def velocity_matrix(ra: MatrixVector,
rb: MatrixVector,
rc: MatrixVector,
betm: float = 1.0,
tol: float = 1e-12):
if ra.shape != rb.shape:
return ValueError()
numi = rc.shape[0]
numj = ra.shape[1]
ra = ra.repeat(numi, axis=0)
rb = rb.repeat(numi, axis=0)
rc = rc.repeat(numj, axis=1)
a = rc - ra
b = rc - rb
a.x = a.x / betm
b.x = b.x / betm
am = a.return_magnitude()
bm = b.return_magnitude()
# Velocity from Bound Vortex
adb = elementwise_dot_product(a, b)
abm = multiply(am, bm)
dm = multiply(abm, abm + adb)
axb = elementwise_cross_product(a, b)
axbm = axb.return_magnitude()
chki = (axbm == 0.0)
chki = logical_and(axbm >= -tol, axbm <= tol)
veli = elementwise_multiply(axb, divide(am + bm, dm))
veli.x[chki] = 0.0
veli.y[chki] = 0.0
veli.z[chki] = 0.0
# Velocity from Trailing Vortex A
axx = MatrixVector(zeros(a.shape, dtype=float), a.z, -a.y)
axxm = axx.return_magnitude()
chka = (axxm == 0.0)
vela = elementwise_divide(axx, multiply(am, am - a.x))
vela.x[chka] = 0.0
vela.y[chka] = 0.0
vela.z[chka] = 0.0
# Velocity from Trailing Vortex B
bxx = MatrixVector(zeros(b.shape, dtype=float), b.z, -b.y)
bxxm = bxx.return_magnitude()
chkb = (bxxm == 0.0)
velb = elementwise_divide(bxx, multiply(bm, bm - b.x))
velb.x[chkb] = 0.0
velb.y[chkb] = 0.0
velb.z[chkb] = 0.0
return veli, vela, velb
def vel_doublet_matrix(av, am, bv, bm):
adb = elementwise_dot_product(av, bv)
abm = multiply(am, bm)
dm = multiply(abm, abm + adb)
axb = elementwise_cross_product(av, bv)
axbm = axb.return_magnitude()
chki = (axbm == 0.0)
chki = logical_and(axbm >= -tol, axbm <= tol)
velvl = elementwise_multiply(axb, divide(am + bm, dm))
velvl.x[chki] = 0.0
velvl.y[chki] = 0.0
velvl.z[chki] = 0.0
return velvl
def vel_doublet_matrix(av, am, bv, bm):
adb = elementwise_dot_product(av, bv)
abm = multiply(am, bm)
dm = multiply(abm, abm+adb)
axb = elementwise_cross_product(av, bv)
axbm = axb.return_magnitude()
chki = (axbm == 0.0)
chki = logical_and(axbm >= -tol, axbm <= tol)
chkd = absolute(dm) < tol
fac = zeros(axbm.shape, dtype=float)
divide(am+bm, dm, where=logical_not(chkd), out=fac)
velvl = elementwise_multiply(axb, fac)
velvl.x[chki] = 0.0
velvl.y[chki] = 0.0
velvl.z[chki] = 0.0
return velvl
def unsig(self, mach: float=0.0):
if self._unsig is None:
self._unsig = {}
if mach not in self._unsig:
unsig = zero_matrix_vector((self.numpnl, 2+4*self.numctrl), dtype=float)
unsig[:, 0] = -self.nrms
unsig[:, 1] = elementwise_cross_product(self.rrel, self.nrms)
if self.srfcs is not None:
for srfc in self.srfcs:
for sht in srfc.shts:
for control in sht.ctrls:
ctrl = sht.ctrls[control]
ctup = self.ctrls[control]
for pnl in ctrl.pnls:
ind = pnl.ind
rrel = self.rrel[ind, 0]
dndlp = pnl.dndl(ctrl.posgain, ctrl.uhvec)
unsig[ind, ctup[0]] = -dndlp
unsig[ind, ctup[1]] = -rrel**dndlp
