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Model reference

This page summarises the built‑in PDE models in flexipde. Each model inherits from :class:flexipde.models.base.PDEModel and implements a rhs method returning the time derivatives of its fields.

LinearAdvection

Advection of a scalar field u with constant velocity v:

.. math:: \partial_t u + \sum_i v_i \partial_{x_i} u = 0.

Parameters:

  • velocity: list of floats specifying the advection velocity in each dimension.

Diffusion

Heat equation for a scalar field u with diffusivity D:

.. math:: \partial_t u = D \nabla^2 u.

Parameters:

  • diffusivity: diffusion coefficient.

ResistiveMHD

Toy model of resistive magnetohydrodynamics in 1D, evolving transverse velocity v and magnetic field B:

.. math:: \partial_t v = \partial_x B, \qquad \partial_t B = \partial_x v + \eta \nabla^2 B.

Parameters:

  • eta: resistivity.

TwoFluid

Simplified two‑fluid model where ion and electron densities advect with prescribed velocities v_i and v_e:

.. math:: \partial_t n_s + \sum_i v_{s,i} \partial_{x_i} n_s = 0,\qquad s \in {i,e}.

Parameters:

  • velocities: list of two lists giving velocities for ions and electrons.

DriftKinetic

Simplified drift–kinetic equation in 1D phase space without self‑consistency:

.. math:: \partial_t f + v \partial_x f + E \partial_v f = 0.

Parameters:

  • nv: number of velocity grid points.
  • v_min, v_max: velocity range.
  • E: constant electric field.

IdealAlfven

Toy model of shear Alfvén waves in 1D, evolving v and B according to

.. math:: \partial_t v = \partial_x B, \qquad \partial_t B = \partial_x v.

No parameters.

VlasovTwoStream

1D Vlasov–Poisson solver modelling the two‑stream instability with Maxwellian streams. See the code for details.