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import numpy as np
import numpy.linalg as la # noqa: F401
import pyopencl as cl # noqa: F401
import pyopencl.array # noqa
import pyopencl.tools # noqa
import pyopencl.clrandom # noqa
import loopy as lp # noqa
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# FIXME: add new file ideal_gas.py that has flux, pressure, etc. (any
# computation that depends on EOS
def pressure(state):
# FIXME: for ideal gas stuff, make nvars, ndim, gamma, etc module level
# constants
# FIXME: also split out velocity, rho, energy into separate routines
gamma = 1.4
ndim = state.size - 2
rho = state[0]
energy = state[ndim+1]
ke = 0.0
for i in range(ndim):
ke += (state[i+1]/rho)**2
ke = 0.5*rho*ke
return (gamma - 1)*(energy - ke)
def flux(state):
nvars = state.size
ndim = nvars - 2
result = np.empty((nvars, ndim))
rho = state[0]
u = state[1:ndim+1]/rho
energy = state[ndim+1]
p = pressure(state)
for i in range(ndim):
result[:,i] = u[i]*state
result[i+1,i] += p
result[ndim+1,i] += u[i]*p
return result
def pointwise_fluxes(states):
nvars, npoints = states.shape
ndim = 3
result = np.empty((nvars, ndim, npoints))
for k in range(npoints):
result[:,:,k] = flux(states[:,k])
return result
def split_char_fluxes(states, wavespeeds, frozen_metrics, frozen_jacobian, R_inv):
nvars, npoints = states.shape
ndim = frozen_metrics.size
fluxes = pointwise_fluxes(states)
char_fluxes_pos = np.empty((nvars, npoints))
char_fluxes_neg = np.empty((nvars, npoints))
for k in range(npoints):
generalized_fluxes = np.zeros(nvars)
for i in range(ndim):
generalized_fluxes += frozen_metrics[i]*fluxes[:,i,k]
generalized_states = states[:,k]/frozen_jacobian
combination_pos = np.empty((nvars, nvars))
combination_neg = np.empty((nvars, nvars))
for i in range(nvars):
char_fluxes_pos[i,k] = 0.5*np.dot(R_inv[i,:],
(generalized_fluxes + wavespeeds[i]*generalized_states))
char_fluxes_neg[i,k] = 0.5*np.dot(R_inv[i,:],
(generalized_fluxes - wavespeeds[i]*generalized_states))
return char_fluxes_pos, char_fluxes_neg
def oscillation(fluxes):
sum1 = np.empty((fluxes.shape[0], 3))
sum2 = np.empty((fluxes.shape[0], 3))
sum1[:,0] = fluxes[:,0] - 4*fluxes[:,1] + 3*fluxes[:,2]
sum1[:,1] = -fluxes[:,1] + fluxes[:,3]
sum1[:,2] = -3*fluxes[:,2] + 4*fluxes[:,3] - fluxes[:,4]
for i in range(3):
sum2[:,i] = fluxes[:,i] - 2*fluxes[:,i+1] + fluxes[:,i+2]
result = (1.0/4)*(sum1**2) + (13.0/12)*(sum2**2)
return result
def weno_weights(oscillation, frozen_metric):
linear = np.array([0.1, 0.6, 0.3])
eps = 1e-6*frozen_metric
raw_weights = np.empty((5,3))
for i in range(5):
for j in range(3):
raw_weights[i,j] = linear[j]/(oscillation[i,j] + eps)**2
weight_sum = raw_weights.sum(axis=1)
weights = np.empty((5,3))
for i in range(5):
for j in range(3):
weights[i,j] = raw_weights[i,j]/weight_sum[i]
return weights
def flux_differences(f):
w = np.array([-1, 3, -3, 1])
res = np.empty((5, 3))
for j in range(res.shape[1]):
res[:,j] = f[:,j:j+4]@w
return res
def combination_weighting(w):
return np.array(
[20*w[:,0] - 1, -10*(w[:,0] + w[:,1]) + 5, np.ones(w.shape[0])]
).T
def combine_fluxes(w, f):
cw = combination_weighting(w)
return np.sum(np.multiply(cw, f), axis=1)
def dissipation_part(R, char_fluxes, w, sign):
flux_diff = flux_differences(char_fluxes)[:,::sign]
flux_comb = combine_fluxes(w, flux_diff)
return -sign*R@flux_comb/60
def weno_flux(consistent, dissipation_pos, dissipation_neg):
return consistent + dissipation_pos + dissipation_neg