, xp, yp, zp, dt, maxz, minz)
return xp, yp, zp
def write_particles_to_file(
h5file: h5py.File,
xp: cuda.device_array,
yp: cuda.device_array,
zp: cuda.device_array,
timestep: int,
mask: List[int]
):
print(f"Writing timestep: # {timestep}")
sys.stdout.flush()
dset_1 = h5file["Particle_xyz"]
#with dset_1.collective:
dset_1[timestep, 0, mask[0]:mask[-1]] = np.array(xp)
dset_1[timestep, 1, mask[0]:mask[-1]] = np.array(yp)
dset_1[timestep, 2, mask[0]:mask[-1]] = np.array(zp)
return
@njit(parallel=True, fastmath=False, nogil=True)
def __irregular_mesh_refine(x, y, z, ref_x, ref_y, ref_z):
Nx, Ny, Nz = x.shape
newx = np.zeros((Nx * ref_x, Ny * ref_y, Nz*ref_z), dtype = x.dtype) + np.min(x)
newy = np.zeros((Nx * ref_x, Ny * ref_y, Nz*ref_z), dtype = y.dtype) + np.min(y)
newz = np.zeros((Nx * ref_x, Ny * ref_y, Nz*ref_z), dtype = z.dtype) + np.min(z)
for ii in prange(1, Nx+1):
for jj in range(1, Ny+1):
for kk in range(1, Nz+1):
for io in range(ref_x):
for jo in range(ref_y):
for ko in range(ref_z):
idx = (ii - 1)*ref_x + io
idy = (jj - 1)*ref_y + jo
idz = (kk - 1)*ref_z + ko
xcube = x[max(0, ii-1):min(Nx, ii+1), max(0, jj-1):min(Ny, jj+1), max(0, kk-1):min(Nz, kk+1)]
ycube = y[max(0, ii-1):min(Nx, ii+1), max(0, jj-1):min(Ny, jj+1), max(0, kk-1):min(Nz, kk+1)]
zcube = z[max(0, ii-1):min(Nx, ii+1), max(0, jj-1):min(Ny, jj+1), max(0, kk-1):min(Nz, kk+1)]
dx = (io) / (ref_x)
dy = (jo) / (ref_y)
dz = (ko) / (ref_z)
Uc = xcube
Vc = ycube
Wc = zcube
c0u = (Uc[0,0,0])
c1u = (Uc[-1,0,0] - Uc[0,0,0])
c2u = (Uc[0,-1,0] - Uc[0,0,0])
c3u = (Uc[0,0,-1] - Uc[0,0,0])
c4u = (Uc[-1,-1,0] - Uc[0,-1,0] - Uc[-1,0,0] + Uc[0,0,0])
c5u = (Uc[0,-1,-1] - Uc[0,0,-1] - Uc[0,-1,0] + Uc[0,0,0])
c6u = (Uc[-1,0,-1] - Uc[0,0,-1] - Uc[-1,0,0] + Uc[0,0,0])
c7u = (Uc[-1,-1,-1] - Uc[0,-1,-1] - Uc[-1,0,-1] - Uc[-1,-1,0] + Uc[-1,0,0] + Uc[0,0,-1] + Uc[0,-1,0] - Uc[0,0,0])
c0v = (Vc[0,0,0])
c1v = (Vc[-1,0,0] - Vc[0,0,0])
c2v = (Vc[0,-1,0] - Vc[0,0,0])
c3v = (Vc[0,0,-1] - Vc[0,0,0])
c4v = (Vc[-1,-1,0] - Vc[0,-1,0] - Vc[-1,0,0] + Vc[0,0,0])
c5v = (Vc[0,-1,-1] - Vc[0,0,-1] - Vc[0,-1,0] + Vc[0,0,0])
c6v = (Vc[-1,0,-1] - Vc[0,0,-1] - Vc[-1,0,0] + Vc[0,0,0])
c7v = (Vc[-1,-1,-1] - Vc[0,-1,-1] - Vc[-1,0,-1] - Vc[-1,-1,0] + Vc[-1,0,0] + Vc[0,0,-1] + Vc[0,-1,0] - Vc[0,0,0])
c0w = (Wc[0,0,0])
c1w = (Wc[-1,0,0] - Wc[0,0,0])
c2w = (Wc[0,-1,0] - Wc[0,0,0])
c3w = (Wc[0,0,-1] - Wc[0,0,0])
