def __init__(self, \
gpu_ctx, \
eta0, hu0, hv0, H, \
nx, ny, \
dx, dy, dt, \
g, f, r, \
angle=np.array([[0]], dtype=np.float32), \
t=0.0, \
theta=1.3, rk_order=2, \
coriolis_beta=0.0, \
max_wind_direction_perturbation = 0, \
wind_stress=WindStress.WindStress(), \
boundary_conditions=Common.BoundaryConditions(), \
boundary_conditions_data=Common.BoundaryConditionsData(), \
small_scale_perturbation=False, \
small_scale_perturbation_amplitude=None, \
small_scale_perturbation_interpolation_factor = 1, \
model_time_step=None,
reportGeostrophicEquilibrium=False, \
use_lcg=False, \
write_netcdf=False, \
comm=None, \
netcdf_filename=None, \
ignore_ghostcells=False, \
courant_number=0.8, \
offset_x=0, offset_y=0, \
flux_slope_eps = 1.0e-1, \
desingularization_eps = 1.0e-1, \
depth_cutoff = 1.0e-5, \
block_width=32, block_height=8, num_threads_dt=256,
block_width_model_error=16, block_height_model_error=16):
"""
Initialization routine
eta0: Initial deviation from mean sea level incl ghost cells, (nx+2)*(ny+2) cells
hu0: Initial momentum along x-axis incl ghost cells, (nx+1)*(ny+2) cells
hv0: Initial momentum along y-axis incl ghost cells, (nx+2)*(ny+1) cells
H: Depth from equilibrium defined on cell corners, (nx+5)*(ny+5) corners
nx: Number of cells along x-axis
ny: Number of cells along y-axis
dx: Grid cell spacing along x-axis (20 000 m)
dy: Grid cell spacing along y-axis (20 000 m)
dt: Size of each timestep (90 s)
g: Gravitational accelleration (9.81 m/s^2)
f: Coriolis parameter (1.2e-4 s^1), effectively as f = f + beta*y
r: Bottom friction coefficient (2.4e-3 m/s)
angle: Angle of rotation from North to y-axis
t: Start simulation at time t
theta: MINMOD theta used the reconstructions of the derivatives in the numerical scheme
rk_order: Order of Runge Kutta method {1,2*,3}
coriolis_beta: Coriolis linear factor -> f = f + beta*(y-y_0)
max_wind_direction_perturbation: Large-scale model error emulation by per-time-step perturbation of wind direction by +/- max_wind_direction_perturbation (degrees)
wind_stress: Wind stress parameters
boundary_conditions: Boundary condition object
small_scale_perturbation: Boolean value for applying a stochastic model error
small_scale_perturbation_amplitude: Amplitude (q0 coefficient) for model error
small_scale_perturbation_interpolation_factor: Width factor for correlation in model error
model_time_step: The size of a data assimilation model step (default same as dt)
reportGeostrophicEquilibrium: Calculate the Geostrophic Equilibrium variables for each superstep
use_lcg: Use LCG as the random number generator. Default is False, which means using curand.
write_netcdf: Write the results after each superstep to a netCDF file
comm: MPI communicator
desingularization_eps: Used for desingularizing hu/h
flux_slope_eps: Used for setting zero flux for symmetric Riemann fan
depth_cutoff: Used for defining dry cells
netcdf_filename: Use this filename. (If not defined, a filename will be generated by SimWriter.)
"""
self.logger = logging.getLogger(__name__)
assert( rk_order < 4 or rk_order > 0 ), "Only 1st, 2nd and 3rd order Runge Kutta supported"
if (rk_order == 3):
assert(r == 0.0), "3rd order Runge Kutta supported only without friction"
# Sort out internally represented ghost_cells in the presence of given
# boundary conditions
ghost_cells_x = 2
ghost_cells_y = 2
#Coriolis at "first" cell
x_zero_reference_cell = ghost_cells_x
y_zero_reference_cell = ghost_cells_y # In order to pass it to the super constructor
# Boundary conditions
self.boundary_conditions = boundary_conditions
if (boundary_conditions.isSponge()):
nx = nx + boundary_conditions.spongeCells[1] + boundary_conditions.spongeCells[3] - 2*ghost_cells_x
ny = ny + boundary_conditions.spongeCells[0] + boundary_conditions.spongeCells[2] - 2*ghost_cells_y
x_zero_reference_cell += boundary_conditions.spongeCells[3]
y_zero_reference_cell += boundary_conditions.spongeCells[2]
#Compensate f for reference cell (first cell in internal of domain)
north = np.array([np.sin(angle[0,0]), np.cos(angle[0,0])])
f = f - coriolis_beta * (x_zero_reference_cell*dx*north[0] + y_zero_reference_cell*dy*north[1])
x_zero_reference_cell = 0
y_zero_reference_cell = 0
A = None
self.max_wind_direction_perturbation = max_wind_direction_perturbation
super(CDKLM16, self).__init__(gpu_ctx, \
nx, ny, \
ghost_cells_x, \
ghost_cells_y, \
dx, dy, dt, \
g, f, r, A, \
t, \
theta, rk_order, \
coriolis_beta, \
y_zero_reference_cell, \
wind_stress, \
write_netcdf, \
ignore_ghostcells, \
offset_x, offset_y, \
comm, \
block_width, block_height)
# Index range for interior domain (north, east, south, west)
# so that interior domain of eta is
# eta[self.interior_domain_indices[2]:self.interior_domain_indices[0], \
# self.interior_domain_indices[3]:self.interior_domain_indices[1] ]
self.interior_domain_indices = np.array([-2,-2,2,2])
