def loop(self, d_idx, s_idx, d_au, d_av, d_aw, d_ae, s_au, s_av, s_aw,
d_u0, d_v0, d_w0, s_u0, s_v0, s_w0, d_u, d_v, d_w, s_u, s_v, s_w,
d_p, d_rho, s_p, s_rho):
gamma = self.gamma
d = declare('int')
d = self.dim
auij, delu = declare('matrix(3)', 2)
auij[0] = d_au[d_idx] - s_au[s_idx]
auij[1] = d_av[d_idx] - s_av[s_idx]
auij[2] = d_aw[d_idx] - s_aw[s_idx]
delu[0] = s_u0[s_idx] + s_u[s_idx] - d_u0[d_idx] - d_u[d_idx]
delu[1] = s_v0[s_idx] + s_v[s_idx] - d_v0[d_idx] - d_v[d_idx]
delu[2] = s_w0[s_idx] + s_w[s_idx] - d_w0[d_idx] - d_w[d_idx]
aeij = dot(delu, auij, d)
si = d_p[d_idx]/((d_rho[d_idx])**gamma)
sj = s_p[s_idx]/((s_rho[s_idx])**gamma)
smin = min(abs(si), abs(sj))
smax = max(abs(si), abs(sj))
fij = 0.5
sdiff = si - sj
if sdiff * aeij > 0:
fij = smin/(smin + smax)
elif sdiff * aeij < 0:
fij = smax/(smin + smax)
d_ae[d_idx] += 0.5*fij * aeij
def loop(self, d_idx, s_idx, d_au, d_av, d_aw, d_ae, s_au, s_av, s_aw,
d_u0, d_v0, d_w0, s_u0, s_v0, s_w0, d_u, d_v, d_w, s_u, s_v, s_w,
d_p, d_rho, s_p, s_rho, d_m, d_V, s_V, d_cs, s_cs, d_h, s_h, XIJ,
d_gradv, s_gradv, EPS, DWIJ):
Cl = self.cl
Cq = self.cq
eta_fold = self.eta_fold
eta_crit = self.eta_crit
mi = d_m[d_idx]
Vi = 1.0 / d_V[d_idx]
Vj = 1.0 / s_V[s_idx]
pi = d_p[d_idx]
pj = s_p[s_idx]
rhoi = d_rho[d_idx]
rhoj = s_rho[s_idx]
ci = d_cs[d_idx]
cj = s_cs[s_idx]
hi = d_h[d_idx]
hj = s_h[s_idx]
alp, bet, i, d = declare('int', 4)
uijhat, tmpdvxij = declare('matrix(3)', 2)
d = self.dim
tmpri = 0.0
tmprj = 0.0
for alp in range(d):
for bet in range(d):
tmpri += d_gradv[d * d * d_idx + d * alp +
bet] * XIJ[alp] * XIJ[bet]
tmprj += s_gradv[d * d * s_idx + d * alp +
bet] * XIJ[alp] * XIJ[bet]
rij = tmpri / tmprj
tmprij = min(1, 4 * rij / ((1 + rij) * (1 + rij)))
phiij = max(0, tmprij)
tmpxij = dot(XIJ, XIJ, d)
tmpxij2 = sqrt(tmpxij)
etai_scalar = tmpxij2 / hi
etaj_scalar = tmpxij2 / hj
etaij = min(etai_scalar, etaj_scalar)
if etaij < eta_crit:
tmpphi = (etaij - eta_crit) / eta_fold
phiij = phiij * exp(-tmpphi * tmpphi)
for alp in range(d):
s = 0.0
for bet in range(d):
s += (d_gradv[d * d * d_idx + d * alp + bet] +
s_gradv[d * d * s_idx + d * alp + bet]) * XIJ[bet]
tmpdvxij[alp] = s
uijhat[0] = d_u0[d_idx] - s_u0[s_idx] - 0.5 * phiij * tmpdvxij[0]
uijhat[1] = d_v0[d_idx] - s_v0[s_idx] - 0.5 * phiij * tmpdvxij[1]
uijhat[2] = d_w0[d_idx] - s_w0[s_idx] - 0.5 * phiij * tmpdvxij[2]
tmpmui = dot(uijhat, XIJ, d) / (tmpxij / hi + EPS * hi)
mui = min(0, tmpmui)
tmpmuj = dot(uijhat, XIJ, d) / (tmpxij / hi + EPS * hj)
muj = min(0, tmpmuj)
Qi = rhoi * (-Cl * ci * mui + Cq * mui * mui)
Qj = rhoj * (-Cl * cj * muj + Cq * muj * muj)
fac = -(1.0 / mi) * Vi * Vj * (pi + pj + Qi + Qj)
gamma = self.gamma
d = self.dim
auij, delu = declare('matrix(3)', 2)
auij[0] = fac * DWIJ[0]
auij[1] = fac * DWIJ[1]
auij[2] = fac * DWIJ[2]