c4w = (Wc[-1,-1,0] - Wc[0,-1,0] - Wc[-1,0,0] + Wc[0,0,0])
c5w = (Wc[0,-1,-1] - Wc[0,0,-1] - Wc[0,-1,0] + Wc[0,0,0])
c6w = (Wc[-1,0,-1] - Wc[0,0,-1] - Wc[-1,0,0] + Wc[0,0,0])
c7w = (Wc[-1,-1,-1] - Wc[0,-1,-1] - Wc[-1,0,-1] - Wc[-1,-1,0] + Wc[-1,0,0] + Wc[0,0,-1] + Wc[0,-1,0] - Wc[0,0,0])
newx[idx,idy,idz] = c0u + c1u * dx + c2u * dy + c3u * dz + c4u * dx * dy + c5u * dy * dz + c6u * dz * dx + c7u * dx * dy * dz
newy[idx,idy,idz] = c0v + c1v * dx + c2v * dy + c3v * dz + c4v * dx * dy + c5v * dy * dz + c6v * dz * dx + c7v * dx * dy * dz
newz[idx,idy,idz] = c0w + c1w * dx + c2w * dy + c3w * dz + c4w * dx * dy + c5w * dy * dz + c6w * dz * dx + c7w * dx * dy * dz
return newx, newy, newz
def refine_mesh(
x, y, z, ref_x = 10, ref_y = 10, ref_z = 1, regular_mesh=False
):
Nx, Ny, Nz = x.shape
if regular_mesh:
min_x = np.min(x)
min_y = np.min(y)
max_x = np.max(x)
max_y = np.max(y)
min_z = np.min(z)
max_z = np.max(z)
newx, newy, newz = np.meshgrid(
np.linspace(min_x, max_x, num=Nx * ref_x, endpoint=True),
np.linspace(min_y, max_y, num=Ny * ref_y, endpoint=True),
np.linspace(min_z, max_z, num=Nz * ref_z, endpoint=True),
indexing='ij'
)
else:
newx, newy, newz = __irregular_mesh_refine(x, y, z, ref_x, ref_y, ref_z)
return newx.astype(x.dtype), newy.astype(x.dtype), newz.astype(x.dtype)
def particle_simulator(
filenames: str,
x: np.ndarray,
y: np.ndarray,
z: np.ndarray,
dt: float,
output_filename: str,
upscale: int = 10,
make_2d_simulation: bool = False,
refinement_parameters: Tuple[int, int, int] = (1, 1, 1),
write_all_time_steps: bool = True,
number_of_time_steps=-1,
initial_time_step=0,
):
comm = MPI.COMM_WORLD
my_rank = comm.rank
total_ranks = comm.size
stream = cuda.default_stream()
print("Creating output HDF5 files...")
h5Out = h5py.File(output_filename, "w", driver='mpio', comm=MPI.COMM_WORLD)
#filenames = sorted(filenames)
U, V, W = read_UVW(filenames[0], gen_2d=make_2d_simulation)
newx, newy, newz = refine_mesh(
x, y, z, refinement_parameters[0], refinement_parameters[1], refinement_parameters[2]
)
Nx, Ny, Nz = newy.shape
TotalElements = Nx * Ny * Nz
localN = -(TotalElements // -total_ranks)
MyIndexList = [ii for ii in range(my_rank*localN, min((my_rank+1)*localN, TotalElements))]
print(f" * Rank {my_rank} to process {len(MyIndexList)} particles out of {TotalElements} in the range: [{MyIndexList[0]}, {MyIndexList[-1]})")
print(f"Allocating HDF5 datasets for {TotalElements} particles...")