self._set_interior_domain_from_sponge_cells()
defines={'block_width': block_width, 'block_height': block_height,
'KPSIMULATOR_DESING_EPS': str(desingularization_eps)+'f',
'KPSIMULATOR_FLUX_SLOPE_EPS': str(flux_slope_eps)+'f',
'KPSIMULATOR_DEPTH_CUTOFF': str(depth_cutoff)+'f'}
#Get kernels
self.kernel = gpu_ctx.get_kernel("CDKLM16_kernel.cu",
defines=defines,
compile_args={ # default, fast_math, optimal
'options' : ["--ftz=true", # false, true, true
"--prec-div=false", # true, false, false,
"--prec-sqrt=false", # true, false, false
"--fmad=false"] # true, true, false
#'options': ["--use_fast_math"]
#'options': ["--generate-line-info"],
#nvcc_options=["--maxrregcount=39"],
#'arch': "compute_50",
#'code': "sm_50"
},
jit_compile_args={
#jit_options=[(cuda.jit_option.MAX_REGISTERS, 39)]
}
)
# Get CUDA functions and define data types for prepared_{async_}call()
self.cdklm_swe_2D = self.kernel.get_function("cdklm_swe_2D")
self.cdklm_swe_2D.prepare("iiffffffffiiPiPiPiPiPiPiPiPiffi")
self.update_wind_stress(self.kernel, self.cdklm_swe_2D)
# CUDA functions for finding max time step size:
self.num_threads_dt = num_threads_dt
self.num_blocks_dt = np.int32(self.global_size[0]*self.global_size[1])
self.update_dt_kernels = gpu_ctx.get_kernel("max_dt.cu",
defines={'block_width': block_width,
'block_height': block_height,
'NUM_THREADS': self.num_threads_dt})
self.per_block_max_dt_kernel = self.update_dt_kernels.get_function("per_block_max_dt")
self.per_block_max_dt_kernel.prepare("iifffPiPiPiPifPi")
self.max_dt_reduction_kernel = self.update_dt_kernels.get_function("max_dt_reduction")
self.max_dt_reduction_kernel.prepare("iPP")
# Bathymetry
self.bathymetry = Common.Bathymetry(gpu_ctx, self.gpu_stream, nx, ny, ghost_cells_x, ghost_cells_y, H, boundary_conditions)
# Adjust eta for possible dry states
Hm = self.downloadBathymetry()[1]
eta0 = np.maximum(eta0, -Hm)
# Create data by uploading to device
self.gpu_data = Common.SWEDataArakawaA(self.gpu_stream, nx, ny, ghost_cells_x, ghost_cells_y, eta0, hu0, hv0)
# Allocate memory for calculating maximum timestep
host_dt = np.zeros((self.global_size[1], self.global_size[0]), dtype=np.float32)
self.device_dt = Common.CUDAArray2D(self.gpu_stream, self.global_size[0], self.global_size[1],
0, 0, host_dt)
host_max_dt_buffer = np.zeros((1,1), dtype=np.float32)
self.max_dt_buffer = Common.CUDAArray2D(self.gpu_stream, 1, 1, 0, 0, host_max_dt_buffer)
self.courant_number = courant_number
## Allocating memory for geostrophical equilibrium variables
self.reportGeostrophicEquilibrium = np.int32(reportGeostrophicEquilibrium)
self.geoEq_uxpvy = None
self.geoEq_Kx = None
self.geoEq_Ly = None
if self.reportGeostrophicEquilibrium:
dummy_zero_array = np.zeros((ny+2*ghost_cells_y, nx+2*ghost_cells_x), dtype=np.float32, order='C')
self.geoEq_uxpvy = Common.CUDAArray2D(self.gpu_stream, nx, ny, ghost_cells_x, ghost_cells_y, dummy_zero_array)
self.geoEq_Kx = Common.CUDAArray2D(self.gpu_stream, nx, ny, ghost_cells_x, ghost_cells_y, dummy_zero_array)
self.geoEq_Ly = Common.CUDAArray2D(self.gpu_stream, nx, ny, ghost_cells_x, ghost_cells_y, dummy_zero_array)
self.constant_equilibrium_depth = np.max(H)
self.bc_kernel = Common.BoundaryConditionsArakawaA(gpu_ctx, \
self.nx, \
self.ny, \
ghost_cells_x, \
ghost_cells_y, \
self.boundary_conditions, \
boundary_conditions_data, \
)
# Small scale perturbation:
self.small_scale_perturbation = small_scale_perturbation
self.small_scale_model_error = None
self.small_scale_perturbation_interpolation_factor = small_scale_perturbation_interpolation_factor
if small_scale_perturbation:
if small_scale_perturbation_amplitude is None:
self.small_scale_model_error = OceanStateNoise.OceanStateNoise.fromsim(self,
interpolation_factor=small_scale_perturbation_interpolation_factor,
use_lcg=use_lcg,
block_width=block_width_model_error,
block_height=block_height_model_error)
else:
self.small_scale_model_error = OceanStateNoise.OceanStateNoise.fromsim(self,
soar_q0=small_scale_perturbation_amplitude,
interpolation_factor=small_scale_perturbation_interpolation_factor,
use_lcg=use_lcg,
block_width=block_width_model_error,
block_height=block_height_model_error)
# Data assimilation model step size
self.model_time_step = model_time_step
if model_time_step is None:
self.model_time_step = self.dt
self.total_time_steps = 0
if self.write_netcdf:
self.sim_writer = SimWriter.SimNetCDFWriter(self, filename=netcdf_filename, ignore_ghostcells=self.ignore_ghostcells, \
offset_x=self.offset_x, offset_y=self.offset_y)
#Upload data to GPU and bind to texture reference
self.angle_texref = self.kernel.get_texref("angle_tex")
self.angle_texref.set_array(cuda.np_to_array(np.ascontiguousarray(angle, dtype=np.float32), order="C"))
