def plate_with_hole(size=.05):
fd = lambda p: dm.ddiff(dm.drectangle(p, -1, 1, -1, 1),
dm.dcircle(p, 0, 0, 0.5))
fh = lambda p: 0.05 + 0.3 * dm.dcircle(p, 0, 0, 0.5)
p, t = dm.distmesh2d(fd, fh, size, (-1, -1, 1, 1), [(-1, -1), (-1, 1),
(1, -1), (1, 1)])
return p, t
def plate_with_hole(size=.05):
fd = lambda p: dm.ddiff(dm.drectangle(p,-1,1,-1,1),
dm.dcircle(p,0,0,0.5))
fh = lambda p: 0.05+0.3*dm.dcircle(p,0,0,0.5)
p, t = dm.distmesh2d(fd, fh, size, (-1,-1,1,1),
[(-1,-1),(-1,1),(1,-1),(1,1)])
return p, t
def naca0012_airfoil():
"""NACA0012 airfoil"""
hlead = 0.01
htrail = 0.04
hmax = 2
circx = 2
circr = 4
a = .12 / .2 * np.array([0.2969, -0.1260, -0.3516, 0.2843, -0.1036])
a0 = a[0]
a1 = np.hstack((a[5:0:-1], 0.0))
fd = lambda p: dm.ddiff(dm.dcircle(p, circx, 0, circr), (abs(
p[:, 1]) - np.polyval(a1, p[:, 0]))**2 - a0**2 * p[:, 0])
fh = lambda p: np.minimum(
np.minimum(hlead + 0.3 * dm.dcircle(p, 0, 0, 0), htrail + 0.3 * dm.
dcircle(p, 1, 0, 0)), hmax)
fixx = 1.0 - htrail * np.cumsum(1.3**np.arange(5))
fixy = a0 * np.sqrt(fixx) + np.polyval(a1, fixx)
fix = np.vstack(
(np.array([(circx - circr, 0), (circx + circr, 0), (circx, -circr),
(circx, circr), (0, 0), (1, 0)]), np.vstack(
(fixx, fixy)).T, np.vstack((fixx, -fixy)).T))
box = (circx - circr, -circr, circx + circr, circr)
h0 = min(hlead, htrail, hmax)
return dm.distmesh2d(fd, fh, h0, box, fix)
def rectangle_with_circular_hole():
"""Rectangle with circular hole, refined at circle boundary"""
fd = lambda p: dm.ddiff(dm.drectangle(p, -1, 1, -1, 1),
dm.dcircle(p, 0, 0, 0.5))
fh = lambda p: 0.05 + 0.3 * dm.dcircle(p, 0, 0, 0.5)
return dm.distmesh2d(fd, fh, 0.05, (-1, -1, 1, 1), [(-1, -1), (-1, 1),
(1, -1), (1, 1)])
def square():
"""Square, with size function point and line sources"""
fd = lambda p: dm.drectangle(p,0,1,0,1)
fh = lambda p: np.minimum(np.minimum(
0.01+0.3*abs(dm.dcircle(p,0,0,0)),
0.025+0.3*abs(dm.dpoly(p,[(0.3,0.7),(0.7,0.5)]))), 0.15)
return dm.distmesh2d(fd, fh, 0.01, (0,0,1,1), [(0,0), (1,0), (0,1), (1,1)])
def square():
"""Square, with size function point and line sources"""
fd = lambda p: dm.drectangle(p, 0, 1, 0, 1)
fh = lambda p: np.minimum(
np.minimum(0.01 + 0.3 * abs(dm.dcircle(p, 0, 0, 0)), 0.025 + 0.3 * abs(
dm.dpoly(p, [(0.3, 0.7), (0.7, 0.5)]))), 0.15)
return dm.distmesh2d(fd, fh, 0.01, (0, 0, 1, 1), [(0, 0), (1, 0), (0, 1),
(1, 1)])
def naca0012_airfoil():
"""NACA0012 airfoil"""
hlead=0.01; htrail=0.04; hmax=2; circx=2; circr=4
a=.12/.2*np.array([0.2969,-0.1260,-0.3516,0.2843,-0.1036])
a0=a[0]; a1=np.hstack((a[5:0:-1], 0.0))
fd = lambda p: dm.ddiff(
dm.dcircle(p,circx,0,circr),
(abs(p[:,1])-np.polyval(a1, p[:,0]))**2-a0**2*p[:,0])
fh = lambda p: np.minimum(np.minimum(
hlead+0.3*dm.dcircle(p,0,0,0),
htrail+0.3*dm.dcircle(p,1,0,0)),hmax)
fixx = 1.0-htrail*np.cumsum(1.3**np.arange(5))
fixy = a0*np.sqrt(fixx)+np.polyval(a1, fixx)
fix = np.vstack((
np.array([(circx-circr,0),(circx+circr,0),
(circx,-circr),(circx,circr),
(0,0),(1,0)]),
np.vstack((fixx, fixy)).T,
np.vstack((fixx, -fixy)).T))
box = (circx-circr,-circr, circx+circr,circr)
h0 = min(hlead, htrail, hmax)
return dm.distmesh2d(fd, fh, h0, box, fix)
def __init__(self, lx, ly, cx, cy, r): fd = lambda p: dm.ddiff(dm.drectangle(p,-lx,lx,-ly,ly), dm.dcircle(p,cx,cx,r)) fh = lambda p: 0.05+0.03*dm.dcircle(p,cx,cy,r) p, t = dm.distmeshnd(fd, fh, 0.5, (-lx,-ly,lx,ly),[(-lx,-ly),(-lx,ly),(lx,-ly),(lx,ly)]) self.nodes = p self.conn = t
# Problem 2 Mesh Generation
h0_rect = 0.05
h0_cell = h0_rect * (7 / 8)
h0_elec = h0_cell
xi = -5
xf = 5
yi = 0
yf = 6
x_elec1 = [-3, -1]
x_elec2 = [1, 3]
x_range = [xi, xf]
y_range = [yi, yf]
bbox = [xi - 0.1, yi - 0.1, xf + 0.1, yf + 0.1]
# Mesh inside the cell
fd_rod1 = lambda p: dm.dcircle(p, 0, 2, 1)
p_r1, t_r1 = dm.distmesh2d(fd_rod1, dm.huniform, h0_cell, bbox)
plt.scatter(p_r1[:, 0], p_r1[:, 1], s=1, marker=".")