sys.stdout.flush()
h5Out.create_dataset(
f"refined_x",
data = newx
)
h5Out.create_dataset(
f"refined_y",
data = newy
)
h5Out.create_dataset(
f"refined_z",
data = newz
)
filenames = filenames[initial_time_step:(initial_time_step+number_of_time_steps)]
if write_all_time_steps:
length_of_files = len(filenames) + 1
else:
length_of_files = 2
h5Out.create_dataset(
f"Particle_xyz",
shape=(length_of_files, 3, TotalElements),
dtype=REAL_NP,
)
#h5Out.flush()
timestep = 0
write_particles_to_file(
h5Out,
newx.ravel()[MyIndexList[0]:MyIndexList[-1]],
newy.ravel()[MyIndexList[0]:MyIndexList[-1]],
newz.ravel()[MyIndexList[0]:MyIndexList[-1]],
timestep,
MyIndexList
)
with stream.auto_synchronize():
d_U = cuda.to_device(np.ascontiguousarray(U), stream)
d_V = cuda.to_device(np.ascontiguousarray(V), stream)
d_W = cuda.to_device(np.ascontiguousarray(W), stream)
d_x = cuda.to_device(np.ascontiguousarray(x), stream)
d_y = cuda.to_device(np.ascontiguousarray(y), stream)
d_z = cuda.to_device(np.ascontiguousarray(z), stream)
d_U0 = cuda.device_array(U.shape, dtype=REAL_NP, stream=stream)
d_V0 = cuda.device_array(V.shape, dtype=REAL_NP, stream=stream)
d_W0 = cuda.device_array(W.shape, dtype=REAL_NP, stream=stream)
d_Un = cuda.device_array(U.shape, dtype=REAL_NP, stream=stream)
d_Vn = cuda.device_array(V.shape, dtype=REAL_NP, stream=stream)
d_Wn = cuda.device_array(W.shape, dtype=REAL_NP, stream=stream)
print("Initializing the simulation and allocating additional arrays...")
xp, yp, zp = particle_first_step(
d_U,
d_V,
d_W,
d_x,
d_y,
d_z,
dt/upscale,
MyIndexList,
step_particles_euler,
make_2d_simulation,
newx,
newy,
newz,
stream
)
timestep += 1
if write_all_time_steps:
write_particles_to_file(h5Out, xp, yp, zp, timestep, MyIndexList)
reader = lambda filename: read_UVW(filename, gen_2d=make_2d_simulation)
with ProgressBar(max_value=len(filenames)) as bar, Executor(1) as pool:
FRACTION = 1./upscale
TIMER_LEN = len(filenames[1:]) - 1
for ii, (U, V, W) in enumerate(pool.map(read_UVW, filenames[1:])):
if (ii % TIMER_LEN) == 0:
gc.collect()
bar.update(ii)
with stream.auto_synchronize():
d_U0, d_U = d_U, d_U0
d_V0, d_V = d_V, d_V0
d_W0, d_W = d_W, d_W0
d_U.copy_to_device(np.ascontiguousarray(U), stream)
d_V.copy_to_device(np.ascontiguousarray(V), stream)
d_W.copy_to_device(np.ascontiguousarray(W), stream)
for N in range(1, upscale):
interp_UVW_flat[BLOCKS_PER_GRID, THREADS_PER_BLOCK](
d_U0.reshape(-1), d_V0.reshape(-1), d_W0.reshape(-1),
d_U.reshape(-1), d_V.reshape(-1), d_W.reshape(-1),
d_Un.reshape(-1), d_Vn.reshape(-1), d_Wn.reshape(-1),
dt, FRACTION, N
)
xp, yp, zp = particle_update_velocities(
