import paraBEM
from paraBEM.pan2d import doublet_2_0, source_2_0, source_2_0_v
from paraBEM.vtk_export import VtkWriter
from paraBEM.utils import check_path
a = list(map(paraBEM.PanelVector2, [[-1, -1], [-1, 1]]))
b = list(map(paraBEM.PanelVector2, [[1, -1], [1, 1]]))
pan_a = paraBEM.Panel2(a)
pan_b = paraBEM.Panel2(b)
n = 100
space = numpy.linspace(-2, 2, n)
grid = [paraBEM.Vector2(x, y) for y in space for x in space]
pot = [source_2_0(v, pan_a) - source_2_0(v, pan_b) for v in grid]
vel = [source_2_0_v(v, pan_a) - source_2_0_v(v, pan_b) for v in grid]
writer = VtkWriter()
with open(check_path("results/parallel_flow.vtk"), "w") as _file:
writer.structed_grid(_file, "doublet_2", [n, n, 1])
writer.points(_file, grid)
writer.data(_file,
pot,
name="potential",
_type="SCALARS",
data_type="POINT_DATA")
writer.data(_file,
vel,
name="velocity",
_type="VECTORS",
data_type="POINT_DATA")
v1 = paraBEM.PanelVector2(-2, 0)
v2 = paraBEM.PanelVector2(2, 0)
panel = paraBEM.Panel2([v1, v2])
n = 500
space = np.linspace(-5, 5, n)
grid = [paraBEM.Vector2([x, y]) for y in space for x in space]
dub_vals = [doublet_2_0(target, panel) for target in grid]
dub_vals_lin_1 = [doublet_2_1(target, panel, True) for target in grid]
dub_vals_lin_2 = [doublet_2_1(target, panel, False) for target in grid]
src_vals = [source_2_0(target, panel) for target in grid]
dublinv1_vals = [doublet_2_1_v(target, panel, True) for target in grid]
dublinv2_vals = [doublet_2_1_v(target, panel, False) for target in grid]
dubv_vals = [doublet_2_0_v(target, panel) for target in grid]
srcv_vals = [source_2_0_v(target, panel) for target in grid]
writer = VtkWriter()
with open(check_path("results/element_2.vtk"), "w") as _file:
writer.structed_grid(_file, "element_2", [n, n, 1])
writer.points(_file, grid)
writer.data(_file, dub_vals, name="doublet", _type="SCALARS", data_type="POINT_DATA")
writer.data(_file, dub_vals_lin_1, name="doublet_lin_1", _type="SCALARS", data_type="POINT_DATA")
writer.data(_file, dub_vals_lin_2, name="doublet_lin_2", _type="SCALARS", data_type="POINT_DATA")
writer.data(_file, src_vals, name="source", _type="SCALARS", data_type="POINT_DATA")
writer.data(_file, dublinv1_vals, name="doublet_lin_1_v", _type="VECTORS", data_type="POINT_DATA")
writer.data(_file, dublinv2_vals, name="doublet_lin_2_v", _type="VECTORS", data_type="POINT_DATA")
writer.data(_file, dubv_vals, name="doublet_v", _type="VECTORS", data_type="POINT_DATA")
writer.data(_file, srcv_vals, name="source_v", _type="VECTORS", data_type="POINT_DATA")
ny = 300
x_grid = np.linspace(-3, 3, nx)
y_grid = np.linspace(-3, 3, ny)
grid = [paraBEM.Vector2(x, y) for y in y_grid for x in x_grid]
temp_list = []
for point in grid:
t = 0
t -= doublet_2_0(point, pan1) * sol[0] * R1 * l
t -= doublet_2_0(point, pan2) * sol[1] * R2 * l
t += source_2_0(point, pan1) * sol[0]
t += source_2_0(point, pan2) * sol[1]
temp_list.append(t)
q_list = []
for point in grid:
q = paraBEM.Vector2(0, 0)
q -= doublet_2_0_v(point, pan1) * sol[0] * R1 * l
q -= doublet_2_0_v(point, pan2) * sol[1] * R2 * l
q += source_2_0_v(point, pan1) * sol[0]
q += source_2_0_v(point, pan2) * sol[1]
q_list.append(q)
writer = VtkWriter()
with open(check_path("results/heat_test.vtk"), "w") as _file:
writer.structed_grid(_file, "element_2", [nx, ny, 1])
writer.points(_file, grid)
writer.data(_file, temp_list, name="temperature", _type="SCALARS", data_type="POINT_DATA")
writer.data(_file, q_list, name="q", _type="VECTORS", data_type="POINT_DATA")
nx = 300
ny = 300
x_grid = np.linspace(-3, 3, nx)
y_grid = np.linspace(-3, 3, ny)
