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 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()