# Set texture parameters
self.angle_texref.set_filter_mode(cuda.filter_mode.LINEAR) #bilinear interpolation
self.angle_texref.set_address_mode(0, cuda.address_mode.CLAMP) #no indexing outside domain
self.angle_texref.set_address_mode(1, cuda.address_mode.CLAMP)
self.angle_texref.set_flags(cuda.TRSF_NORMALIZED_COORDINATES) #Use [0, 1] indexing
def __init__(self, \
gpu_ctx, \
eta0, H, hu0, hv0, \
nx, ny, \
dx, dy, dt, \
g, f=0.0, r=0.0, \
t=0.0, \
theta=1.3, use_rk2=True,
coriolis_beta=0.0, \
y_zero_reference_cell = 0, \
wind_stress=WindStress.WindStress(), \
boundary_conditions=Common.BoundaryConditions(), \
write_netcdf=False, \
comm=None, \
ignore_ghostcells=False, \
offset_x=0, offset_y=0, \
flux_slope_eps = 1.0e-1, \
depth_cutoff = 1.0e-5, \
block_width=32, block_height=16):
"""
Initialization routine
eta0: Initial deviation from mean sea level incl ghost cells, (nx+2)*(ny+2) cells
hu0: Initial momentum along x-axis incl ghost cells, (nx+1)*(ny+2) cells
hv0: Initial momentum along y-axis incl ghost cells, (nx+2)*(ny+1) cells
H: Depth from equilibrium defined on cell corners, (nx+5)*(ny+5) corners
nx: Number of cells along x-axis
ny: Number of cells along y-axis
dx: Grid cell spacing along x-axis (20 000 m)
dy: Grid cell spacing along y-axis (20 000 m)
dt: Size of each timestep (90 s)
g: Gravitational accelleration (9.81 m/s^2)
f: Coriolis parameter (1.2e-4 s^1), effectively as f = f + beta*y
r: Bottom friction coefficient (2.4e-3 m/s)
t: Start simulation at time t
theta: MINMOD theta used the reconstructions of the derivatives in the numerical scheme
use_rk2: Boolean if to use 2nd order Runge-Kutta (false -> 1st order forward Euler)
coriolis_beta: Coriolis linear factor -> f = f + beta*(y-y_0)
y_zero_reference_cell: The cell representing y_0 in the above, defined as the lower face of the cell .
wind_stress: Wind stress parameters
boundary_conditions: Boundary condition object
write_netcdf: Write the results after each superstep to a netCDF file
comm: MPI communicator
depth_cutoff: Used for defining dry cells
flux_slope_eps: Used for desingularization with dry cells
"""
ghost_cells_x = 2
ghost_cells_y = 2
y_zero_reference_cell = 2.0 + y_zero_reference_cell
# Boundary conditions
self.boundary_conditions = boundary_conditions
# Extend the computational domain if the boundary conditions
# require it
if (boundary_conditions.isSponge()):
nx = nx + boundary_conditions.spongeCells[
1] + boundary_conditions.spongeCells[3] - 2 * ghost_cells_x
ny = ny + boundary_conditions.spongeCells[
0] + boundary_conditions.spongeCells[2] - 2 * ghost_cells_y
y_zero_reference_cell = boundary_conditions.spongeCells[
2] + y_zero_reference_cell
self.use_rk2 = use_rk2
rk_order = np.int32(use_rk2 + 1)
A = None
super(KP07, self).__init__(gpu_ctx, \
nx, ny, \
ghost_cells_x, \
ghost_cells_y, \
dx, dy, dt, \
g, f, r, A, \
t, \
theta, rk_order, \
coriolis_beta, \
y_zero_reference_cell, \
wind_stress, \
write_netcdf, \
ignore_ghostcells, \
offset_x, offset_y, \
comm, \
block_width, block_height)
# Index range for interior domain (north, east, south, west)
# so that interior domain of eta is
# eta[self.interior_domain_indices[2]:self.interior_domain_indices[0], \
# self.interior_domain_indices[3]:self.interior_domain_indices[1] ]
self.interior_domain_indices = np.array([-2, -2, 2, 2])
self._set_interior_domain_from_sponge_cells()
# The ocean simulators and the swashes cases are defined on
# completely different scales. We therefore specify a different
# desingularization parameter if we run a swashes case.
# Typical values:
#ifndef SWASHES
#define KPSIMULATOR_FLUX_SLOPE_EPS 1e-1f
#define KPSIMULATOR_FLUX_SLOPE_EPS_4 1.0e-4f
#else
#define KPSIMULATOR_FLUX_SLOPE_EPS 1.0e-4f
#define KPSIMULATOR_FLUX_SLOPE_EPS_4 1.0e-16f
#endif
defines = {
'block_width': block_width,
'block_height': block_height,
'KPSIMULATOR_FLUX_SLOPE_EPS': str(flux_slope_eps) + 'f',
'KPSIMULATOR_FLUX_SLOPE_EPS_4': str(flux_slope_eps**4) + 'f',
'KPSIMULATOR_DEPTH_CUTOFF': str(depth_cutoff) + 'f'
}
#Get kernels
self.kp07_kernel = gpu_ctx.get_kernel(
"KP07_kernel.cu",
defines=defines,
compile_args={ # default, fast_math, optimal
'options': [
"--ftz=true", # false, true, true
"--prec-div=false", # true, false, false,
"--prec-sqrt=false", # true, false, false
"--fmad=false"
] # true, true, false
#'options': ["--use_fast_math"]
#'options': ["--generate-line-info"],
#nvcc_options=["--maxrregcount=39"],
#'arch': "compute_50",
#'code': "sm_50"
},
jit_compile_args={
#jit_options=[(cuda.jit_option.MAX_REGISTERS, 39)]
})
# Get CUDA functions and define data types for prepared_{async_}call()
self.swe_2D = self.kp07_kernel.get_function("swe_2D")
self.swe_2D.prepare("iifffffffffiPiPiPiPiPiPiPiPiiiiif")
self.update_wind_stress(self.kp07_kernel, self.swe_2D)
