Field propagator

HasegawaWakataniStep

Advances n and omega.

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What it solves

FEEC discretization of the following equations:

find $(n, ω) \in H^{1} \times H^{1}$ such that

\int_{Ω} \frac{\partial n}{\partial t} m d x = \int_{Ω} C (x, y) (ϕ - n) m d x - \int_{Ω} ϕ [n, m] d x - κ \int_{Ω} \partial_{y} ϕ m d x - ν \int_{Ω} \nabla n \cdot \nabla m d x \forall m \in H^{1}, \int_{Ω} \frac{\partial ω}{\partial t} ψ d x = \int_{Ω} C (x, y) (ϕ - n) ψ d x - \int_{Ω} ϕ [ω, ψ] d x - ν \int_{Ω} \nabla ω \cdot \nabla ψ d x \forall ψ \in H^{1},

where $ϕ \in H^{1}$ is a given stream function, $C = C (x, y)$ , $κ$ and $ν$ are constants and $[a, b] = \partial_{x} a \partial_{y} b - \partial_{y} a \partial_{x} b$ .

time_discret: explicit Runge-Kutta, see struphy.ode.solvers.ODEsolverFEEC.

Variables it advances

The variables this step updates over a time step dt, and the discrete spaces each one accepts.

Name	Kind	Accepted spaces
`n`	FEECVariable	`H1`
`omega`	FEECVariable	`H1`

Options

Set these on the propagator in a parameter file, for example HasegawaWakataniStep.Options(c_fun=...).

Option	Default	Choices	Description
`c_fun`	`const`	`const`	Choice of coupling profile $C (x, y)$ used in the model.
`kappa`	`1`	float	Constant multiplying the background-gradient drift term.
`nu`	`0.01`	float	Diffusion coefficient in density and vorticity equations.
`butcher`	`None`	ButcherTableau	Butcher tableau for explicit Runge-Kutta integration. If `None`, defaults to `ButcherTableau()`.
`solver`	`pcg`	`pcgcg`	Symmetric iterative solver used for `M0` inversions.
`precond`	`MassMatrixPreconditioner`	`MassMatrixPreconditionerMassMatrixDiagonalPreconditionerNone`	Preconditioner used with `M0` inversions.
`solver_params`	`None`	SolverParameters	Iterative-solver controls. If `None`, defaults to `SolverParameters()`.

Used by

Each model splits its time step into a sequence of propagators. This one appears in 1 model, at the position shown.

HasegawaWakataniFluidstep 2 of 2 · hw