d_Un, d_Vn, d_Wn, d_x, d_y, d_z, dt/upscale, xp, yp, zp, step_particles_euler, make_2d_simulation, stream
)
#bar.update(ii)
xp, yp, zp = particle_update_velocities(
d_U, d_V, d_W, d_x, d_y, d_z, dt/upscale, xp, yp, zp, step_particles_euler, make_2d_simulation, stream
)
timestep += 1
if write_all_time_steps:
write_particles_to_file(h5Out, xp, yp, zp, timestep, MyIndexList)
if not write_all_time_steps:
write_particles_to_file(h5Out, xp, yp, zp, 1, MyIndexList)
bar.update(ii+1)
h5Out.close()
return xp, yp, zp
@cuda.jit(fastmath=FAST_MATH, device=True, inline=True)
def power_iteration_3d(A, b_k, b_k1):
b_k[0] = 0.801784
b_k[1] = 0.534522
b_k[2] = -0.267261
bkp_0 = b_k[0]
bkp_1 = b_k[1]
bkp_2 = b_k[2]
difference = 100
while difference > 1e-6:
b_k1[0] = A[0, 0] * b_k[0] + A[0, 1] * b_k[1] + A[0, 2] * b_k[2]
b_k1[1] = A[1, 0] * b_k[0] + A[1, 1] * b_k[1] + A[1, 2] * b_k[2]
b_k1[2] = A[2, 0] * b_k[0] + A[2, 1] * b_k[1] + A[2, 2] * b_k[2]
b_k1_norm_inv = 1./sqrt(b_k1[0] * b_k1[0] + b_k1[1] * b_k1[1] + b_k1[2] * b_k1[2])
bkp_0 = b_k[0]
bkp_1 = b_k[1]
bkp_2 = b_k[2]
b_k[0] = b_k1[0] * b_k1_norm_inv
b_k[1] = b_k1[1] * b_k1_norm_inv
b_k[2] = b_k1[2] * b_k1_norm_inv
difference = fsqrt_rn((bkp_0 - b_k[0])*(bkp_0 - b_k[0]) + (bkp_1 - b_k[1])*(bkp_1 - b_k[1]) + (bkp_2 - b_k[2])*(bkp_2 - b_k[2]))
rho = (b_k1[0]* b_k[0] + b_k1[1]* b_k[1] + b_k1[2] * b_k[2]) / (b_k[0]* b_k[0] + b_k[1]* b_k[1] + b_k[2] * b_k[2])
return rho
@cuda.jit(fastmath=FAST_MATH, device=True, inline=True)
def power_iteration_2d(A, b_k, b_k1):
# 0.81901029, 0.57377882
b_k[0] = 0.81901029
b_k[1] = 0.57377882
rho_k = 1024.
for _ in range(100000):
b_k1[0] = A[0, 0] * b_k[0] + A[0, 1] * b_k[1]
b_k1[1] = A[1, 0] * b_k[0] + A[1, 1] * b_k[1]
b_k1_norm_inv = 1./sqrt(b_k1[0] * b_k1[0] + b_k1[1] * b_k1[1])
b_k[0] = b_k1[0] * b_k1_norm_inv
b_k[1] = b_k1[1] * b_k1_norm_inv
rho = (b_k1[0]* b_k[0] + b_k1[1]* b_k[1]) / (b_k[0]* b_k[0] + b_k[1]* b_k[1])
if abs(rho - rho_k) < 1.192093e-07:
break
rho_k = rho
return rho
@cuda.jit(fastmath=FAST_MATH, device=True, inline=True)
def device_transposed_matmul_and_make_symmetric_2d(J, C):
# C = J.T @ J
for ii in range(2):
for jj in range(2):
C[ii,jj] = REAL_CP(0.)
for kk in range(2):
C[ii,jj] += J[kk,ii] * J[kk,jj]
# C = (C + C.T)/2.
for ii in range(2):
for jj in range(ii, 2):
C[jj,ii] = REAL_CP(0.5) * (C[ii,jj] + C[jj,ii])
C[ii,jj] = C[jj,ii]
return C
@cuda.jit(fastmath=FAST_MATH, device=True, inline=True)
def device_transposed_matmul_and_make_symmetric_3d(J, C):
# C = J.T @ J
for ii in range(3):
for jj in range(3):
C[ii,jj] = REAL_CP(0.)
for kk in range(3):
C[ii,jj] += J[kk,ii] * J[kk,jj]