grid = [paraBEM.Vector2(x, y) for y in y_grid for x in x_grid]
t_list = []
for point in grid:
t = 0
for i, panel_i in enumerate(panels):
t -= source_2_0(point, panel_i) * sol[i]
t += doublet_2_0(point, panel_i) * sol[i] * R
t_list.append(t)
q_list = []
for point in grid:
q = paraBEM.Vector2(0, 0)
for i, panel_i in enumerate(panels):
q -= source_2_0_v(point, panel_i) * sol[i]
q += doublet_2_0_v(point, panel_i) * sol[i] * R
q_list.append(q)
writer = VtkWriter()
with open(check_path("results/heat_test.vtk"), "w") as _file:
writer.structed_grid(_file, "element_2", [nx, ny, 1])
writer.points(_file, grid)
writer.data(_file, t_list, name="temperature", _type="SCALARS", data_type="POINT_DATA")
writer.data(_file, q_list, name="q", _type="VECTORS", data_type="POINT_DATA")
x_grid = np.linspace(-3, 3, nx)
y_grid = np.linspace(-3, 3, ny)
grid = [paraBEM.Vector2(x, y) for y in y_grid for x in x_grid]
t_list = []
for point in grid:
t = 0
for i, panel_i in enumerate(panels):
t -= source_2_0(point, panel_i) * sol[i]
t += doublet_2_0(point, panel_i) * sol[i] * R
t_list.append(t)
q_list = []
for point in grid:
q = paraBEM.Vector2(0, 0)
for i, panel_i in enumerate(panels):
q -= source_2_0_v(point, panel_i) * sol[i]
q += doublet_2_0_v(point, panel_i) * sol[i] * R
q_list.append(q)
writer = VtkWriter()
with open(check_path("results/heat_test.vtk"), "w") as _file:
writer.structed_grid(_file, "element_2", [nx, ny, 1])
writer.points(_file, grid)
writer.data(_file,
t_list,
name="temperature",
_type="SCALARS",
data_type="POINT_DATA")
writer.data(_file,
q_list,
name="q",
import paraBEM
from paraBEM.pan2d import doublet_2_0, source_2_0, source_2_0_v
from paraBEM.vtk_export import VtkWriter
from paraBEM.utils import check_path
a = list(map(paraBEM.PanelVector2, [[-1, -1], [-1, 1]]))
b = list(map(paraBEM.PanelVector2, [[1, -1], [1, 1]]))
pan_a = paraBEM.Panel2(a)
pan_b = paraBEM.Panel2(b)
n = 100
space = numpy.linspace(-2, 2, n)
grid = [paraBEM.Vector2(x, y) for y in space for x in space]
pot = [
source_2_0(v, pan_a) -
source_2_0(v, pan_b)
for v in grid]
vel = [
source_2_0_v(v, pan_a) -
source_2_0_v(v, pan_b)
for v in grid]
writer = VtkWriter()
with open(check_path("results/parallel_flow.vtk"), "w") as _file:
writer.structed_grid(_file, "doublet_2", [n, n, 1])
writer.points(_file, grid)
writer.data(_file, pot, name="potential", _type="SCALARS", data_type="POINT_DATA")
writer.data(_file, vel, name="velocity", _type="VECTORS", data_type="POINT_DATA")
# T 0 ? 1 # l 1 2 # panel1: temp-formulation T1 = -10 T2 = 10 l1 = 1 l2 = 2 mat[0, 0] = source_2_0(panels[0].center, panels[0]) mat[0, 1] = source_2_0(panels[0].center, panels[1]) * (1 - l2 / l1) mat[0, 2] = source_2_0(panels[0].center, panels[2]) rhs[0] += doublet_2_0(panels[0].center, panels[0]) * T1 rhs[0] += doublet_2_0(panels[0].center, panels[2]) * T2 rhs[0] += T1 # panel2: velocity formulation mat[1, 0] = source_2_0_v(panels[1].center, panels[0]).dot(panels[1].n) mat[1, 1] = source_2_0_v(panels[1].center, panels[1]).dot(panels[1].n) * (1 - l2 / l1) - 1 mat[1, 2] = source_2_0_v(panels[1].center, panels[2]).dot(panels[1].n) rhs[1] += doublet_2_0_v(panels[1].center, panels[0]).dot(panels[1].n) * T1 rhs[1] += doublet_2_0_v(panels[1].center, panels[2]).dot(panels[1].n) * T2 # panel3: temp-formulation mat[2, 0] = source_2_0(panels[2].center, panels[0]) mat[2, 1] = source_2_0(panels[2].center, panels[1]) * (1 - l2 / l1) mat[2, 2] = source_2_0(panels[2].center, panels[2]) rhs[2] += doublet_2_0(panels[2].center, panels[0]) * T1 rhs[2] += doublet_2_0(panels[2].center, panels[2]) * T2 rhs[2] += T2 sol = np.linalg.solve(mat, rhs) print(mat)
