def plotcp(nelem, chord, thick, u):
# Geometry
xnode = geomwing(nelem, chord, thick)
TEat1 = 1
dt = 1.0
# Boundary conditions
chisrf = bcondvel(xnode, u)
# Integral equation solution
B, C = srfmatbc(xnode)
phisrf = solvephi(B, C, chisrf)
cpoint = collocation(xnode)
# Pressure figure
spl = subplot(111)
spl.set_aspect("equal", "box")
plotgeom(xnode)
# Pressure calculation and plotting
U = u.reshape((1, 2))
cp = calccp(xnode, TEat1, dt, U, phisrf, chisrf)
cl = calchalfcl(xnode, TEat1, dt, U, phisrf, chisrf)
print cl
plot(cpoint[: nelem / 2 + 1, 0], cp[: nelem / 2 + 1, 0])
title(r"Stationary pressure coefficient, $c_L = %9.3f$" % cl[0])
ylabel(r"$c_p$", size=18)
xlabel(r"$x/c$", size=18)
xticks(arange(-0.2, 1.3, 0.2))
yticks(arange(-0.8, 1.3, 0.2))
def plotcp(nelem, chord, thick, u):
#Geometry
xnode = geomwing(nelem, chord, thick)
TEat1 = 1
dt = 1.
#Boundary conditions
chisrf = bcondvel(xnode, u)
#Integral equation solution
B, C = srfmatbc(xnode)
phisrf = solvephi(B, C, chisrf)
cpoint = collocation(xnode)
#Pressure figure
spl = subplot(111)
spl.set_aspect('equal', 'box')
plotgeom(xnode)
#Pressure calculation and plotting
U = u.reshape((1, 2))
cp = calccp(xnode, TEat1, dt, U, phisrf, chisrf)
cl = calchalfcl(xnode, TEat1, dt, U, phisrf, chisrf)
print cl
plot(cpoint[:nelem / 2 + 1, 0], cp[:nelem / 2 + 1, 0])
title(r'Stationary pressure coefficient, $c_L = %9.3f$' % cl[0])
ylabel(r'$c_p$', size=18)
xlabel(r'$x/c$', size=18)
xticks(arange(-0.2, 1.3, 0.2))
yticks(arange(-0.8, 1.3, 0.2))
def solvebem(xnode, uarr, TEat1, dt):
from numpy import zeros
ne = xnode.shape[0]
nt = uarr.shape[0]
B, C = srfmatbc(xnode)
phi = zeros((ne, nt))
chi = phi.copy()
for i in xrange(nt):
chi[:, i] = bcondvel(xnode, uarr[i, :])
phi[:, i] = solvephi(B, C, chi[:, i])
pres = calcpres(xnode, TEat1, dt, uarr, phi, chi)
lift = calchalflift(xnode, TEat1, dt, uarr, phi, chi)
return pres, lift
def solvebem(xnode, uarr, TEat1, dt):
from numpy import zeros
ne = xnode.shape[0]
nt = uarr.shape[0]
B,C = srfmatbc(xnode)
phi = zeros((ne,nt))
chi = phi.copy()
for i in xrange(nt):
chi[:,i] = bcondvel(xnode, uarr[i,:])
phi[:,i] = solvephi(B,C,chi[:,i])
pres = calcpres(xnode,TEat1,dt,uarr,phi,chi)
lift = calchalflift(xnode,TEat1,dt,uarr,phi,chi)
return pres, lift
def main():
from bempy2d import circlegeom, srfmatbc, bcondvel, solvephi, \
circlefld, calcphifld, fldmatbc, fldmatbcv, \
calcvelfld, fieldgrid, calcdphidx, calcsrfvel, \
collocation, calcpres, geomwing, normals
from numpy import array, zeros, savetxt, eye, linspace, sqrt, \
arctan2, cos, pi, sin
from numpy.linalg import norm
from pylab import plot, show, grid, figure, subplot, quiver, xlim
#Geometry
figure(1)
nelem = 100
R = 1.
chord = 1.
thick = 0.2
ntstep = 10
Ttot = 1.
dt = Ttot/(ntstep-1.)