delu[0] = s_u0[s_idx] + s_u[s_idx] - d_u0[d_idx] - d_u[d_idx]
delu[1] = s_v0[s_idx] + s_v[s_idx] - d_v0[d_idx] - d_v[d_idx]
delu[2] = s_w0[s_idx] + s_w[s_idx] - d_w0[d_idx] - d_w[d_idx]
aeij = dot(delu, auij, d)
si = d_p[d_idx] / ((d_rho[d_idx])**gamma)
sj = s_p[s_idx] / ((s_rho[s_idx])**gamma)
smin = min(abs(si), abs(sj))
smax = max(abs(si), abs(sj))
fij = 0.5
sdiff = si - sj
if sdiff * aeij > 0:
fij = smin / (smin + smax)
elif sdiff * aeij < 0:
fij = smax / (smin + smax)
d_ae[d_idx] += 0.5 * fij * aeij
def loop(self, d_idx, s_idx, d_m, s_m, d_rho, s_rho, d_p, s_p, d_cs, s_cs,
d_u, d_v, d_w, s_u, s_v, s_w, d_gradv, s_gradv, d_h, s_h, s_ai,
s_bi, s_gradai, s_gradbi, d_au, d_av, d_aw, d_V, s_V, XIJ, VIJ,
DWIJ, EPS, HIJ, WIJ, DWI, DWJ):
Cl = self.cl
Cq = self.cq
eta_fold = self.eta_fold
eta_crit = self.eta_crit
mi = d_m[d_idx]
Vi = 1.0 / d_V[d_idx]
Vj = 1.0 / s_V[s_idx]
pi = d_p[d_idx]
pj = s_p[s_idx]
rhoi = d_rho[d_idx]
rhoj = s_rho[s_idx]
ci = d_cs[d_idx]
cj = s_cs[s_idx]
hi = d_h[d_idx]
hj = s_h[s_idx]
alp, bet, i, d = declare('int', 4)
uijhat, tmpdvxij = declare('matrix(3)', 2)
d = self.dim
tmpri = 0.0
tmprj = 0.0
for alp in range(d):
for bet in range(d):
tmpri += d_gradv[d * d * d_idx + d * alp +
bet] * XIJ[alp] * XIJ[bet]
tmprj += s_gradv[d * d * s_idx + d * alp +
bet] * XIJ[alp] * XIJ[bet]
rij = tmpri / tmprj
tmprij = min(1, 4 * rij / ((1 + rij) * (1 + rij)))
phiij = max(0, tmprij)
tmpxij = dot(XIJ, XIJ, d)
tmpxij2 = sqrt(tmpxij)
etai_scalar = tmpxij2 / hi
etaj_scalar = tmpxij2 / hj
etaij = min(etai_scalar, etaj_scalar)
if etaij < eta_crit:
tmpphi = (etaij - eta_crit) / eta_fold
phiij = phiij * exp(-tmpphi * tmpphi)
for alp in range(d):
s = 0.0
for bet in range(d):
s += (d_gradv[d * d * d_idx + d * alp + bet] +
s_gradv[d * d * s_idx + d * alp + bet]) * XIJ[bet]
tmpdvxij[alp] = s
uijhat[0] = d_u[d_idx] - s_u[s_idx] - 0.5 * phiij * tmpdvxij[0]
uijhat[1] = d_v[d_idx] - s_v[s_idx] - 0.5 * phiij * tmpdvxij[1]
uijhat[2] = d_w[d_idx] - s_w[s_idx] - 0.5 * phiij * tmpdvxij[2]
tmpmui = dot(uijhat, XIJ, d) / (tmpxij / hi + EPS * hi)
mui = min(0, tmpmui)
tmpmuj = dot(uijhat, XIJ, d) / (tmpxij / hi + EPS * hj)
muj = min(0, tmpmuj)
Qi = rhoi * (-Cl * ci * mui + Cq * mui * mui)
Qj = rhoj * (-Cl * cj * muj + Cq * muj * muj)
fac = -(1.0 / mi) * Vi * Vj * (pi + pj + Qi + Qj)
d_au[d_idx] += fac * DWIJ[0]
d_av[d_idx] += fac * DWIJ[1]
d_aw[d_idx] += fac * DWIJ[2]
def loop_all(self, d_idx, d_x, d_y, d_z, d_h, s_x, s_y, s_z, s_h, s_m,
s_rho, SPH_KERNEL, NBRS, N_NBRS, d_ai, d_gradai, d_bi, s_V,
d_gradbi):
x = d_x[d_idx]
y = d_y[d_idx]
z = d_z[d_idx]
h = d_h[d_idx]
i, j, k, s_idx, d, d2 = declare('int', 6)
alp, bet, gam, phi, psi = declare('int', 5)
xij = declare('matrix(3)')
dwij = declare('matrix(3)')
d = self.dim
d2 = d * d
m0 = 0.0
m1 = declare('matrix(3)')