# C = (C + C.T)/2.
for ii in range(3):
for jj in range(ii, 3):
C[jj,ii] = REAL_CP(0.5) * (C[ii,jj] + C[jj,ii])
C[ii,jj] = C[jj,ii]
return C
@cuda.jit(fastmath=FAST_MATH)
def calculate_particle_ftle_and_fsle(xp0, yp0, zp0, xp1, yp1, zp1, ftle, fsle, T):
EPS = REAL_CP(1.192093e-07)
Nx, Ny, Nz = xp0.shape
dz = abs(zp0[0,0,1] - zp0[0,0,0])
sp0 = xp0 #np.zeros_like(xp0)
np0 = yp0 #np.zeros_like(yp0)
T_inv = REAL_CP(REAL_CP(1.)/REAL_CP(T))
global_idx, global_idy, global_idz = cuda.grid(3)
gridDimX, gridDimY, gridDimZ = cuda.gridsize(3)
distance_mean_factor = REAL_CP(0.038461538461538)
J = cuda.local.array((3, 3), REAL_CP)
_C = cuda.local.array((3, 3), REAL_CP)
b_k = cuda.local.array((3,), REAL_CP)
b_k1 = cuda.local.array((3,), REAL_CP)
for ii in range(global_idx, Nx, gridDimX):
for jj in range(global_idy, Ny, gridDimY):
for kk in range(global_idz, Nz, gridDimZ):
# X Derivatives
if ii == 0:
J[0, 0] = (xp1[ii+1,jj,kk] - xp1[ii,jj,kk]) / (sp0[ii+1,jj,kk] - sp0[ii,jj,kk] + EPS)
J[1, 0] = (yp1[ii+1,jj,kk] - yp1[ii,jj,kk]) / (sp0[ii+1,jj,kk] - sp0[ii,jj,kk] + EPS)
J[2, 0] = (zp1[ii+1,jj,kk] - zp1[ii,jj,kk]) / (sp0[ii+1,jj,kk] - sp0[ii,jj,kk] + EPS)
elif ii == Nx - 1:
J[0, 0] = (xp1[ii,jj,kk] - xp1[ii-1,jj,kk]) / (sp0[ii,jj,kk] - sp0[ii-1,jj,kk] + EPS)
J[1, 0] = (yp1[ii,jj,kk] - yp1[ii-1,jj,kk]) / (sp0[ii,jj,kk] - sp0[ii-1,jj,kk] + EPS)
J[2, 0] = (zp1[ii,jj,kk] - zp1[ii-1,jj,kk]) / (sp0[ii,jj,kk] - sp0[ii-1,jj,kk] + EPS)
else:
J[0, 0] = (xp1[ii+1,jj,kk] - xp1[ii-1,jj,kk]) / (sp0[ii+1,jj,kk] - sp0[ii-1,jj,kk] + EPS)
J[1, 0] = (yp1[ii+1,jj,kk] - yp1[ii-1,jj,kk]) / (sp0[ii+1,jj,kk] - sp0[ii-1,jj,kk] + EPS)
J[2, 0] = (zp1[ii+1,jj,kk] - zp1[ii-1,jj,kk]) / (sp0[ii+1,jj,kk] - sp0[ii-1,jj,kk] + EPS)
# Y Derivatives
if jj == 0:
J[0, 1] = (xp1[ii,jj+1,kk] - xp1[ii,jj,kk]) / (np0[ii,jj+1,kk] - np0[ii,jj,kk] + EPS)
J[1, 1] = (yp1[ii,jj+1,kk] - yp1[ii,jj,kk]) / (np0[ii,jj+1,kk] - np0[ii,jj,kk] + EPS)
J[2, 1] = (zp1[ii,jj+1,kk] - zp1[ii,jj,kk]) / (np0[ii,jj+1,kk] - np0[ii,jj,kk] + EPS)
elif jj == Ny - 1:
J[0, 1] = (xp1[ii,jj,kk] - xp1[ii,jj-1,kk]) / (np0[ii,jj,kk] - np0[ii,jj-1,kk] + EPS)
J[1, 1] = (yp1[ii,jj,kk] - yp1[ii,jj-1,kk]) / (np0[ii,jj,kk] - np0[ii,jj-1,kk] + EPS)
J[2, 1] = (zp1[ii,jj,kk] - zp1[ii,jj-1,kk]) / (np0[ii,jj,kk] - np0[ii,jj-1,kk] + EPS)
else:
h1 = (np0[ii,jj+1,kk] - np0[ii,jj,kk])
h2 = (np0[ii,jj,kk] - np0[ii,jj-1,kk])
alpha = h1 / h2
