API Reference

class oasisx.DirichletBC(value: Union[float64, Constant, Callable[[ndarray[Any, dtype[float64]]], ndarray[Any, dtype[float64]]]], method: LocatorMethod, marker: Union[Tuple[MeshTags, int32], Callable[[ndarray[Any, dtype[float64]]], ndarray[Any, dtype[bool_]]]])

Create a Dirichlet boundary condition based on topological or geometrical info from the mesh This boundary condtion should only be used for velocity function spaces.

Parameters

• value – The value the degrees of freedom should have. It can be a float, a dolfinx.fem.Constant or a lambda-function.

• method – Locator method for marker.

• marker – If oasisx.LocatorMethod.TOPOLOGICAL the input should be a tuple of a mesh tag and the corresponding value for the entities to assign Dirichlet conditions to. If oasisx.LocatorMethod.GEOMETRICAL the input is a lambda function taking in x, y, and z coordinates (ordered as [[x0, x1,…,xn], [y0,…,yn], [z0,…,zn]]), and return a boolean marker where the ith entry indicates if [xi, yi, zi] should have a diriclet bc.

Example

Assigning a topological condition

entities = np.array([0,3,8],dtype=np.int32)
values = np.full_like(entities, 2, dtype=np.int32)
mt  = dolfinx.fem.meshtags(mesh, mesh.topology.dim-1, entities, values)
bc = DirichletBC(5., LocatorMethod.TOPOLOGICAL, (mt, 2))

Assigning a geometrical condition

bc = DirchletBC(dolfinx.fem.Constant(mesh, 3.), lambda x: np.isclose(x[0]))

apply(x: Vec)

Apply boundary condition to a PETSc vector

create_bc(V: FunctionSpace)

update_bc()

Update the underlying function if input value is a lambda function

class oasisx.FractionalStep_AB_CN(mesh: Mesh, u_element: Union[Tuple[str, int], FiniteElement], p_element: Union[Tuple[str, int], FiniteElement], bcs_u: List[List[DirichletBC]], bcs_p: List[PressureBC], rotational: bool = False, solver_options: Optional[dict] = None, jit_options: Optional[dict] = None, body_force: Optional[Expr] = None, options: Optional[dict] = None)

Create the fractional step solver with Adam-Bashforth linearization of the convective term, and Crank-Nicholson time discretization.

Parameters

• mesh – The computational domain

• u_element – A tuple describing the finite element family and degree of the element used for the velocity

• p_element – A tuple describing the finite element family and degree of the element used for the pressure

• bcs_u – List of Dirichlet BCs for each component of the velocity

• bcs_p – List of Dirichlet BCs for the pressure

• rotational – If True, use rotational form of pressure update

• solver_options – Dictionary with keys ‘tentative’, ‘pressure’ and ‘scalar’, where each key leads to a dictionary of of PETSc options for each problem

• jit_options – Just in time parameters, to optimize form compilation

• options – Options for the Oasis solver. “low_memory_version” True/False changes if \(\int\nabla_k p^* v~\mathrm{d}x\) is assembled as True: directly into a vector or False: matrix-vector product. Default value: True ‘“bc_topological”` True/False. changes how the Dirichlet dofs are located. If True facet_markers has to be supplied.

• body_force – List of forces acting in each direction (x,y,z)

assemble_first(dt: float, nu: float)

Assembly routine for first iteration of pressure/velocity system.

\[A=\frac{1}{\delta t}M + \frac{1}{2} C +\frac{1}{2}\nu K\]

where M is the mass matrix, K the stiffness matrix and C the convective term. We also assemble parts of the right hand side:

\[b_k=\left(\frac{1}{\delta t}M 0 \frac{1}{2} C -\frac{1}{2}\nu K\right)u_k^{n-1} + \int_{\Omega} f_k^{n-\frac{1}{2}}v_k~\mathrm{d}x + \int h^{n-\frac{1}{2}} n_k \nabla_k v~\mathrm{d}x\]

Parameters

• dt – The time step

• nu – The kinematic viscosity

pressure_assemble(dt: float)

Assemble RHS for pressure correction term

\[b_c = \int_{\Omega} \mathrm{div} u^l q~\mathrm{d}x.\]

pressure_solve(nu: Optional[float] = None, rotational: bool = False) → int32

Solve pressure correction problem

solve(dt: float, nu: float, max_error: float = 1e-12, max_iter: int = 10)

