zoomy_core.symsolver.discretization.time

Time discretization of the solver templates: the SSP-RK stages, the IMEX Runge-Kutta tableaux and the CFL step size.

Module Contents

Classes

Imex	How a step treats the SystemModel’s implicit slots: lie splits them off after the SSP-RK step (first order), ssp2 solves the implicit source in every stage of IMEX-SSP2(2,2,2).
CflWaveSpeed	Where the CFL step takes its wave speeds.
ImexTableau	Double Butcher tableau: explicit (At, wt, ct) and diagonally implicit (A, w, c).

Functions

cfl_dt	CFL step cfl * 2 r_f / (d |lambda|_f), min over faces, from the wave speeds of the cell states of each face and capped by dt_max.
cell_wavespeed	Max |eigenvalue| per face over the cell states of its two cells.
face_dt	The CFL step from the face wave speeds speed, capped by dt_max.
step_size	Adaptive CFL step, or a constant step that warns when above it.
face_rule	dt_rule taking the step from the first stage’s face wave speeds (no eigensolve of its own), capped by cap.
checked	dt, warning once if it exceeds the CFL step dt_cfl(); tested every every steps (1: each step, 0: never).

Data

SSP_RK
IMEX_RK

API

zoomy_core.symsolver.discretization.time.SSP_RK

None

class zoomy_core.symsolver.discretization.time.Imex

Bases: zoomy_core.misc.options.Option

How a step treats the SystemModel’s implicit slots: lie splits them off after the SSP-RK step (first order), ssp2 solves the implicit source in every stage of IMEX-SSP2(2,2,2).

Initialization

Initialize self. See help(type(self)) for accurate signature.

lie

‘lie’

ssp2

‘ssp2’

class zoomy_core.symsolver.discretization.time.CflWaveSpeed

Bases: zoomy_core.misc.options.Option

Where the CFL step takes its wave speeds.

Initialization

Initialize self. See help(type(self)) for accurate signature.

faces

‘faces’

cells

‘cells’

class zoomy_core.symsolver.discretization.time.ImexTableau

Bases: typing.NamedTuple

Double Butcher tableau: explicit (At, wt, ct) and diagonally implicit (A, w, c).

References

• Pareschi, Russo 2005, https://doi.org/10.1007/s10915-004-4636-4

At: tuple

None

wt: tuple

None

ct: tuple

None

A: tuple

None

w: tuple

None

c: tuple

None

zoomy_core.symsolver.discretization.time.IMEX_RK

None

zoomy_core.symsolver.discretization.time.cfl_dt(nsm, Q, Qaux, p, mesh, cfl, dimension)

CFL step cfl * 2 r_f / (d |lambda|_f), min over faces, from the wave speeds of the cell states of each face and capped by dt_max.

References

• Audusse et al. 2004, https://doi.org/10.1137/S1064827503431090

zoomy_core.symsolver.discretization.time.cell_wavespeed(nsm, Q, Qaux, p, mesh)

Max |eigenvalue| per face over the cell states of its two cells.

zoomy_core.symsolver.discretization.time.face_dt(nsm, speed, mesh, cfl, dimension)

The CFL step from the face wave speeds speed, capped by dt_max.

References

• Audusse et al. 2004, https://doi.org/10.1137/S1064827503431090

zoomy_core.symsolver.discretization.time.step_size(nsm, Q, Qaux, p, mesh, cfl, dimension, dt_constant, time, check_every=10)

Adaptive CFL step, or a constant step that warns when above it.

zoomy_core.symsolver.discretization.time.face_rule(nsm, mesh, cfl, dimension, dt_constant, time, cap, check_every=10)

dt_rule taking the step from the first stage’s face wave speeds (no eigensolve of its own), capped by cap.

zoomy_core.symsolver.discretization.time.checked(dt, time, every, dt_cfl)

dt, warning once if it exceeds the CFL step dt_cfl(); tested every every steps (1: each step, 0: never).