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185 lines
7.1 KiB
Python
185 lines
7.1 KiB
Python
# -*- coding: utf-8 -*-
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"""
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This python module implements the Kurganov-Petrova numerical scheme
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for the shallow water equations, described in
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A. Kurganov & Guergana Petrova
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A Second-Order Well-Balanced Positivity Preserving Central-Upwind
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Scheme for the Saint-Venant System Communications in Mathematical
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Sciences, 5 (2007), 133-160.
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Copyright (C) 2016 SINTEF ICT
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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"""
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#Import packages we need
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import numpy as np
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import pycuda.compiler as cuda_compiler
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import pycuda.gpuarray
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import pycuda.driver as cuda
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from SWESimulators import Common
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"""
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Class that solves the SW equations using the Forward-Backward linear scheme
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"""
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class KP07:
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"""
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Initialization routine
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h0: Water depth incl ghost cells, (nx+1)*(ny+1) cells
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hu0: Initial momentum along x-axis incl ghost cells, (nx+1)*(ny+1) cells
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hv0: Initial momentum along y-axis incl ghost cells, (nx+1)*(ny+1) cells
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nx: Number of cells along x-axis
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ny: Number of cells along y-axis
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dx: Grid cell spacing along x-axis (20 000 m)
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dy: Grid cell spacing along y-axis (20 000 m)
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dt: Size of each timestep (90 s)
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g: Gravitational accelleration (9.81 m/s^2)
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f: Coriolis parameter (1.2e-4 s^1)
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r: Bottom friction coefficient (2.4e-3 m/s)
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wind_type: Type of wind stress, 0=Uniform along shore, 1=bell shaped along shore, 2=moving cyclone
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wind_tau0: Amplitude of wind stress (Pa)
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wind_rho: Density of sea water (1025.0 kg / m^3)
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wind_alpha: Offshore e-folding length (1/(10*dx) = 5e-6 m^-1)
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wind_xm: Maximum wind stress for bell shaped wind stress
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wind_Rc: Distance to max wind stress from center of cyclone (10dx = 200 000 m)
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wind_x0: Initial x position of moving cyclone (dx*(nx/2) - u0*3600.0*48.0)
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wind_y0: Initial y position of moving cyclone (dy*(ny/2) - v0*3600.0*48.0)
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wind_u0: Translation speed along x for moving cyclone (30.0/sqrt(5.0))
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wind_v0: Translation speed along y for moving cyclone (-0.5*u0)
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"""
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def __init__(self, \
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context, \
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h0, hu0, hv0, \
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nx, ny, \
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dx, dy, dt, \
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g, theta=1.3, \
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r=0.0, use_rk2=True,
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block_width=16, block_height=16):
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#Create a CUDA stream
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self.stream = cuda.Stream()
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#Get kernels
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self.kp07_module = context.get_kernel("KP07_kernel.cu", block_width, block_height)
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self.kp07_kernel = self.kp07_module.get_function("KP07Kernel")
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self.kp07_kernel.prepare("iiffffffiPiPiPiPiPiPi")
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#Create data by uploading to device
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ghost_cells_x = 2
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ghost_cells_y = 2
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self.data = Common.SWEDataArakawaA(self.stream, nx, ny, ghost_cells_x, ghost_cells_y, h0, hu0, hv0)
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#Save input parameters
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#Notice that we need to specify them in the correct dataformat for the
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#OpenCL kernel
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self.nx = np.int32(nx)
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self.ny = np.int32(ny)
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self.dx = np.float32(dx)
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self.dy = np.float32(dy)
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self.dt = np.float32(dt)
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self.g = np.float32(g)
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self.r = np.float32(r)
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self.theta = np.float32(theta)
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self.use_rk2 = use_rk2
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#Initialize time
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self.t = np.float32(0.0)
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#Compute kernel launch parameters
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self.local_size = (block_width, block_height, 1)
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self.global_size = ( \
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int(np.ceil(self.nx / float(self.local_size[0]))), \
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int(np.ceil(self.ny / float(self.local_size[1]))) \
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)
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def __str__(self):
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return "Kurganov-Petrova 2007"
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"""
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Function which steps n timesteps
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"""
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def step(self, t_end=0.0):
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n = int(t_end / self.dt + 1)
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for i in range(0, n):
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local_dt = np.float32(min(self.dt, t_end-i*self.dt))
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if (local_dt <= 0.0):
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break
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if (self.use_rk2):
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self.kp07_kernel.prepared_async_call(self.global_size, self.local_size, self.stream, \
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self.nx, self.ny, \
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self.dx, self.dy, local_dt, \
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self.g, \
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self.theta, \
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self.r, \
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np.int32(0), \
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self.data.h0.data.gpudata, self.data.h0.pitch, \
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self.data.hu0.data.gpudata, self.data.hu0.pitch, \
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self.data.hv0.data.gpudata, self.data.hv0.pitch, \
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self.data.h1.data.gpudata, self.data.h1.pitch, \
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self.data.hu1.data.gpudata, self.data.hu1.pitch, \
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self.data.hv1.data.gpudata, self.data.hv1.pitch)
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self.kp07_kernel.prepared_async_call(self.global_size, self.local_size, self.stream, \
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self.nx, self.ny, \
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self.dx, self.dy, local_dt, \
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self.g, \
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self.theta, \
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self.r, \
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np.int32(1), \
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self.data.h1.data.gpudata, self.data.h1.pitch, \
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self.data.hu1.data.gpudata, self.data.hu1.pitch, \
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self.data.hv1.data.gpudata, self.data.hv1.pitch, \
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self.data.h0.data.gpudata, self.data.h0.pitch, \
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self.data.hu0.data.gpudata, self.data.hu0.pitch, \
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self.data.hv0.data.gpudata, self.data.hv0.pitch)
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else:
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self.kp07_kernel.prepared_async_call(self.global_size, self.local_size, self.stream, \
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self.nx, self.ny, \
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self.dx, self.dy, local_dt, \
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self.g, \
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self.theta, \
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self.r, \
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np.int32(0), \
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self.data.h0.data.gpudata, self.data.h0.pitch, \
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self.data.hu0.data.gpudata, self.data.hu0.pitch, \
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self.data.hv0.data.gpudata, self.data.hv0.pitch, \
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self.data.h1.data.gpudata, self.data.h1.pitch, \
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self.data.hu1.data.gpudata, self.data.hu1.pitch, \
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self.data.hv1.data.gpudata, self.data.hv1.pitch)
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self.cl_data.swap()
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self.t += local_dt
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return self.t
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def download(self):
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return self.data.download(self.stream)
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