def update_density(x, rho, particles, bins, bins_index):
''' function for density summation '''
ng_l = particles[0].ng[0]
ng_r = particles[0].ng[1]
ng_particles = len(particles)
n_particles = ng_particles - (ng_l + ng_r)
one = np.ones(ng_particles)
m_j = particles[0].m
r_j = np.copy(x)
h_ij = one * particles[0].h
rho_a = np.zeros(n_particles)
W_ij = np.zeros(ng_particles)
for i in range(ng_l, n_particles + ng_l):
r_i = x[i]
r_ij = x[i] - r_j
bin_min = bins[bins_index[i] - 1][0]
bin_max = bins[bins_index[i] + 1][-1]
W_ij[bin_min:bin_max] = interp.cubic_spline(r_ij[bin_min:bin_max],
h_ij[bin_min:bin_max])
rho_a[i - ng_l] = np.sum(m_j * W_ij)
return rho_a
def update_density(x, rho, particles, bins, bins_index): ''' function for density summation ''' ng_l = particles[0].ng[0] ng_r = particles[0].ng[1] ng_particles = len(particles) n_particles = ng_particles - (ng_l + ng_r) one = np.ones(ng_particles) m_j = particles[0].m r_j = np.copy(x) h_ij = one*particles[0].h rho_a = np.zeros(n_particles) W_ij = np.zeros(ng_particles) for i in range(ng_l, n_particles + ng_l): r_i = x[i] r_ij = x[i] - r_j bin_min = bins[bins_index[i]-1][0] bin_max = bins[bins_index[i]+1][-1] W_ij[bin_min:bin_max] = interp.cubic_spline(r_ij[bin_min:bin_max], h_ij[bin_min:bin_max]) rho_a[i - ng_l] = np.sum(m_j*W_ij) return rho_a
def update_density(x, rho, particles):
''' function for density summation '''
ng_l = particles[0].ng[0]
ng_r = particles[0].ng[1]
ng_particles = len(particles)
n_particles = ng_particles - (ng_l + ng_r)
one = np.ones(ng_particles)
m_j = particles[0].m
r_j = np.copy(x)
h_ij = one * particles[0].h
rho_a = np.zeros(n_particles)
for i in range(ng_l, n_particles + ng_l):
r_i = x[i]
r_ij = x[i] - r_j
W_ij = interp.cubic_spline(r_ij, h_ij)
rho_a[i - ng_l] = np.sum(m_j * W_ij)
return rho_a
def update_density(x, rho, particles): ''' function for density summation ''' ng_l = particles[0].ng[0] ng_r = particles[0].ng[1] ng_particles = len(particles) n_particles = ng_particles - (ng_l + ng_r) one = np.ones(ng_particles) m_j = particles[0].m r_j = np.copy(x) h_ij = one*particles[0].h rho_a = np.zeros(n_particles) for i in range(ng_l, n_particles + ng_l): r_i = x[i] r_ij = x[i] - r_j W_ij = interp.cubic_spline(r_ij, h_ij) rho_a[i - ng_l] = np.sum(m_j*W_ij) return rho_a
def euler_rhs(x, rho, v, p, particles, bins, bins_index):
''' computes the acceleration terms in the Euler Gas Dynamics
equations
'''
ng_l = particles[0].ng[0]
ng_r = particles[0].ng[1]
ng_particles = len(particles)
n_particles = ng_particles - (ng_l + ng_r)
rho_a = np.zeros(n_particles)
v_a = np.zeros(n_particles)
ener_a = np.zeros(n_particles)
x_sph = np.zeros(n_particles)
one = np.ones(ng_particles)
m_i = particles[0].m
m_j = m_i
r_j = np.copy(x)
h_ij = particles[0].h * one
v_j = np.copy(v)
c_j = sound_speed(rho, p)
rho_j = np.copy(rho)
p_j = np.copy(p)
W_ij = np.zeros(ng_particles)
W_ij_prime = np.zeros(ng_particles)
for i in range(ng_l, ng_l + n_particles):
r_i = x[i]
r_ij = r_i - r_j
bin_min = bins[bins_index[i] - 1][0]
bin_max = bins[bins_index[i] + 1][-1]
W_ij[bin_min:bin_max] = interp.cubic_spline(r_ij[bin_min:bin_max],
h_ij[bin_min:bin_max])
