我将继续深入研究计算流体动力学。我想构建一个简单的测试用例，用于在 FEniCS 中对围绕圆柱体的流动进行建模，然后继续对湍流建模以观察卡门涡街。
我是 FEniCS 和 CFD 的新手。我已经开始阅读 FEniCS 书，并阅读了教程中的第一个简单脚本。
由于这是一个标准问题，我不喜欢重新发明轮子，我的问题是：是否有一些关于如何做到这一点的教程？即使是没有很好注释的代码/FEniCS 脚本也可以作为参考。
我已经用谷歌搜索了这个并没有从中得到太多，这就是我在这里问的原因。
FEniCS 中围绕圆柱体流动的教程
计算科学
流体动力学
芬尼克斯
涡度
2021-12-16 13:23:58
3个回答
我建议您首先查看此处记录的 FEniCS Navier-Stokes 演示：
对于您的特定测试用例，您可能需要查看 NSBENCH 测试问题集（在 FEniCS 书的第 21 章中进行了描述）。该书章节的代码可在
可以在此处找到您的测试用例（围绕圆柱体流动）的代码：
http://bazaar.launchpad.net/~nsbench/nsbench/main/view/head:/problems/cylinder.py
请注意，此代码取决于 NSBENCH 中求解器定义的接口，但了解如何设置边界条件以及如何为您自己的求解器设计接口可能仍然有用。
这就是我认为它背后的旋转圆柱和卡门涡街。您也可以取消注释 SUPG/PSPG 稳定。但我怀疑h计算为 2*circumradius 的网格尺寸不是很好的数量，并且更喜欢以这种方式计算的单元直径https://scicomp.stackexchange.com/a/7181/4254
from dolfin import *
import time
#set_log_level(PROGRESS)
parameters['form_compiler']['representation'] = 'quadrature'
parameters['form_compiler']['optimize'] = True
parameters['form_compiler']['cpp_optimize'] = True
center = Point(0.2, 0.2)
radius = 0.05
class Cylinder(SubDomain):
def inside(self,x,on_boundary):
r = sqrt((x[0] - center[0])**2 + (x[1] - center[1])**2)
return(on_boundary and (r < 2*radius + sqrt(DOLFIN_EPS)))
def snap(self, x):
r = sqrt((x[0] - center[0])**2 + (x[1] - center[1])**2)
if r <= radius:
x[0] = center[0] + (radius / r)*(x[0] - center[0])
x[1] = center[1] + (radius / r)*(x[1] - center[1])
class Walls(SubDomain):
def inside(self, x, on_boundary):
return (on_boundary and ((x[1] < DOLFIN_EPS) or (x[1] > (0.41 - DOLFIN_EPS))))
class Inflow(SubDomain):
def inside(self, x, on_boundary):
return (on_boundary and (x[0] < DOLFIN_EPS))
class Outflow(SubDomain):
def inside(self, x, on_boundary):
return (on_boundary and (x[0] > (2.2 - DOLFIN_EPS)))
# Parameters
nu = Constant(0.001)
dt = 0.1
idt = Constant(1./dt)
t_end = 10.0
theta=0.5 # Crank-Nicholson timestepping
# Mesh
mesh = Mesh("bench_L1.xml")
boundary_parts = MeshFunction("size_t", mesh, mesh.topology().dim()-1)
boundary_parts.set_all(0)
Gamma = Cylinder()
Gamma.mark(boundary_parts, 1)
#refine the mesh and snap boundary
mesh = refine(mesh)
mesh.snap_boundary(Gamma, False)
# Define function spaces (Taylor-Hood)
V = VectorFunctionSpace(mesh, "CG", 2)
P = FunctionSpace(mesh, "CG", 1)
W = MixedFunctionSpace([V, P])
# No-slip boundary condition for velocity
noslip = Constant((0, 0))
bc0 = DirichletBC(W.sub(0), noslip, Walls())
vc = Expression(("-cos(atan2(x[0]-0.2,x[1]-0.2))","sin(atan2(x[0]-0.2,x[1]-0.2))"))
bc_cylinder = DirichletBC(W.sub(0), vc, Cylinder())
# Inflow boundary condition for velocity and temperature
v_in = Expression(("1.5 * 4.0 * x[1] * (0.41 - x[1]) / ( 0.41 * 0.41 )","0.0"))
bc1 = DirichletBC(W.sub(0), v_in, Inflow())
# Collect boundary conditions
bcs = [bc_cylinder, bc0, bc1]
# Define unknown and test function(s)
(u, q) = TestFunctions(W)
n = FacetNormal(mesh)
I = Identity(V.cell().d) # Identity tensor
# current time step
w = Function(W)
(v, p) = (as_vector((w[0], w[1])), w[2])
D = 0.5*(grad(v)+grad(v).T)
T = -p*I + 2.0*nu*D
# previous time step
w0 = Function(W)
(v0, p0) = (as_vector((w0[0], w0[1])), w0[2])
D0 = 0.5*(grad(v0)+grad(v0).T)
T0 = -p*I + 2.0*nu*D0
# Define variational forms without time derivative in previous time
F0_eq1 = (inner(T0, grad(u)))*dx + inner(grad(v0)*v0, u)*dx
F0_eq2 = 0*q*dx
F0 = F0_eq1 + F0_eq2
# variational form without time derivative in current time
F1_eq1 = (inner(T, grad(u)) + inner(grad(v)*v, u))*dx
F1_eq2 = q*div(v)*dx
F1 = F1_eq1 + F1_eq2
# combine variational forms with time derivative
#
# dw/dt + F(t) = 0 is approximated as
# (w-w0)/dt + (1-theta)*F(t0) + theta*F(t) = 0
#
F = idt*inner((v-v0),u)*dx + (1.0-theta)*F0 + theta*F1
# residual of strong Navier-Stokes
r = idt*(v-v0) + theta*grad(v)*v + (1.0-theta)*grad(v0)*v0 \
- theta*div(T) - (1.0-theta)*div(T0)
# stabilization parameter
h = CellSize(mesh)
velocity = v0
vnorm = sqrt(dot(velocity, velocity))
tau = ( (2.0*idt)**2 + (2.0*vnorm/h)**2 + (4.0*nu/h**2)**2 )**(-0.5)
# add SUPG stabilization
#F += tau*inner(grad(u)*v, r)*dx
# add PSPG stabilization
#F += tau*inner(grad(q), r)*dx
# define Jacobian
J = derivative(F, w)
# Create files for storing solution
ufile = File("results/velocity.pvd")
pfile = File("results/pressure.pvd")
# create variational problem and solver
problem = NonlinearVariationalProblem(F, w, bcs, J)
solver = NonlinearVariationalSolver(problem)
solver.parameters['newton_solver']['maximum_iterations'] = 20
# Time-stepping
t = dt
while t < t_end:
print "t =", t
# Compute
begin("Solving ....")
solver.solve()
end()
# Extract solutions:
(v, p) = w.split()
# Plot
#plot(v)
# Save to file
ufile << v
pfile << p
# Move to next time step
w0.assign(w)
t += dt
和网格文件
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SUPG / PSPG 实施存在问题。测试不收敛。我该如何解决这个问题？
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