Python diffusion Examples

Example #1

File: composition.py Project: live-clones/dolfin-adjoint

def transport(Q, dt, u, phi_):

    # Define test and trial functions
    phi = TrialFunction(Q)
    v = TestFunction(Q)

    # Constants associated with DG scheme
    alpha = StaticConstant(10.0)
    mesh = Q.mesh()
    h = CellSize(mesh)
    n = FacetNormal(mesh)

    # Diffusivity constant
    kappa = StaticConstant(0.0001)

    # Define discrete time derivative operator
    Dt = lambda phi: backward_euler(phi, phi_, dt)
    a_A = lambda phi, v: advection(phi, v, u, n)
    a_D = lambda phi, v: diffusion(phi, v, kappa, alpha, n, h)

    # Define form
    F = Dt(phi) * v * dx + a_A(phi, v) + a_D(phi, v)

    return (lhs(F), rhs(F))

Example #2

File: temperature.py Project: cpknowles/dolfin-adjoint

def energy(Q, dt, u, T_):

    # Define basis functions
    T = TrialFunction(Q)
    psi = TestFunction(Q)

    # Diffusivity constant
    kappa = Constant(1.0)

    # Variables associated with DG scheme
    alpha = Constant(50.0)
    mesh = Q.mesh()
    h = CellSize(mesh)
    n = FacetNormal(mesh)

    # Define discrete time derivative operator
    Dt =  lambda T:    backward_euler(T, T_, dt)
    a_A = lambda u, T, psi: advection(T, psi, u, n)
    a_D = lambda T, psi: diffusion(T, psi, kappa, alpha, n, h)

    # Define form
    F = Dt(T)*psi*dx + a_A(u, T, psi) + a_D(T, psi)

    return (lhs(F), rhs(F))

Example #3

File: temperature.py Project: zzyatlantise/dolfin-adjoint

def energy(Q, dt, u, T_):

    # Define basis functions
    T = TrialFunction(Q)
    psi = TestFunction(Q)

    # Diffusivity constant
    kappa = StaticConstant(1.0)

    # Variables associated with DG scheme
    alpha = StaticConstant(50.0)
    mesh = Q.mesh()
    h = CellSize(mesh)
    n = FacetNormal(mesh)

    # Define discrete time derivative operator
    Dt = lambda T: backward_euler(T, T_, dt)
    a_A = lambda u, T, psi: advection(T, psi, u, n)
    a_D = lambda T, psi: diffusion(T, psi, kappa, alpha, n, h)

    # Define form
    F = Dt(T) * psi * dx + a_A(u, T, psi) + a_D(T, psi)

    return (lhs(F), rhs(F))

Example #4

def transport(Q, dt, u, phi_):

    # Define test and trial functions
    phi = TrialFunction(Q)
    v = TestFunction(Q)

    # Constants associated with DG scheme
    alpha = StaticConstant(10.0)
    mesh = Q.mesh()
    h = CellSize(mesh)
    n = FacetNormal(mesh)

    # Diffusivity constant
    kappa = StaticConstant(0.0001)

    # Define discrete time derivative operator
    Dt =  lambda phi:    backward_euler(phi, phi_, dt)
    a_A = lambda phi, v: advection(phi, v, u, n)
    a_D = lambda phi, v: diffusion(phi, v, kappa, alpha, n, h)

    # Define form
    F = Dt(phi)*v*dx + a_A(phi, v) + a_D(phi, v)

    return (lhs(F), rhs(F))

Example #5

File: temperature.py Project: cpknowles/dolfin-adjoint

 def a_D(T, psi):
     return diffusion(T, psi, k_c, alpha, n, h, theta=0.5)

Example #6

File: temperature.py Project: zzyatlantise/dolfin-adjoint

 def a_D(T, psi):
     return diffusion(T, psi, k_c, alpha, n, h, theta=0.5)