dy = h1 * (1. + alpha) + EPS
J[0, 1] = (xp1[ii,jj+1,kk] - alpha**2 * xp1[ii,jj-1,kk] - (1 - alpha**2) * xp1[ii,jj,kk]) / dy
J[1, 1] = (yp1[ii,jj+1,kk] - alpha**2 * yp1[ii,jj-1,kk] - (1 - alpha**2) * yp1[ii,jj,kk]) / dy
J[2, 1] = (zp1[ii,jj+1,kk] - alpha**2 * zp1[ii,jj-1,kk] - (1 - alpha**2) * zp1[ii,jj,kk]) / dy
# Z Derivatives
if kk == 0:
J[0, 2] = (xp1[ii,jj,1] - xp1[ii,jj,Nz - 1]) / (2 * dz + EPS)
J[1, 2] = (yp1[ii,jj,1] - yp1[ii,jj,Nz - 1]) / (2 * dz + EPS)
J[2, 2] = (zp1[ii,jj,kk+1] - zp1[ii,jj,kk]) / (dz + EPS)
elif kk == Nz - 1:
J[0, 2] = (xp1[ii,jj,0] - xp1[ii,jj,kk-1]) / (2 * dz + EPS)
J[1, 2] = (yp1[ii,jj,0] - yp1[ii,jj,kk-1]) / (2 * dz + EPS)
J[2, 2] = (zp1[ii,jj,kk] - zp1[ii,jj,kk-1]) / (dz + EPS)
else:
J[0, 2] = (xp1[ii,jj,kk+1] - xp1[ii,jj,kk-1]) / (2 * dz + EPS)
J[1, 2] = (yp1[ii,jj,kk+1] - yp1[ii,jj,kk-1]) / (2 * dz + EPS)
J[2, 2] = (zp1[ii,jj,kk+1] - zp1[ii,jj,kk-1]) / (2 * dz + EPS)
if (0 < ii) and (ii < Nx - 1) and (0 < jj) and (jj < Ny - 1) and (0 < kk) and (kk < Nz - 1):
for _i in range(-1, 2):
for _j in range(-1, 2):
for _k in range(-1, 2):
if (_i != 0) or (_j != 0) or (_k != 0):
d0 = fsqrt_rn(
(xp0[ii+_i,jj+_j,kk+_k] - xp0[ii,jj,kk])*(xp0[ii+_i,jj+_j,kk+_k] - xp0[ii,jj,kk]) +
(yp0[ii+_i,jj+_j,kk+_k] - yp0[ii,jj,kk])*(yp0[ii+_i,jj+_j,kk+_k] - yp0[ii,jj,kk]) +
(zp0[ii+_i,jj+_j,kk+_k] - zp0[ii,jj,kk])*(zp0[ii+_i,jj+_j,kk+_k] - zp0[ii,jj,kk])
)
d1 = fsqrt_rn(
(xp1[ii+_i,jj+_j,kk+_k] - xp1[ii,jj,kk])*(xp1[ii+_i,jj+_j,kk+_k] - xp1[ii,jj,kk]) +
(yp1[ii+_i,jj+_j,kk+_k] - yp1[ii,jj,kk])*(yp1[ii+_i,jj+_j,kk+_k] - yp1[ii,jj,kk]) +
(zp1[ii+_i,jj+_j,kk+_k] - zp1[ii,jj,kk])*(zp1[ii+_i,jj+_j,kk+_k] - zp1[ii,jj,kk])
)
fsle[ii, jj, kk] += distance_mean_factor * T_inv * fast_logf(d1 / d0)
_C = device_transposed_matmul_and_make_symmetric_3d(J, _C)
ftle[ii, jj, kk] = fast_logf( fsqrt_rn( power_iteration_3d(_C, b_k, b_k1) )) * T_inv
@cuda.jit(fastmath=FAST_MATH)
def calculate_particle_ftle_2d(xp0, yp0, zp0, xp1, yp1, zp1, C, N, dt):
EPS = REAL_CP(1e-6)
Nx, Ny, Nz = xp0.shape
sp0 = xp0 #np.zeros_like(xp0)
np0 = yp0 #np.zeros_like(yp0)
global_idx, global_idy = cuda.grid(2)
gridDimX, gridDimY = cuda.gridsize(2) #cuda.gridDim.x * cuda.blockDim.x
#gridDimY = #cuda.gridDim.y * cuda.blockDim.y
T = (N * dt)
kk = 0
J = cuda.local.array((2, 2), REAL_CP)
_C = cuda.local.array((2, 2), REAL_CP)
for ii in range(global_idx, Nx, gridDimX):
for jj in range(global_idy, Ny, gridDimY):