# Upload Bathymetry
self.bathymetry = Common.Bathymetry(self.gpu_ctx, self.gpu_stream, \
nx, ny, ghost_cells_x, ghost_cells_y, H, boundary_conditions)
# Adjust eta for possible dry states
Hm = self.downloadBathymetry()[1]
eta0 = np.maximum(eta0, -Hm)
#Create data by uploading to device
self.gpu_data = Common.SWEDataArakawaA(self.gpu_stream, nx, ny,
ghost_cells_x, ghost_cells_y,
eta0, hu0, hv0)
self.bc_kernel = Common.BoundaryConditionsArakawaA(gpu_ctx, \
self.nx, \
self.ny, \
ghost_cells_x, \
ghost_cells_y, \
self.boundary_conditions)
if self.write_netcdf:
self.sim_writer = SimWriter.SimNetCDFWriter(self, ignore_ghostcells=self.ignore_ghostcells, \
offset_x=self.offset_x, offset_y=self.offset_y)
def __init__(self, \
gpu_ctx, \
eta0, Hi, hu0, hv0, \
nx, ny, \
dx, dy, dt, \
g, f=0.0, r=0.0, \
t=0.0, \
theta=1.3, use_rk2=True,
coriolis_beta=0.0, \
y_zero_reference_cell = 0, \
wind_stress=WindStress.WindStress(), \
boundary_conditions=Common.BoundaryConditions(), \
write_netcdf=False, \
ignore_ghostcells=False, \
offset_x=0, offset_y=0, \
block_width=32, block_height=16):
"""
Initialization routine
eta0: Initial deviation from mean sea level incl ghost cells, (nx+2)*(ny+2) cells
hu0: Initial momentum along x-axis incl ghost cells, (nx+1)*(ny+2) cells
hv0: Initial momentum along y-axis incl ghost cells, (nx+2)*(ny+1) cells
Hi: Depth from equilibrium defined on cell corners, (nx+5)*(ny+5) corners
nx: Number of cells along x-axis
ny: Number of cells along y-axis
dx: Grid cell spacing along x-axis (20 000 m)
dy: Grid cell spacing along y-axis (20 000 m)
dt: Size of each timestep (90 s)
g: Gravitational accelleration (9.81 m/s^2)
f: Coriolis parameter (1.2e-4 s^1), effectively as f = f + beta*y
r: Bottom friction coefficient (2.4e-3 m/s)
t: Start simulation at time t
theta: MINMOD theta used the reconstructions of the derivatives in the numerical scheme
use_rk2: Boolean if to use 2nd order Runge-Kutta (false -> 1st order forward Euler)
coriolis_beta: Coriolis linear factor -> f = f + beta*(y-y_0)
y_zero_reference_cell: The cell representing y_0 in the above, defined as the lower face of the cell .
wind_stress: Wind stress parameters
boundary_conditions: Boundary condition object
write_netcdf: Write the results after each superstep to a netCDF file
"""
## After changing from (h, B) to (eta, H), several of the simulator settings used are wrong. This check will help detect that.
if ( np.sum(eta0 - Hi[:-1, :-1] > 0) > nx):
assert(False), "It seems you are using water depth/elevation h and bottom topography B, while you should use water level eta and equillibrium depth H."
ghost_cells_x = 2
ghost_cells_y = 2
y_zero_reference_cell = 2.0 + y_zero_reference_cell
# Boundary conditions
self.boundary_conditions = boundary_conditions
# Extend the computational domain if the boundary conditions
# require it
if (boundary_conditions.isSponge()):
nx = nx + boundary_conditions.spongeCells[1] + boundary_conditions.spongeCells[3] - 2*ghost_cells_x
ny = ny + boundary_conditions.spongeCells[0] + boundary_conditions.spongeCells[2] - 2*ghost_cells_y
y_zero_reference_cell = boundary_conditions.spongeCells[2] + y_zero_reference_cell
self.use_rk2 = use_rk2
rk_order = np.int32(use_rk2 + 1)
A = None
super(KP07, self).__init__(gpu_ctx, \
nx, ny, \
ghost_cells_x, \
ghost_cells_y, \
dx, dy, dt, \
g, f, r, A, \
t, \
theta, rk_order, \
coriolis_beta, \
y_zero_reference_cell, \
wind_stress, \
write_netcdf, \
ignore_ghostcells, \
offset_x, offset_y, \
block_width, block_height)
# Index range for interior domain (north, east, south, west)
# so that interior domain of eta is
# eta[self.interior_domain_indices[2]:self.interior_domain_indices[0], \
# self.interior_domain_indices[3]:self.interior_domain_indices[1] ]
self.interior_domain_indices = np.array([-2,-2,2,2])
self._set_interior_domain_from_sponge_cells()
#Get kernels
self.kp07_kernel = gpu_ctx.get_kernel("KP07_kernel.cu", defines={'block_width': block_width, 'block_height': block_height})
# Get CUDA functions and define data types for prepared_{async_}call()
self.swe_2D = self.kp07_kernel.get_function("swe_2D")
self.swe_2D.prepare("iifffffffffiPiPiPiPiPiPiPiPiiiiif")
self.update_wind_stress(self.kp07_kernel, self.swe_2D)
#Create data by uploading to device
self.gpu_data = Common.SWEDataArakawaA(self.gpu_stream, nx, ny, ghost_cells_x, ghost_cells_y, eta0, hu0, hv0)
#Bathymetry
self.bathymetry = Common.Bathymetry(self.gpu_ctx, self.gpu_stream, \
nx, ny, ghost_cells_x, ghost_cells_y, Hi, boundary_conditions)
self.bc_kernel = Common.BoundaryConditionsArakawaA(gpu_ctx, \
self.nx, \
self.ny, \
ghost_cells_x, \
ghost_cells_y, \
self.boundary_conditions)
if self.write_netcdf:
self.sim_writer = SimWriter.SimNetCDFWriter(self, ignore_ghostcells=self.ignore_ghostcells, \
offset_x=self.offset_x, offset_y=self.offset_y)