m2 = declare('matrix(9)')
temp_vec = declare('matrix(3)')
temp_aug_m2 = declare('matrix(18)')
m2inv = declare('matrix(9)')
grad_m0 = declare('matrix(3)')
grad_m1 = declare('matrix(9)')
grad_m2 = declare('matrix(27)')
ai = 0.0
bi = declare('matrix(3)')
grad_ai = declare('matrix(3)')
grad_bi = declare('matrix(9)')
for i in range(3):
m1[i] = 0.0
grad_m0[i] = 0.0
bi[i] = 0.0
grad_ai[i] = 0.0
for j in range(3):
m2[3 * i + j] = 0.0
grad_m1[3 * i + j] = 0.0
grad_bi[3 * i + j] = 0.0
for k in range(3):
grad_m2[9 * i + 3 * j + k] = 0.0
for i in range(N_NBRS):
s_idx = NBRS[i]
xij[0] = x - s_x[s_idx]
xij[1] = y - s_y[s_idx]
xij[2] = z - s_z[s_idx]
hij = (h + s_h[s_idx]) * 0.5
rij = sqrt(xij[0] * xij[0] + xij[1] * xij[1] + xij[2] * xij[2])
wij = SPH_KERNEL.kernel(xij, rij, hij)
SPH_KERNEL.gradient(xij, rij, hij, dwij)
V = 1.0 / s_V[s_idx]
m0 += V * wij
for alp in range(d):
m1[alp] += V * wij * xij[alp]
for bet in range(d):
m2[d * alp + bet] += V * wij * xij[alp] * xij[bet]
for gam in range(d):
grad_m0[gam] += V * dwij[gam]
for alp in range(d):
fac = 1.0 if alp == gam else 0.0
temp = (xij[alp] * dwij[gam] + fac * wij)
grad_m1[d * gam + alp] += V * temp
for bet in range(d):
fac2 = 1.0 if bet == gam else 0.0
temp = xij[alp] * fac2 + xij[bet] * fac
temp2 = (xij[alp] * xij[bet] * dwij[gam] + temp * wij)
grad_m2[d2 * gam + d * alp + bet] += V * temp2
identity(m2inv, d)
augmented_matrix(m2, m2inv, d, d, d, temp_aug_m2)
# If is_singular > 0 then matrix was singular
is_singular = gj_solve(temp_aug_m2, d, d, m2inv)
if is_singular > 0.0:
# Cannot do much if the matrix is singular. Perhaps later
# we can tag such particles to see if the user can do something.
pass
else:
mat_vec_mult(m2inv, m1, d, temp_vec)
# Eq. 12.
ai = 1.0 / (m0 - dot(temp_vec, m1, d))
# Eq. 13.
mat_vec_mult(m2inv, m1, d, bi)
for gam in range(d):
bi[gam] = -bi[gam]
# Eq. 14. and 15.
for gam in range(d):
temp1 = grad_m0[gam]
for alp in range(d):
temp2 = 0.0
for bet in range(d):
temp1 -= m2inv[d * alp + bet] * (
m1[bet] * grad_m1[d * gam + alp] +
m1[alp] * grad_m1[d * gam + bet])
temp2 -= (m2inv[d * alp + bet] *
grad_m1[d * gam + bet])
for phi in range(d):
for psi in range(d):
temp1 += (m2inv[d * alp + phi] *
m2inv[d * psi + bet] *
grad_m2[d2 * gam + d * phi + psi] *
m1[bet] * m1[alp])
temp2 += (m2inv[d * alp + phi] *
m2inv[d * psi + bet] *
grad_m2[d2 * gam + d * phi + psi] *
m1[bet])
grad_bi[d * gam + alp] = temp2
grad_ai[gam] = -ai * ai * temp1
if N_NBRS < 2 or is_singular > 0.0:
d_ai[d_idx] = 1.0
for i in range(d):
d_gradai[d * d_idx + i] = 0.0
d_bi[d * d_idx + i] = 0.0
for j in range(d):
d_gradbi[d2 * d_idx + d * i + j] = 0.0
else:
d_ai[d_idx] = ai
for i in range(d):
d_gradai[d * d_idx + i] = grad_ai[i]
d_bi[d * d_idx + i] = bi[i]
for j in range(d):
d_gradbi[d2 * d_idx + d * i + j] = grad_bi[d * i + j]