Propagate splitting scheme one time step

Parameters

• dt – The time step

• nu – The kinematic velocity

• max_error – The maximal difference for inner iterations of solving u

• max_iter – Maximal number of inner iterations for u

property u

Return the solution to the tentative velocity equation as a vector function

velocity_tentative_assemble()

Assemble RHS of tentative velocity equation computing the \(p^*\)-dependent term of

\[b_k \mathrel{+}= b(u_k^{n-1}) + \int_{\Omega} p^*\frac{\partial v_k}{\partial x_k}~\mathrm{d}x.\]

\(b(u_k^{n-1})\) is computed in FractionalStep_AB_CN.assemble_first.

velocity_tentative_solve() → Tuple[float, ndarray[Any, dtype[int32]]]

Apply Dirichlet boundary condition to RHS vector and solver linear algebra system

Returns the difference between the two solutions and the solver error codes

velocity_update(dt) → ndarray[Any, dtype[int32]]

Compute Velocity update

class oasisx.LocatorMethod(value)

Search methods for Dirichlet BCs

GEOMETRICAL = 1

TOPOLOGICAL = 2

class oasisx.PressureBC(value: Union[float64, Constant, Callable[[ndarray[Any, dtype[float64]]], ndarray[Any, dtype[float64]]]], marker: Tuple[MeshTags, Union[int32, Tuple[int32]]])

Create a Pressure boundary condition (natural bc) based on a set of facets of a mesh and some value.

Parameters

• value – The value the degrees of freedom should have. It can be a float, a dolfinx.fem.Constant or a lambda-function. If value is a lambda-function it is interpolated into the pressure space.

• marker – Tuple of a mesh tag and the corresponding value for the entities to assign Dirichlet conditions to. The meshtag dimension has to be mesh.topology.dim -1.

Example

Assigning a constant condition

entities = np.array([0,3,8],dtype=np.int32)
values = np.full_like(entities, 2, dtype=np.int32)
mt  = dolfinx.fem.meshtags(mesh, mesh.topology.dim-1, entities, values)
bc = DirichletBC(5., (mt, 2))

Assigning a time-dependent condition

class OutletPressure():
    def __init__(self, t:float):
        self.t = t
    def eval(self, x: numpy.typing.NDArray[np.float64]):
        return self.t*x[0]

p = OutletPressure(0.)
entities = np.array([0,3,8],dtype=np.int32)
values = np.full_like(entities, 2, dtype=np.int32)
mt  = dolfinx.fem.meshtags(mesh, mesh.topology.dim-1, entities, values)
bc = PressureBC(p,  (mt, 2))

Q = dolfinx.fem.functionspace(mesh, ("Lagrange", 1))
# Create appropriate structures for assigning bcs
bc.create_bc(Q)
# Update time in bc
p.t = 1

create_bcs(V: FunctionSpace, Q: FunctionSpace)

Create boundary conditions for the pressure conditions for a given velocity and pressure function space

Parameters

• V – The velocity function space

• Q – The pressure function space

update_bc()

Update boundary condition if input-value is a lambda function

class oasisx.Projector(function: Expr, space: FunctionSpace, bcs: Optional[List[DirichletBC]] = None, petsc_options: Optional[dict] = None, jit_options: Optional[dict] = None, form_compiler_options: Optional[dict] = None, metadata: Optional[dict] = None)

Projector for a given function. Solves Ax=b, where

u, v = ufl.TrialFunction(Space), ufl.TestFunction(space)
dx = ufl.Measure("dx", metadata=metadata)
A = inner(u, v) * dx
b = inner(function, v) * dx

Parameters

• function – UFL expression of function to project

• space – Space to project function into

• bcs – List of BCS to apply to projection

• petsc_options – Options to pass to PETSc

• jit_options – Options to pass to just in time compiler

• form_compiler_options – Options to pass to the form compiler

• metadata – Data to pass to the integration measure

assemble_rhs()

Update RHS by re-assembling

solve(assemble_rhs: bool = True) → int

Compute projection using PETSc a KSP solver

Parameters

assemble_rhs – Re-assemble RHS and re-apply boundary conditions if true