def __init__(self, \
gpu_ctx, \
eta0, hu0, hv0, H, \
nx, ny, \
dx, dy, dt, \
g, f, r, \
subsample_f=10, \
angle=np.array([[0]], dtype=np.float32), \
subsample_angle=10, \
latitude=None, \
t=0.0, \
theta=1.3, rk_order=2, \
coriolis_beta=0.0, \
max_wind_direction_perturbation = 0, \
wind_stress=WindStress.WindStress(), \
boundary_conditions=Common.BoundaryConditions(), \
boundary_conditions_data=Common.BoundaryConditionsData(), \
small_scale_perturbation=False, \
small_scale_perturbation_amplitude=None, \
small_scale_perturbation_interpolation_factor = 1, \
model_time_step=None,
reportGeostrophicEquilibrium=False, \
use_lcg=False, \
write_netcdf=False, \
comm=None, \
local_particle_id=0, \
super_dir_name=None, \
netcdf_filename=None, \
ignore_ghostcells=False, \
courant_number=0.8, \
offset_x=0, offset_y=0, \
flux_slope_eps = 1.0e-1, \
desingularization_eps = 1.0e-1, \
depth_cutoff = 1.0e-5, \
block_width=12, block_height=32, num_threads_dt=256,
block_width_model_error=16, block_height_model_error=16):
"""
Initialization routine
eta0: Initial deviation from mean sea level incl ghost cells, (nx+2)*(ny+2) cells
hu0: Initial momentum along x-axis incl ghost cells, (nx+1)*(ny+2) cells
hv0: Initial momentum along y-axis incl ghost cells, (nx+2)*(ny+1) cells
H: Depth from equilibrium defined on cell corners, (nx+5)*(ny+5) corners
nx: Number of cells along x-axis
ny: Number of cells along y-axis
dx: Grid cell spacing along x-axis (20 000 m)
dy: Grid cell spacing along y-axis (20 000 m)
dt: Size of each timestep (90 s)
g: Gravitational accelleration (9.81 m/s^2)
f: Coriolis parameter (1.2e-4 s^1), effectively as f = f + beta*y
r: Bottom friction coefficient (2.4e-3 m/s)
subsample_f: Subsample the coriolis f when creating texture by factor
angle: Angle of rotation from North to y-axis as a texture (cuda.Array) or numpy array (in radians)
subsample_angle: Subsample the angles given as input when creating texture by factor
latitude: Specify latitude. This will override any f and beta plane already set (in radians)
t: Start simulation at time t
theta: MINMOD theta used the reconstructions of the derivatives in the numerical scheme
rk_order: Order of Runge Kutta method {1,2*,3}
coriolis_beta: Coriolis linear factor -> f = f + beta*(y-y_0)
max_wind_direction_perturbation: Large-scale model error emulation by per-time-step perturbation of wind direction by +/- max_wind_direction_perturbation (degrees)
wind_stress: Wind stress parameters
boundary_conditions: Boundary condition object
small_scale_perturbation: Boolean value for applying a stochastic model error
small_scale_perturbation_amplitude: Amplitude (q0 coefficient) for model error
small_scale_perturbation_interpolation_factor: Width factor for correlation in model error
model_time_step: The size of a data assimilation model step (default same as dt)
reportGeostrophicEquilibrium: Calculate the Geostrophic Equilibrium variables for each superstep
use_lcg: Use LCG as the random number generator. Default is False, which means using curand.
write_netcdf: Write the results after each superstep to a netCDF file
comm: MPI communicator
local_particle_id: Local (for each MPI process) particle id
desingularization_eps: Used for desingularizing hu/h
flux_slope_eps: Used for setting zero flux for symmetric Riemann fan
depth_cutoff: Used for defining dry cells
super_dir_name: Directory to write netcdf files to
netcdf_filename: Use this filename. (If not defined, a filename will be generated by SimWriter.)
"""
self.logger = logging.getLogger(__name__)
assert (rk_order < 4 or rk_order > 0
), "Only 1st, 2nd and 3rd order Runge Kutta supported"
if (rk_order == 3):
assert (r == 0.0
), "3rd order Runge Kutta supported only without friction"
# Sort out internally represented ghost_cells in the presence of given
# boundary conditions
ghost_cells_x = 2
ghost_cells_y = 2
#Coriolis at "first" cell
x_zero_reference_cell = ghost_cells_x
y_zero_reference_cell = ghost_cells_y # In order to pass it to the super constructor
# Boundary conditions
self.boundary_conditions = boundary_conditions
#Compensate f for reference cell (first cell in internal of domain)
north = np.array([np.sin(angle[0, 0]), np.cos(angle[0, 0])])
f = f - coriolis_beta * (x_zero_reference_cell * dx * north[0] +
y_zero_reference_cell * dy * north[1])
x_zero_reference_cell = 0
y_zero_reference_cell = 0
A = None
self.max_wind_direction_perturbation = max_wind_direction_perturbation
super(CDKLM16, self).__init__(gpu_ctx, \
nx, ny, \
ghost_cells_x, \
ghost_cells_y, \
dx, dy, dt, \
g, f, r, A, \
t, \
theta, rk_order, \
coriolis_beta, \
y_zero_reference_cell, \
wind_stress, \
write_netcdf, \
ignore_ghostcells, \
offset_x, offset_y, \
comm, \
block_width, block_height,
local_particle_id=local_particle_id)