#xnode = circlegeom(nelem,R); TEat1 = 0
xnode = geomwing(nelem, chord, thick); TEat1 = 1
plotgeom(xnode)
#Boundary conditions
u = array([-1.5,0.])
chisrf = bcondvel(xnode, u)
#Integral equation solution
B, C = srfmatbc(xnode)
phisrf = solvephi(B,C,chisrf)
#Surface velocity calculation
v = calcsrfvel(xnode,TEat1,phisrf, chisrf)
#for i in xrange(nelem):
# v[i,0] += norm(u)
cpoint = collocation(xnode)
n = normals(xnode)
#Pressure figure
figure(2)
spl = subplot(111)
spl.set_aspect('equal','box')
plotgeom(xnode)
#Pressure calculation and plotting
pres = calcpres(xnode,TEat1,dt,u,phisrf,chisrf)
#plot(cpoint[:,0], cpoint[:,1], 'o')
presplot = cpoint+pres*n
#plot(presplot[:,0],presplot[:,1])
plot(linspace(chord,0,nelem/2),pres[:nelem/2],'g')
presn = abs(pres)*n
col = zeros(nelem)
for i in xrange(nelem):
if pres[i] > 0.:
col[i] = 1.
quiver(cpoint[:,0], cpoint[:,1],presn[:,0],presn[:,1], col, units='dots', width=0.8)
xlim(-1,chord+1)
grid()
#Analitical for circle
#TH = linspace(pi/nelem,2*pi-pi/nelem,nelem)
#presan = 0.5*norm(u)**2*(1-4*sin(TH)**2)
#presplotan = cpoint+presan.reshape((nelem,1))*n
#plot(presplotan[:,0],presplotan[:,1])
figure(1)
#Field definition
xmin, xmax = -2., 2.
ymin, ymax = -1.5, 1.5
nx, ny = 100, 100
xfield = fieldgrid(xmin,xmax,nx,ymin,ymax,ny)
#r = sqrt(xfield[:,0]**2+xfield[:,1]**2)
#th = arctan2(xfield[:,1], -xfield[:,0])
Bf, Cf = fldmatbc(xfield, xnode)
phifld = calcphifld(phisrf,chisrf,Bf,Cf)
#phifld += r*u[0]*cos(th)
#for i in xrange(nx*ny):
# if r[i] < R:
# phifld[i] = 0.
xcont = linspace(xmin,xmax,nx)
ycont = linspace(ymin,ymax,ny)
Z = phifld.reshape((ny,nx))
plotphicont(xcont,ycont,Z)
plotvelfld(cpoint, v)
show()
def main():
from bempy2d import circlegeom, srfmatbc, bcondvel, solvephi, \
circlefld, calcphifld, fldmatbc, fldmatbcv, \
calcvelfld, fieldgrid, calcdphidx, calcsrfvel, \
collocation, calcpres, geomwing, normals
from numpy import array, zeros, savetxt, eye, linspace, sqrt, \
arctan2, cos, pi, sin
from numpy.linalg import norm
from pylab import plot, show, grid, figure, subplot, quiver, xlim
#Geometry
figure(1)
nelem = 100
R = 1.
chord = 1.
thick = 0.2
ntstep = 10
Ttot = 1.
dt = Ttot / (ntstep - 1.)
#xnode = circlegeom(nelem,R); TEat1 = 0
xnode = geomwing(nelem, chord, thick)
TEat1 = 1
plotgeom(xnode)
#Boundary conditions
u = array([-1.5, 0.])
chisrf = bcondvel(xnode, u)
#Integral equation solution
B, C = srfmatbc(xnode)
phisrf = solvephi(B, C, chisrf)
#Surface velocity calculation
v = calcsrfvel(xnode, TEat1, phisrf, chisrf)
#for i in xrange(nelem):
# v[i,0] += norm(u)
cpoint = collocation(xnode)
n = normals(xnode)
#Pressure figure
figure(2)
spl = subplot(111)
spl.set_aspect('equal', 'box')
plotgeom(xnode)
#Pressure calculation and plotting
pres = calcpres(xnode, TEat1, dt, u, phisrf, chisrf)
#plot(cpoint[:,0], cpoint[:,1], 'o')
presplot = cpoint + pres * n
#plot(presplot[:,0],presplot[:,1])
plot(linspace(chord, 0, nelem / 2), pres[:nelem / 2], 'g')
presn = abs(pres) * n
col = zeros(nelem)
for i in xrange(nelem):
if pres[i] > 0.:
col[i] = 1.
quiver(cpoint[:, 0],
cpoint[:, 1],
presn[:, 0],
presn[:, 1],
col,
units='dots',
width=0.8)
xlim(-1, chord + 1)
grid()
#Analitical for circle
#TH = linspace(pi/nelem,2*pi-pi/nelem,nelem)
#presan = 0.5*norm(u)**2*(1-4*sin(TH)**2)
#presplotan = cpoint+presan.reshape((nelem,1))*n
#plot(presplotan[:,0],presplotan[:,1])
figure(1)
#Field definition
xmin, xmax = -2., 2.