W_ij_prime[bin_min:bin_max] = interp.cubic_spline_kernel_derivative(
r_ij[bin_min:bin_max], h_ij[bin_min:bin_max])
v_i = v[i] * one
v_ij = v_i - v_j
c_i = c_j[i] * one
c_ij = (c_i + c_j) / 2
rho_i = rho[i] * one
rho_ij = (rho_i + rho_j) / 2
pi_ij = get_viscosity(rho_ij, c_ij, r_ij, v_ij, h_ij)
p_i = p[i] * one
multiplier = (p_i / (rho_i * rho_i) + p_j / (rho_j * rho_j) + pi_ij)
multiplier_1 = (p_i / (rho_i * rho_i) + p_j / (rho_j * rho_j))
rho_a[i - ng_l] = np.sum(m_j * W_ij)
# multiple v_a formulations
v_a[i - ng_l] = -np.sum(m_j * multiplier * W_ij_prime)
# v_a[i - ng_l] = -np.sum(m_j * multiplier_1 * W_ij_prime) - 0.5*np.sum(m_j * pi_ij * W_ij_prime)
# multiple ener_a formulations
ener_a[i - ng_l] = 0.5 * np.sum(m_j * multiplier * v_ij * W_ij_prime)
# ener_a[i - ng_l] = np.sum(m_j* (p_i/(rho_i*rho_i)) * v_ij * W_ij_prime) + 0.5*np.sum(m_j * pi_ij * v_ij * W_ij_prime)
# ener_a[i - ng_l] = np.sum(m_j* multiplier_1* v_ij * W_ij_prime) + 0.5*np.sum(m_j* pi_ij * v_ij * W_ij_prime)
# multiple x_sph formulations
x_sph[i - ng_l] = 0.5 * np.sum(m_j * (-v_ij) * W_ij / rho_ij)
# x_sph[i - ng_l] = np.sum(m_j * v_j * W_ij / rho_j)
return x_sph, rho_a, v_a, ener_a
def euler_rhs(x, rho, v, p, particles, bins, bins_index): ''' computes the acceleration terms in the Euler Gas Dynamics equations ''' ng_l = particles[0].ng[0] ng_r = particles[0].ng[1] ng_particles = len(particles) n_particles = ng_particles - (ng_l+ng_r) rho_a = np.zeros(n_particles) v_a = np.zeros(n_particles) ener_a = np.zeros(n_particles) x_sph = np.zeros(n_particles) one = np.ones(ng_particles) m_i = particles[0].m m_j = m_i r_j = np.copy(x) h_ij = particles[0].h*one v_j = np.copy(v) c_j = sound_speed(rho, p) rho_j = np.copy(rho) p_j = np.copy(p) W_ij = np.zeros(ng_particles) W_ij_prime = np.zeros(ng_particles) for i in range(ng_l, ng_l + n_particles): r_i = x[i] r_ij = r_i - r_j bin_min = bins[bins_index[i]-1][0] bin_max = bins[bins_index[i]+1][-1] W_ij[bin_min:bin_max] = interp.cubic_spline(r_ij[bin_min:bin_max], h_ij[bin_min:bin_max]) W_ij_prime[bin_min:bin_max] = interp.cubic_spline_kernel_derivative(r_ij[bin_min:bin_max], h_ij[bin_min:bin_max]) v_i = v[i]*one v_ij = v_i - v_j c_i = c_j[i]*one c_ij = (c_i+c_j)/2 rho_i = rho[i]*one rho_ij = (rho_i+rho_j)/2 pi_ij = get_viscosity(rho_ij, c_ij, r_ij, v_ij, h_ij) p_i = p[i]*one multiplier = (p_i/(rho_i*rho_i) + p_j/(rho_j*rho_j) + pi_ij) multiplier_1 = (p_i/(rho_i*rho_i) + p_j/(rho_j*rho_j)) rho_a[i - ng_l] = np.sum(m_j * W_ij) # multiple v_a formulations v_a[i - ng_l] = -np.sum(m_j * multiplier * W_ij_prime) # v_a[i - ng_l] = -np.sum(m_j * multiplier_1 * W_ij_prime) - 0.5*np.sum(m_j * pi_ij * W_ij_prime) # multiple ener_a formulations ener_a[i - ng_l] = 0.5 * np.sum(m_j * multiplier * v_ij * W_ij_prime) # ener_a[i - ng_l] = np.sum(m_j* (p_i/(rho_i*rho_i)) * v_ij * W_ij_prime) + 0.5*np.sum(m_j * pi_ij * v_ij * W_ij_prime) # ener_a[i - ng_l] = np.sum(m_j* multiplier_1* v_ij * W_ij_prime) + 0.5*np.sum(m_j* pi_ij * v_ij * W_ij_prime) # multiple x_sph formulations x_sph[i - ng_l] = 0.5 * np.sum(m_j * (-v_ij) * W_ij /rho_ij) # x_sph[i - ng_l] = np.sum(m_j * v_j * W_ij / rho_j) return x_sph, rho_a, v_a, ener_a