# Index range for interior domain (north, east, south, west)
# so that interior domain of eta is
# eta[self.interior_domain_indices[2]:self.interior_domain_indices[0], \
# self.interior_domain_indices[3]:self.interior_domain_indices[1] ]
self.interior_domain_indices = np.array([-2, -2, 2, 2])
defines = {
'block_width': block_width,
'block_height': block_height,
'KPSIMULATOR_DESING_EPS': "{:.12f}f".format(desingularization_eps),
'KPSIMULATOR_FLUX_SLOPE_EPS': "{:.12f}f".format(flux_slope_eps),
'KPSIMULATOR_DEPTH_CUTOFF': "{:.12f}f".format(depth_cutoff),
'THETA': "{:.12f}f".format(self.theta),
'RK_ORDER': int(self.rk_order),
'NX': int(self.nx),
'NY': int(self.ny),
'DX': "{:.12f}f".format(self.dx),
'DY': "{:.12f}f".format(self.dy),
'GRAV': "{:.12f}f".format(self.g),
'FRIC': "{:.12f}f".format(self.r)
}
#Get kernels
self.kernel = gpu_ctx.get_kernel(
"CDKLM16_kernel.cu",
defines=defines,
compile_args={ # default, fast_math, optimal
'options': [
"--ftz=true", # false, true, true
"--prec-div=false", # true, false, false,
"--prec-sqrt=false", # true, false, false
"--fmad=false"
] # true, true, false
#'options': ["--use_fast_math"]
#'options': ["--generate-line-info"],
#nvcc_options=["--maxrregcount=39"],
#'arch': "compute_50",
#'code': "sm_50"
},
jit_compile_args={
#jit_options=[(cuda.jit_option.MAX_REGISTERS, 39)]
})
# Get CUDA functions and define data types for prepared_{async_}call()
self.cdklm_swe_2D = self.kernel.get_function("cdklm_swe_2D")
self.cdklm_swe_2D.prepare("fiPiPiPiPiPiPiPiPiffi")
self.update_wind_stress(self.kernel, self.cdklm_swe_2D)
# CUDA functions for finding max time step size:
self.num_threads_dt = num_threads_dt
self.num_blocks_dt = np.int32(self.global_size[0] *
self.global_size[1])
self.update_dt_kernels = gpu_ctx.get_kernel("max_dt.cu",
defines={
'block_width':
block_width,
'block_height':
block_height,
'NUM_THREADS':
self.num_threads_dt
})
self.per_block_max_dt_kernel = self.update_dt_kernels.get_function(
"per_block_max_dt")
self.per_block_max_dt_kernel.prepare("iifffPiPiPiPifPi")
self.max_dt_reduction_kernel = self.update_dt_kernels.get_function(
"max_dt_reduction")
self.max_dt_reduction_kernel.prepare("iPP")
# Bathymetry
self.bathymetry = Common.Bathymetry(gpu_ctx, self.gpu_stream, nx, ny,
ghost_cells_x, ghost_cells_y, H,
boundary_conditions)
# Adjust eta for possible dry states
Hm = self.downloadBathymetry()[1]
eta0 = np.maximum(eta0, -Hm)
# Create data by uploading to device
self.gpu_data = Common.SWEDataArakawaA(self.gpu_stream, nx, ny,
ghost_cells_x, ghost_cells_y,
eta0, hu0, hv0)
# Allocate memory for calculating maximum timestep
host_dt = np.zeros((self.global_size[1], self.global_size[0]),
dtype=np.float32)
self.device_dt = Common.CUDAArray2D(self.gpu_stream,
self.global_size[0],
self.global_size[1], 0, 0, host_dt)
host_max_dt_buffer = np.zeros((1, 1), dtype=np.float32)
self.max_dt_buffer = Common.CUDAArray2D(self.gpu_stream, 1, 1, 0, 0,
host_max_dt_buffer)
self.courant_number = courant_number
## Allocating memory for geostrophical equilibrium variables
self.reportGeostrophicEquilibrium = np.int32(
reportGeostrophicEquilibrium)
self.geoEq_uxpvy = None
self.geoEq_Kx = None
self.geoEq_Ly = None
if self.reportGeostrophicEquilibrium:
dummy_zero_array = np.zeros(
(ny + 2 * ghost_cells_y, nx + 2 * ghost_cells_x),
dtype=np.float32,
order='C')
self.geoEq_uxpvy = Common.CUDAArray2D(self.gpu_stream, nx, ny,
ghost_cells_x, ghost_cells_y,
dummy_zero_array)
self.geoEq_Kx = Common.CUDAArray2D(self.gpu_stream, nx, ny,
ghost_cells_x, ghost_cells_y,
dummy_zero_array)
self.geoEq_Ly = Common.CUDAArray2D(self.gpu_stream, nx, ny,
ghost_cells_x, ghost_cells_y,
dummy_zero_array)
self.constant_equilibrium_depth = np.max(H)
self.bc_kernel = Common.BoundaryConditionsArakawaA(gpu_ctx, \
self.nx, \
self.ny, \
ghost_cells_x, \
ghost_cells_y, \
self.boundary_conditions, \
boundary_conditions_data, \
)
def subsample_texture(data, factor):
ny, nx = data.shape
dx, dy = 1 / nx, 1 / ny
I = interp2d(np.linspace(0.5 * dx, 1 - 0.5 * dx, nx),
np.linspace(0.5 * dy, 1 - 0.5 * dy, ny),
data,
kind='linear')
new_nx, new_ny = max(2, nx // factor), max(2, ny // factor)
new_dx, new_dy = 1 / new_nx, 1 / new_ny
x_new = np.linspace(0.5 * new_dx, 1 - 0.5 * new_dx, new_nx)
y_new = np.linspace(0.5 * new_dy, 1 - 0.5 * new_dy, new_ny)
return I(x_new, y_new)
# Texture for angle
self.angle_texref = self.kernel.get_texref("angle_tex")
if isinstance(angle, cuda.Array):
# angle is already a texture, so we just set the texture reference
self.angle_texref.set_array(angle)
else:
#Upload data to GPU and bind to texture reference
if (subsample_angle and angle.size >= eta0.size):
self.logger.info("Subsampling angle texture by factor " +
str(subsample_angle))
self.logger.warning(
"This will give inaccurate angle along the border!")