ymin, ymax = -1.5, 1.5
nx, ny = 100, 100
xfield = fieldgrid(xmin, xmax, nx, ymin, ymax, ny)
#r = sqrt(xfield[:,0]**2+xfield[:,1]**2)
#th = arctan2(xfield[:,1], -xfield[:,0])
Bf, Cf = fldmatbc(xfield, xnode)
phifld = calcphifld(phisrf, chisrf, Bf, Cf)
#phifld += r*u[0]*cos(th)
#for i in xrange(nx*ny):
# if r[i] < R:
# phifld[i] = 0.
xcont = linspace(xmin, xmax, nx)
ycont = linspace(ymin, ymax, ny)
Z = phifld.reshape((ny, nx))
plotphicont(xcont, ycont, Z)
plotvelfld(cpoint, v)
show()
def main():
from numpy import array, zeros, savetxt, eye, linspace, sqrt, \
arctan2, cos, pi, sin
from numpy.linalg import norm
from pylab import plot, show, grid, figure, subplot, quiver, xlim, \
ion, ioff, draw, savefig, ylim
#Geometry
figure(1)
nelem = 151
R = 1.
chord = 1.
thick = 0.2
ntstep = 20
Ttot = 1.
dt = Ttot/(ntstep-1.)
#xnode = circlegeom(nelem,R); TEat1 = 0
xnode = geomwing(nelem, chord, thick); TEat1 = 1
plotgeom(xnode)
#Boundary conditions
u = array([-1.,0.])
uarr = norm(u)*sinspeedprof(ntstep,Ttot)
chisrf = bcondvel(xnode, u)
#Integral equation solution
B, C = srfmatbc(xnode)
phisrf = solvephi(B,C,chisrf)
#Surface velocity calculation
v = calcsrfvel(xnode,TEat1,phisrf, chisrf)
#for i in xrange(nelem):
# v[i,0] += norm(u)
cpoint = collocation(xnode)
n = normals(xnode)
#Pressure figure
figure(2)
#ion()
spl = subplot(111)
spl.set_aspect('equal','box')
plotgeom(xnode)
#Pressure calculation and plotting
pres, lift = solvebem(xnode, uarr, TEat1, dt)
for t in xrange(ntstep):
hru2 = 0.5*norm(uarr[t,:])**2
if hru2 > 0.001:
pres[:,t] /= hru2
lift[t] /= hru2
#pres = calcpres(xnode,TEat1,dt,u,phisrf,chisrf)
#plot(cpoint[:,0], cpoint[:,1], 'o')
#presplot = cpoint+pres*n
#plot(presplot[:,0],presplot[:,1])
xlim(-1,chord+1)
grid()
ylim(-1,1)
for t in xrange(ntstep):
plot(linspace(chord,0,nelem/2+1),pres[:nelem/2+1,t],'g')
#if t == 0:
# line, = plot(linspace(chord,0,nelem/2),pres[:nelem/2,t],'g')
#else:
# line.set_ydata(pres[:nelem/2,t])
ylim(-1,1)
presn = abs(pres[:,t].reshape((nelem,1)))*n
col = zeros(nelem)
#print pres[:,t]
for i in xrange(nelem):
if pres[i,t] > 0.:
col[i] = 1.
quiver(cpoint[:,0], cpoint[:,1],presn[:,0],presn[:,1], col, units='dots', width=0.8)
#if t == 0:
# qul = quiver(cpoint[:,0], cpoint[:,1],presn[:,0],presn[:,1], col, units='dots', width=0.8)
#else:
# qul.set_UVC(presn[:,0],presn[:,1], col)
#draw()
#savefig('pres%d' % t)
#ioff()
#Analitical for circle
#TH = linspace(pi/nelem,2*pi-pi/nelem,nelem)
#presan = 0.5*norm(u)**2*(1-4*sin(TH)**2)
#presplotan = cpoint+presan.reshape((nelem,1))*n
#plot(presplotan[:,0],presplotan[:,1])
#-----------LIFT------------
figure(3)
print lift
plot(linspace(0,Ttot,ntstep),lift)
figure(1)
#Field definition
xmin, xmax = -2., 2.
