def solve_poisson(self):
"""Solves the Poisson equation for the pressure field."""
b = 1. / Parameters.dt * (grad(Solver.u, 'x') + grad(Solver.v, 'y'))
Solver.p.field = Solver.poisson.solve(Solver.p.laplacian.mat,
b - Solver.p.laplacian.bc_vect,
Solver.p.field)
print '{Poisson} Number of iterations: %d' \
% Solver.poisson.ite
def plot_vorticity(u, v, body=None, limits=None):
"""Plots vorticity field on the mesh.
Arguments
---------
u, v -- instances Variable for the velocity components.
body -- immersed body (default None).
limits -- plot limits (default None).
"""
u.read()
v.read()
# computes vorticity
w = grad(v, 'x') - grad(u, 'y')
# initializes figure
plt.figure(num=None)
plt.grid(False)
plt.xlabel(r'$x$', fontsize=20)
plt.xlabel(r'$y$', fontsize=20)
# creates contour of vorticity
nc = 100
wmin, wmax = w.min(), w.max()
wmin, wmax = -1.0, 1.0
if wmin == wmax:
wmin, wmax = -1.0, 1.0
levels = np.linspace(wmin, wmax, nc)
cont = plt.contourf(Mesh.x,
Mesh.y,
w.reshape(Mesh.Ny, Mesh.Nx),
levels,
extend='both',
cmap=cm.jet)
cbar = plt.colorbar(cont)
cbar.set_label('vorticity')
# plots body of there is one
if Mesh.is_body:
plt.plot(np.append(body.x, body.x[0]),
np.append(body.y, body.y[0]),
'k',
ls='-',
lw=1)
# sets axis limits
plt.xlim(limits[0], limits[1])
plt.ylim(limits[2], limits[3])
# inserts title and saves figure
plt.title('vorticity - ' + str(Parameters.ite))
plt.savefig(Case.path + '/images/' + 'vorticity' +
str('%04d' % (Parameters.ite, )) + '.png')
plt.clf()
plt.close()
def intermediate_velocity(self):
"""Computes the intermediate velocity field.
Solves the Navier-Stokes equations,
without the pressure gradient and boundardy forces,
using Euler's method.
"""
Solver.u.field += Parameters.dt * (
1. / Parameters.Re * lap(Solver.u) - Solver.u.field *
grad(Solver.u, 'x') - Solver.v.field * grad(Solver.u, 'y'))
Solver.v.field += Parameters.dt * (
1. / Parameters.Re * lap(Solver.v) - Solver.u.field *
grad(Solver.v, 'x') - Solver.v.field * grad(Solver.v, 'y'))
def intermediate_velocity(self): """Computes the intermediate velocity field. Solves the Navier-Stokes equations, without the pressure gradient and boundardy forces, using Euler's method. """ Solver.u.field += Parameters.dt * ( 1./Parameters.Re*lap(Solver.u) - Solver.u.field*grad(Solver.u, 'x') - Solver.v.field*grad(Solver.u, 'y')) Solver.v.field += Parameters.dt * ( 1./Parameters.Re*lap(Solver.v) - Solver.u.field*grad(Solver.v, 'x') - Solver.v.field*grad(Solver.v, 'y'))
def plot_vorticity(u, v, body=None, limits=None):
"""Plots vorticity field on the mesh.
Arguments
---------
u, v -- instances Variable for the velocity components.
body -- immersed body (default None).
limits -- plot limits (default None).
"""
u.read()
v.read()
# computes vorticity
w = grad(v,'x') - grad(u,'y')
# initializes figure
plt.figure(num=None)
plt.grid(False)
plt.xlabel(r'$x$', fontsize=20)
plt.xlabel(r'$y$', fontsize=20)
# creates contour of vorticity
nc = 100
wmin, wmax = w.min(), w.max()
wmin, wmax = -1.0, 1.0
if wmin == wmax:
wmin, wmax = -1.0, 1.0
levels = np.linspace(wmin, wmax, nc)
cont = plt.contourf(Mesh.x, Mesh.y, w.reshape(Mesh.Ny, Mesh.Nx),
levels, extend='both', cmap=cm.jet)
cbar = plt.colorbar(cont)
cbar.set_label('vorticity')
# plots body of there is one
if Mesh.is_body:
plt.plot(np.append(body.x,body.x[0]), np.append(body.y, body.y[0]), 'k', ls='-', lw=1)
# sets axis limits
plt.xlim(limits[0], limits[1])
plt.ylim(limits[2], limits[3])
# inserts title and saves figure
plt.title('vorticity - '+str(Parameters.ite))
plt.savefig(Case.path+'/images/'+'vorticity'+str('%04d'%(Parameters.ite,))+'.png')
plt.clf()
plt.close()
def update_velocity(self): """Updates the velocity field with pressure correction to make the field divergence-free. """ Solver.u.field -= Parameters.dt * grad(Solver.p, 'x') Solver.v.field -= Parameters.dt * grad(Solver.p, 'y')
def solve_poisson(self):
"""Solves the Poisson equation for the pressure field."""
b = 1./Parameters.dt * (grad(Solver.u, 'x') + grad(Solver.v, 'y'))
Solver.p.field = Solver.poisson.solve(Solver.p.laplacian.mat, b-Solver.p.laplacian.bc_vect, Solver.p.field)
print '{Poisson} Number of iterations: %d' \
% Solver.poisson.ite
def update_velocity(self):
"""Updates the velocity field with pressure correction
to make the field divergence-free.
"""
Solver.u.field -= Parameters.dt * grad(Solver.p, 'x')
Solver.v.field -= Parameters.dt * grad(Solver.p, 'y')