# X Derivatives
if ii == 0:
J[0, 0] = (xp1[ii+1,jj,kk] - xp1[ii,jj,kk]) / (sp0[ii+1,jj,kk] - sp0[ii,jj,kk] + EPS)
J[1, 0] = (yp1[ii+1,jj,kk] - yp1[ii,jj,kk]) / (sp0[ii+1,jj,kk] - sp0[ii,jj,kk] + EPS)
elif ii == Nx - 1:
J[0, 0] = (xp1[ii,jj,kk] - xp1[ii-1,jj,kk]) / (sp0[ii,jj,kk] - sp0[ii-1,jj,kk] + EPS)
J[1, 0] = (yp1[ii,jj,kk] - yp1[ii-1,jj,kk]) / (sp0[ii,jj,kk] - sp0[ii-1,jj,kk] + EPS)
else:
J[0, 0] = (xp1[ii+1,jj,kk] - xp1[ii-1,jj,kk]) / (sp0[ii+1,jj,kk] - sp0[ii-1,jj,kk] + EPS)
J[1, 0] = (yp1[ii+1,jj,kk] - yp1[ii-1,jj,kk]) / (sp0[ii+1,jj,kk] - sp0[ii-1,jj,kk] + EPS)
# Y Derivatives
if jj == 0:
J[0, 1] = (xp1[ii,jj+1,kk] - xp1[ii,jj,kk]) / (np0[ii,jj+1,kk] - np0[ii,jj,kk] + EPS)
J[1, 1] = (yp1[ii,jj+1,kk] - yp1[ii,jj,kk]) / (np0[ii,jj+1,kk] - np0[ii,jj,kk] + EPS)
elif jj == Ny - 1:
J[0, 1] = (xp1[ii,jj,kk] - xp1[ii,jj-1,kk]) / (np0[ii,jj,kk] - np0[ii,jj-1,kk] + EPS)
J[1, 1] = (yp1[ii,jj,kk] - yp1[ii,jj-1,kk]) / (np0[ii,jj,kk] - np0[ii,jj-1,kk] + EPS)
else:
h1 = (np0[ii,jj+1,kk] - np0[ii,jj,kk])
h2 = (np0[ii,jj,kk] - np0[ii,jj-1,kk])
alpha = h1 / h2
dy = h1 * (1. + alpha) + EPS
J[0, 1] = (xp1[ii,jj+1,kk] - alpha**2 * xp1[ii,jj-1,kk] - (1 - alpha**2) * xp1[ii,jj,kk]) / dy
J[1, 1] = (yp1[ii,jj+1,kk] - alpha**2 * yp1[ii,jj-1,kk] - (1 - alpha**2) * yp1[ii,jj,kk]) / dy
_C = device_transposed_matmul_and_make_symmetric_2d(J, _C)
for i in range(2):
for j in range(2):
C[ii, jj, 0, i, j] = _C[i,j]
def write_viz_files(xp0, yp0, zp0, xp1, yp1, zp1, ftle, fsle, N, filename):
filename_ftle = filename + f".ftle"
filename_particles = filename + f".particles.{N}"
gridToVTK(filename_ftle, xp0, yp0, zp0, pointData={'FTLE': ftle, 'FSLE': fsle})
pointsToVTK(
filename_particles,
np.array(xp1.reshape((-1))),
np.array(yp1.reshape((-1))),
np.array(zp1.reshape((-1)))
)
return
@njit(parallel=True, fastmath=False, nogil=True)
def correct_ftle(U, ftle):
Nx, Ny, Nz = U.shape
for ii in prange(1, Nx-1):
for jj in range(1, Ny - 1):
for kk in range(Nz):
if np.abs(ftle[ii,jj,kk]) > 0.5:
ftle[ii-1:ii+1, jj-1:jj+2, kk] = 0.0
return ftle
def process_multiple_parallel_final_particle_info(filename, dt, output_file, viz_filename, x, y, z, make_2d_simulation = False, NFlowFields = None):
with h5py.File(filename, 'r') as f, \
h5py.File(output_file, 'w') as h5Out:
xyz_particle = f["Particle_xyz"]
x = f["refined_x"][...]
y = f["refined_y"][...]
z = f["refined_z"][...]