ymin, ymax = -1.5, 1.5
nx, ny = 100, 100
xfield = fieldgrid(xmin,xmax,nx,ymin,ymax,ny)
#r = sqrt(xfield[:,0]**2+xfield[:,1]**2)
#th = arctan2(xfield[:,1], -xfield[:,0])
Bf, Cf = fldmatbc(xfield, xnode)
phifld = calcphifld(phisrf,chisrf,Bf,Cf)
#phifld += r*u[0]*cos(th)
#for i in xrange(nx*ny):
# if r[i] < R:
# phifld[i] = 0.
xcont = linspace(xmin,xmax,nx)
ycont = linspace(ymin,ymax,ny)
Z = phifld.reshape((ny,nx))
plotphicont(xcont,ycont,Z)
plotvelfld(cpoint, v)
show()
def main():
from numpy import array, zeros, savetxt, eye, linspace, sqrt, \
arctan2, cos, pi, sin
from numpy.linalg import norm
from pylab import plot, show, grid, figure, subplot, quiver, xlim, \
ion, ioff, draw, savefig, ylim
#Geometry
figure(1)
nelem = 151
R = 1.
chord = 1.
thick = 0.2
ntstep = 20
Ttot = 1.
dt = Ttot / (ntstep - 1.)
#xnode = circlegeom(nelem,R); TEat1 = 0
xnode = geomwing(nelem, chord, thick)
TEat1 = 1
plotgeom(xnode)
#Boundary conditions
u = array([-1., 0.])
uarr = norm(u) * sinspeedprof(ntstep, Ttot)
chisrf = bcondvel(xnode, u)
#Integral equation solution
B, C = srfmatbc(xnode)
phisrf = solvephi(B, C, chisrf)
#Surface velocity calculation
v = calcsrfvel(xnode, TEat1, phisrf, chisrf)
#for i in xrange(nelem):
# v[i,0] += norm(u)
cpoint = collocation(xnode)
n = normals(xnode)
#Pressure figure
figure(2)
#ion()
spl = subplot(111)
spl.set_aspect('equal', 'box')
plotgeom(xnode)
#Pressure calculation and plotting
pres, lift = solvebem(xnode, uarr, TEat1, dt)
for t in xrange(ntstep):
hru2 = 0.5 * norm(uarr[t, :])**2
if hru2 > 0.001:
pres[:, t] /= hru2
lift[t] /= hru2
#pres = calcpres(xnode,TEat1,dt,u,phisrf,chisrf)
#plot(cpoint[:,0], cpoint[:,1], 'o')
#presplot = cpoint+pres*n
#plot(presplot[:,0],presplot[:,1])
xlim(-1, chord + 1)
grid()
ylim(-1, 1)
for t in xrange(ntstep):
plot(linspace(chord, 0, nelem / 2 + 1), pres[:nelem / 2 + 1, t], 'g')
#if t == 0:
# line, = plot(linspace(chord,0,nelem/2),pres[:nelem/2,t],'g')
#else:
# line.set_ydata(pres[:nelem/2,t])
ylim(-1, 1)
presn = abs(pres[:, t].reshape((nelem, 1))) * n
col = zeros(nelem)
#print pres[:,t]
for i in xrange(nelem):
if pres[i, t] > 0.:
col[i] = 1.
quiver(cpoint[:, 0],
cpoint[:, 1],
presn[:, 0],
presn[:, 1],
col,
units='dots',
width=0.8)
#if t == 0:
# qul = quiver(cpoint[:,0], cpoint[:,1],presn[:,0],presn[:,1], col, units='dots', width=0.8)
#else:
# qul.set_UVC(presn[:,0],presn[:,1], col)
#draw()
#savefig('pres%d' % t)
#ioff()
#Analitical for circle
#TH = linspace(pi/nelem,2*pi-pi/nelem,nelem)
#presan = 0.5*norm(u)**2*(1-4*sin(TH)**2)
#presplotan = cpoint+presan.reshape((nelem,1))*n
#plot(presplotan[:,0],presplotan[:,1])
#-----------LIFT------------
figure(3)
print lift
plot(linspace(0, Ttot, ntstep), lift)
figure(1)
#Field definition
xmin, xmax = -2., 2.
ymin, ymax = -1.5, 1.5
nx, ny = 100, 100
xfield = fieldgrid(xmin, xmax, nx, ymin, ymax, ny)
#r = sqrt(xfield[:,0]**2+xfield[:,1]**2)
#th = arctan2(xfield[:,1], -xfield[:,0])
Bf, Cf = fldmatbc(xfield, xnode)
phifld = calcphifld(phisrf, chisrf, Bf, Cf)
#phifld += r*u[0]*cos(th)
#for i in xrange(nx*ny):
# if r[i] < R:
# phifld[i] = 0.
xcont = linspace(xmin, xmax, nx)
ycont = linspace(ymin, ymax, ny)
Z = phifld.reshape((ny, nx))
plotphicont(xcont, ycont, Z)
plotvelfld(cpoint, v)
show()