angle = subsample_texture(angle, subsample_angle)
self.angle_texref.set_array(
cuda.np_to_array(np.ascontiguousarray(angle, dtype=np.float32),
order="C"))
# Set texture parameters
self.angle_texref.set_filter_mode(
cuda.filter_mode.LINEAR) #bilinear interpolation
self.angle_texref.set_address_mode(
0, cuda.address_mode.CLAMP) #no indexing outside domain
self.angle_texref.set_address_mode(1, cuda.address_mode.CLAMP)
self.angle_texref.set_flags(
cuda.TRSF_NORMALIZED_COORDINATES) #Use [0, 1] indexing
# Texture for coriolis f
self.coriolis_texref = self.kernel.get_texref("coriolis_f_tex")
# Create the CPU coriolis
if (latitude is not None):
if (self.f != 0.0):
raise RuntimeError(
"Cannot specify both latitude and f. Make your mind up.")
coriolis_f, _ = OceanographicUtilities.calcCoriolisParams(latitude)
coriolis_f = coriolis_f.astype(np.float32)
else:
if (self.coriolis_beta != 0.0):
if (angle.size != 1):
raise RuntimeError(
"non-constant angle cannot be combined with beta plane model (makes no sense)"
)
#Generate coordinates for all cells, including ghost cells from center to center
# [-3/2dx, nx+3/2dx] for ghost_cells_x == 2
x = np.linspace((-self.ghost_cells_x + 0.5) * self.dx,
(self.nx + self.ghost_cells_x - 0.5) * self.dx,
self.nx + 2 * self.ghost_cells_x)
y = np.linspace((-self.ghost_cells_y + 0.5) * self.dy,
(self.ny + self.ghost_cells_y - 0.5) * self.dy,
self.ny + 2 * self.ghost_cells_x)
self.logger.info(
"Using latitude to create Coriolis f texture ({:f}x{:f} cells)"
.format(x.size, y.size))
x, y = np.meshgrid(x, y)
n = x * np.sin(angle[0, 0]) + y * np.cos(
angle[0, 0]) #North vector
coriolis_f = self.f + self.coriolis_beta * n
else:
if (self.f.size == 1):
coriolis_f = np.array([[self.f]], dtype=np.float32)
elif (self.f.shape == eta0.shape):
coriolis_f = np.array(self.f, dtype=np.float32)
else:
raise RuntimeError(
"The shape of f should match up with eta or be scalar."
)
if (subsample_f and coriolis_f.size >= eta0.size):
self.logger.info("Subsampling coriolis texture by factor " +
str(subsample_f))
self.logger.warning(
"This will give inaccurate coriolis along the border!")
coriolis_f = subsample_texture(coriolis_f, subsample_f)
#Upload data to GPU and bind to texture reference
self.coriolis_texref.set_array(
cuda.np_to_array(np.ascontiguousarray(coriolis_f,
dtype=np.float32),
order="C"))
# Set texture parameters
self.coriolis_texref.set_filter_mode(
cuda.filter_mode.LINEAR) #bilinear interpolation
self.coriolis_texref.set_address_mode(
0, cuda.address_mode.CLAMP) #no indexing outside domain
self.coriolis_texref.set_address_mode(1, cuda.address_mode.CLAMP)
self.coriolis_texref.set_flags(
cuda.TRSF_NORMALIZED_COORDINATES) #Use [0, 1] indexing
# Small scale perturbation:
self.small_scale_perturbation = small_scale_perturbation
self.small_scale_model_error = None
self.small_scale_perturbation_interpolation_factor = small_scale_perturbation_interpolation_factor
if small_scale_perturbation:
self.small_scale_model_error = OceanStateNoise.OceanStateNoise.fromsim(
self,
soar_q0=small_scale_perturbation_amplitude,
interpolation_factor=
small_scale_perturbation_interpolation_factor,
use_lcg=use_lcg,
block_width=block_width_model_error,
block_height=block_height_model_error)
# Data assimilation model step size
self.model_time_step = model_time_step
self.total_time_steps = 0
if model_time_step is None:
self.model_time_step = self.dt
if self.write_netcdf:
self.sim_writer = SimWriter.SimNetCDFWriter(self, super_dir_name=super_dir_name, filename=netcdf_filename, \
ignore_ghostcells=self.ignore_ghostcells, offset_x=self.offset_x, offset_y=self.offset_y)
# Update timestep if dt is given as zero
if self.dt <= 0:
self.updateDt()
def __init__(self, \
gpu_ctx, \
eta0, hu0, hv0, Hi, \
nx, ny, \
dx, dy, dt, \
g, f, r, \
t=0.0, \
theta=1.3, rk_order=2, \
coriolis_beta=0.0, \
y_zero_reference_cell = 0, \
max_wind_direction_perturbation = 0, \
wind_stress=WindStress.WindStress(), \
boundary_conditions=Common.BoundaryConditions(), \
small_scale_perturbation=False, \
small_scale_perturbation_amplitude=None, \
h0AsWaterElevation=False, \
reportGeostrophicEquilibrium=False, \
write_netcdf=False, \
ignore_ghostcells=False, \
offset_x=0, offset_y=0, \
block_width=32, block_height=4):
"""
Initialization routine
eta0: Initial deviation from mean sea level incl ghost cells, (nx+2)*(ny+2) cells
hu0: Initial momentum along x-axis incl ghost cells, (nx+1)*(ny+2) cells
hv0: Initial momentum along y-axis incl ghost cells, (nx+2)*(ny+1) cells
Hi: Depth from equilibrium defined on cell corners, (nx+5)*(ny+5) corners
nx: Number of cells along x-axis
ny: Number of cells along y-axis
dx: Grid cell spacing along x-axis (20 000 m)
dy: Grid cell spacing along y-axis (20 000 m)
dt: Size of each timestep (90 s)
g: Gravitational accelleration (9.81 m/s^2)
f: Coriolis parameter (1.2e-4 s^1), effectively as f = f + beta*y
r: Bottom friction coefficient (2.4e-3 m/s)
t: Start simulation at time t
theta: MINMOD theta used the reconstructions of the derivatives in the numerical scheme
rk_order: Order of Runge Kutta method {1,2*,3}
coriolis_beta: Coriolis linear factor -> f = f + beta*(y-y_0)
y_zero_reference_cell: The cell representing y_0 in the above, defined as the lower face of the cell .