plt.title("Cell mesh - Problem #2")
plt.show()
# Rectangle mesh
fd_rect = lambda p: dm.drectangle0(p, xi, xf, yi, yf)
# Add denser mesh around the electrodes
N_elec = int((max(x_elec1) - min(x_elec1)) / h0_elec)
p_e1 = np.zeros((N_elec, 2))
p_e1[:, 0] = np.linspace(min(x_elec1), max(x_elec1), N_elec)
p_e2 = p_e1.copy()
def rectangle_with_circle_at_corner():
# Does not terminate!
fd = lambda p: dm.ddiff(dm.drectangle(p, 0, 10, 0, 6),
dm.dcircle(p, 10, 0, 4))
return dm.distmesh2d(fd, dm.huniform, 0.9, (0, 0, 10, 6))
def fh(p):
return dm.dunion(dm.dunion(0.0004-0.3*fdout(p), 0.0004+0.3*dm.dcircle(p,0,0,vfr)), 0.0004+0.3*dm.dcircle(p,2*rad,0,vfr))
import distmesh as dm fd = lambda p: dm.ddiff(dm.drectangle(p,-1,1,-1,1), dm.dcircle(p,0,0,0.5)) fh = lambda p: 0.05+0.3*dm.dcircle(p,0,0,0.5) p, t = dm.distmesh2d(fd, fh, 0.05, (-1,-1,1,1), [(-1,-1),(-1,1),(1,-1),(1,1)])
def rectangle_with_circle_at_corner():
# Does not terminate!
fd = lambda p: dm.ddiff(dm.drectangle(p,0,10,0,6), dm.dcircle(p,10,0,4))
return dm.distmesh2d(fd, dm.huniform, 0.9, (0, 0, 10, 6))
def rectangle_with_circle_at_centre():
# Does not terminate!
fd = lambda p: dm.ddiff(dm.drectangle(p,0,20,0,12), dm.dcircle(p,10,6,4))
return dm.distmesh2d(fd, dm.huniform, 0.5, (0, 0, 20, 12), max_iter=100)
def fdout(p):
return dm.dunion(dm.dunion(dm.dcircle(p,0,0,rad), dm.drectangle(p,0.0,2*rad, -rad,rad)), dm.dcircle(p,2*rad,0,rad))
def fd(p):
return dm.ddiff(dm.ddiff(fdout(p), dm.dcircle(p,0,0,vfr)), dm.dcircle(p,2*rad,0,vfr))
def rectangle_with_circular_hole():
"""Rectangle with circular hole, refined at circle boundary"""
fd = lambda p: dm.ddiff(dm.drectangle(p,-1,1,-1,1), dm.dcircle(p,0,0,0.5))
fh = lambda p: 0.05+0.3*dm.dcircle(p,0,0,0.5)
return dm.distmesh2d(fd, fh, 0.05, (-1,-1,1,1),
[(-1,-1),(-1,1),(1,-1),(1,1)])
# Problem 1 Mesh Generation
h0_rect = 0.015
h0_rod1 = 0.8*h0_rect
h0_rod2 = 0.8*h0_rect
xi = -1.5; xf = 1.5
yi = -1.0; yf = 1.0
x_range = [xi, xf]
y_range = [yi, yf]
bbox = [xi-0.1, yi-0.1, xf+0.1, yf+0.1]
# Mesh inside the first circle
fig = plt.figure(dpi=400)
rod_dist = 0.35
fd_rod1 = lambda p: dm.dcircle(p, -rod_dist/2, 0, 0.1)
p_r1, t_r1 = dm.distmesh2d(fd_rod1, dm.huniform, h0_rod1, bbox, pfix=None)
#plt.scatter(p_r1[:, 0], p_r1[:, 1], s=5, color="black", marker=".")
plt.title("Rod1 mesh - Problem #1")
plt.show()
fig = plt.figure(dpi=400)
fd_rod2 = lambda p: dm.dcircle(p, rod_dist/2, 0, 0.05)
p_r2, t_r2 = dm.distmesh2d(fd_rod2, dm.huniform, h0_rod2, bbox, pfix=None)
#plt.scatter(p_r2[:, 0], p_r2[:, 1], s=5, color="black", marker=".")
plt.title("Rod2 mesh - Problem #1")
plt.show()
def rectangle_with_circle_at_centre():
# Does not terminate!
fd = lambda p: dm.ddiff(dm.drectangle(p, 0, 20, 0, 12),
dm.dcircle(p, 10, 6, 4))
return dm.distmesh2d(fd, dm.huniform, 0.5, (0, 0, 20, 12), max_iter=100)