Nx, Ny, Nz = x.shape
NTimeSteps = xyz_particle.shape[0]
xp0 = xyz_particle[0, 0, :].reshape((Nx, Ny, Nz))
yp0 = xyz_particle[0, 1, :].reshape((Nx, Ny, Nz))
zp0 = xyz_particle[0, 2, :].reshape((Nx, Ny, Nz))
h5Out.create_dataset(
f"FTLE",
shape=(NTimeSteps-1, Nx, Ny, Nz),
dtype=REAL_NP,
)
h5Out.create_dataset(
f"FSLE",
shape=(NTimeSteps-1, Nx, Ny, Nz),
dtype=REAL_NP,
)
FTLE = h5Out['FTLE']
FSLE = h5Out['FSLE']
with ProgressBar(max_value=len(list(range(1, NTimeSteps))) + 1) as bar:
iteration = 0
for N in range(1,NTimeSteps):
bar.update(iteration)
sys.stdout.flush()
xp1 = xyz_particle[N, 0, :].reshape((Nx, Ny, Nz))
yp1 = xyz_particle[N, 1, :].reshape((Nx, Ny, Nz))
zp1 = xyz_particle[N, 2, :].reshape((Nx, Ny, Nz))
if make_2d_simulation:
C = cuda.device_array((Nx, Ny, 1, 2, 2), dtype=REAL_NP)
calculate_ftle = calculate_particle_ftle_2d
else:
ftle = cuda.device_array((Nx, Ny, Nz), dtype=REAL_NP)
fsle = cuda.device_array((Nx, Ny, Nz), dtype=REAL_NP)
calculate_ftle_and_fsle = calculate_particle_ftle_and_fsle
T = REAL_NP(1.0 / (N * NFlowFields * dt))
calculate_ftle_and_fsle[BLOCKS_PER_GRID_3D, THREADS_PER_BLOCK_3D](xp0, yp0, zp0, xp1, yp1, zp1, ftle, fsle, T)
ftle = np.array(ftle)
fsle = np.array(fsle)
ftle = np.nan_to_num(ftle, nan=0.0, posinf=0.0, neginf=0.0)
fsle = np.nan_to_num(fsle, nan=0.0, posinf=0.0, neginf=0.0)
if T > 0:
ftle -= np.min(ftle)
ftle /= np.max(ftle)
fsle -= np.min(fsle)
fsle /= np.max(fsle)
else:
ftle -= np.max(ftle)
ftle /= abs(np.min(ftle))
fsle -= np.max(fsle)
fsle /= abs(np.min(fsle))
ftle[:, -3:, :] = ftle[:, -3, np.newaxis, :]
ftle[:, :, -3:] = ftle[:, :, np.newaxis, -3]
ftle[:, :, :3] = ftle[:, :, np.newaxis, 3]
fsle[:, -3:, :] = fsle[:, -3, np.newaxis, :]
fsle[:, :, -3:] = fsle[:, :, np.newaxis, -3]
fsle[:, :, :3] = fsle[:, :, np.newaxis, 3]
FTLE[N-1,...] = ftle
FSLE[N-1,...] = fsle
write_viz_files(x, y, z, xp1, yp1, zp1, ftle, fsle, int(N*NFlowFields), viz_filename)
iteration += 1
bar.update(iteration)
sys.stdout.flush()
return
if __name__ == "__main__":
select_gpu()
RUNSIM = True
CALCULATE_FTLE = True
NFIELDS = 11
UPSCALE = 40 #20 # 8 additional flow fields between every real field.
# Set this value to 1 to avoid upscaling.
DNS_TIMESTEP = 2.00E-03 # Simulation timestep
SAMPLE_RATE = 10 # Simulation sampling rate (every how many timesteps is the flow sampled)