max_wind_direction_perturbation: Large-scale model error emulation by per-time-step perturbation of wind direction by +/- max_wind_direction_perturbation (degrees)
wind_stress: Wind stress parameters
boundary_conditions: Boundary condition object
h0AsWaterElevation: True if h0 is described by the surface elevation, and false if h0 is described by water depth
reportGeostrophicEquilibrium: Calculate the Geostrophic Equilibrium variables for each superstep
write_netcdf: Write the results after each superstep to a netCDF file
"""
## After changing from (h, B) to (eta, H), several of the simulator settings used are wrong. This check will help detect that.
if ( np.sum(eta0 - Hi[:-1, :-1] > 0) > nx):
assert(False), "It seems you are using water depth/elevation h and bottom topography B, while you should use water level eta and equillibrium depth H."
assert( rk_order < 4 or rk_order > 0 ), "Only 1st, 2nd and 3rd order Runge Kutta supported"
if (rk_order == 3):
assert(r == 0.0), "3rd order Runge Kutta supported only without friction"
# Sort out internally represented ghost_cells in the presence of given
# boundary conditions
ghost_cells_x = 2
ghost_cells_y = 2
y_zero_reference_cell = 2 + y_zero_reference_cell
# Boundary conditions
self.boundary_conditions = boundary_conditions
if (boundary_conditions.isSponge()):
nx = nx + boundary_conditions.spongeCells[1] + boundary_conditions.spongeCells[3] - 2*ghost_cells_x
ny = ny + boundary_conditions.spongeCells[0] + boundary_conditions.spongeCells[2] - 2*ghost_cells_y
y_zero_reference_cell = boundary_conditions.spongeCells[2] + y_zero_reference_cell
A = None
self.max_wind_direction_perturbation = max_wind_direction_perturbation
super(CDKLM16, self).__init__(gpu_ctx, \
nx, ny, \
ghost_cells_x, \
ghost_cells_y, \
dx, dy, dt, \
g, f, r, A, \
t, \
theta, rk_order, \
coriolis_beta, \
y_zero_reference_cell, \
wind_stress, \
write_netcdf, \
ignore_ghostcells, \
offset_x, offset_y, \
block_width, block_height)
# Index range for interior domain (north, east, south, west)
# so that interior domain of eta is
# eta[self.interior_domain_indices[2]:self.interior_domain_indices[0], \
# self.interior_domain_indices[3]:self.interior_domain_indices[1] ]
self.interior_domain_indices = np.array([-2,-2,2,2])
self._set_interior_domain_from_sponge_cells()
#Get kernels
self.kernel = gpu_ctx.get_kernel("CDKLM16_kernel.cu", defines={'block_width': block_width, 'block_height': block_height})
# Get CUDA functions and define data types for prepared_{async_}call()
self.swe_2D = self.kernel.get_function("swe_2D")
self.swe_2D.prepare("iifffffffffiiPiPiPiPiPiPiPiPifiiiiiPiPiPi")
self.update_wind_stress(self.kernel, self.swe_2D)
#Create data by uploading to device
self.gpu_data = Common.SWEDataArakawaA(self.gpu_stream, nx, ny, ghost_cells_x, ghost_cells_y, eta0, hu0, hv0)
## Allocating memory for geostrophical equilibrium variables
self.reportGeostrophicEquilibrium = np.int32(reportGeostrophicEquilibrium)
dummy_zero_array = np.zeros((ny+2*ghost_cells_y, nx+2*ghost_cells_x), dtype=np.float32, order='C')
self.geoEq_uxpvy = Common.CUDAArray2D(self.gpu_stream, nx, ny, ghost_cells_x, ghost_cells_y, dummy_zero_array)
self.geoEq_Kx = Common.CUDAArray2D(self.gpu_stream, nx, ny, ghost_cells_x, ghost_cells_y, dummy_zero_array)
self.geoEq_Ly = Common.CUDAArray2D(self.gpu_stream, nx, ny, ghost_cells_x, ghost_cells_y, dummy_zero_array)
#Bathymetry
self.bathymetry = Common.Bathymetry(gpu_ctx, self.gpu_stream, nx, ny, ghost_cells_x, ghost_cells_y, Hi, boundary_conditions)
self.h0AsWaterElevation = h0AsWaterElevation
if self.h0AsWaterElevation:
self.bathymetry.waterElevationToDepth(self.gpu_data.h0)
self.constant_equilibrium_depth = np.max(Hi)
self.bc_kernel = Common.BoundaryConditionsArakawaA(gpu_ctx, \
self.nx, \
self.ny, \
ghost_cells_x, \
ghost_cells_y, \
self.boundary_conditions, \
)
# Small scale perturbation:
self.small_scale_perturbation = small_scale_perturbation
self.small_scale_model_error = None
if small_scale_perturbation:
if small_scale_perturbation_amplitude is None:
self.small_scale_model_error = OceanStateNoise.OceanStateNoise.fromsim(self)
else:
self.small_scale_model_error = OceanStateNoise.OceanStateNoise.fromsim(self, soar_q0=small_scale_perturbation_amplitude)
if self.write_netcdf:
self.sim_writer = SimWriter.SimNetCDFWriter(self, ignore_ghostcells=self.ignore_ghostcells, \
offset_x=self.offset_x, offset_y=self.offset_y)