dndln = pnl.dndl(ctrl.neggain, ctrl.uhvec)
unsig[ind, ctup[2]] = -dndln
unsig[ind, ctup[3]] = -rrel**dndln
self._unsig[mach] = unsig
return self._unsig[mach]
def influence_coefficients(self, pnts: MatrixVector, incvel: bool=True,
betx: float=1.0, bety: float=1.0, betz: float=1.0,
checktol: bool=False):
grdm = self.mach_grids(betx=betx, bety=bety, betz=betz)
vecab = self.edge_vector(grdm)
vecaxb = self.edge_cross(grdm)
dirxab = vecab.to_unit()
dirzab = vecaxb.to_unit()
diryab = elementwise_cross_product(dirzab, dirxab)
nrm = vecaxb.sum().to_unit()
rgcs = self.relative_mach(pnts, self.pnto, betx=betx, bety=bety, betz=betz)
locz = rgcs*nrm
sgnz = ones(locz.shape, dtype=float)
sgnz[locz <= 0.0] = -1.0
vecgcs = []
for i in range(self.num):
vecgcs.append(self.relative_mach(pnts, self.grds[i], betx=betx, bety=bety, betz=betz))
phid = zeros(pnts.shape, dtype=float)
phis = zeros(pnts.shape, dtype=float)
if incvel:
veld = zero_matrix_vector(pnts.shape, dtype=float)
vels = zero_matrix_vector(pnts.shape, dtype=float)
for i in range(self.num):
# Edge Length
dab = vecab[0, i].return_magnitude()
# Local Coordinate System
dirx = dirxab[0, i]
diry = diryab[0, i]
dirz = dirzab[0, i]
# Vector A in Local Coordinate System
veca = vecgcs[i-1]
alcs = MatrixVector(veca*dirx, veca*diry, veca*dirz)
if checktol:
alcs.x[absolute(alcs.x) < tol] = 0.0
alcs.y[absolute(alcs.y) < tol] = 0.0
alcs.z[absolute(alcs.z) < tol] = 0.0
# Vector A Doublet Velocity Potentials
phida, amag = phi_doublet_matrix(alcs, sgnz)
# Vector B in Local Coordinate System
vecb = vecgcs[i]
blcs = MatrixVector(vecb*dirx, vecb*diry, vecb*dirz)
if checktol:
blcs.x[absolute(blcs.x) < tol] = 0.0
blcs.y[absolute(blcs.y) < tol] = 0.0
blcs.z[absolute(blcs.z) < tol] = 0.0
# Vector B Doublet Velocity Potentials
phidb, bmag = phi_doublet_matrix(blcs, sgnz)
# Edge Doublet Velocity Potentials
phidi = phida - phidb
# Edge Source Velocity Potentials
phisi, Qab = phi_source_matrix(amag, bmag, dab, alcs, phidi)
# Add Edge Velocity Potentials
phid += phidi
phis += phisi
# Calculate Edge Velocities
if incvel:
# Velocities in Local Coordinate System
veldi = vel_doublet_matrix(alcs, amag, blcs, bmag)
velsi = vel_source_matrix(Qab, alcs, phidi)
# Transform to Global Coordinate System and Add
dirxi = Vector(dirx.x, diry.x, dirz.x)
diryi = Vector(dirx.y, diry.y, dirz.y)
dirzi = Vector(dirx.z, diry.z, dirz.z)
veld += MatrixVector(veldi*dirxi, veldi*diryi, veldi*dirzi)
vels += MatrixVector(velsi*dirxi, velsi*diryi, velsi*dirzi)
phid = phid/fourPi
phis = phis/fourPi
if incvel:
veld = veld/fourPi
vels = vels/fourPi
output = phid, phis, veld, vels
else:
output = phid, phis
return output
def diryab(self):
if self._diryab is None:
self._diryab = elementwise_cross_product(self.dirzab, self.dirxab)
return self._diryab