[solver-time-integrator]

Parameterises the time-integration scheme used by the solver with

1. formulation — formulation:

   std | dual

   where

   std requires

   • scheme — time-integration scheme

     euler | rk34 | rk4 | rk45 | tvd-rk3

   • tstart — initial time

     float

   • tend — final time

     float

   • dt — time-step

     float

   • controller — time-step controller

     none | pi

     where

     pi only works with rk34 and rk45 and requires

     • atol — absolute error tolerance

       float

     • rtol — relative error tolerance

       float

     • errest-norm — norm to use for estimating the error

       uniform | l2

     • safety-fact — safety factor for step size adjustment (suitable range 0.80-0.95)

       float

     • min-fact — minimum factor by which the time-step can change between iterations (suitable range 0.1-0.5)

       float

     • max-fact — maximum factor by which the time-step can change between iterations (suitable range 2.0-6.0)

       float

     • dt-max — maximum permissible time-step

       float

   dual requires

   • scheme — time-integration scheme

     backward-euler | sdirk33 | sdirk43

   • pseudo-scheme — pseudo time-integration scheme

     euler | rk34 | rk4 | rk45 | tvd-rk3 | vermeire

   • tstart — initial time

     float

   • tend — final time

     float

   • dt — time-step

     float

   • controller — time-step controller

     none

   • pseudo-dt — pseudo time-step

     float

   • pseudo-niters-max — minimum number of iterations

     int

   • pseudo-niters-min — maximum number of iterations

     int

   • pseudo-resid-tol — pseudo residual tolerance

     float

   • pseudo-resid-norm — pseudo residual norm

     uniform | l2

   • pseudo-controller — pseudo time-step controller

     none | local-pi

     where

     local-pi only works with rk34 and rk45 and requires

     • atol — absolute error tolerance

       float

     • safety-fact — safety factor for pseudo time-step size adjustment (suitable range 0.80-0.95)

       float

     • min-fact — minimum factor by which the local pseudo time-step can change between iterations (suitable range 0.98-0.998)

       float

     • max-fact — maximum factor by which the local pseudo time-step can change between iterations (suitable range 1.001-1.01)

       float

     • pseudo-dt-max-mult — maximum permissible local pseudo time-step given as a multiplier of pseudo-dt (suitable range 2.0-5.0)

       float

Example:

[solver-time-integrator]
formulation = std
scheme = rk45
controller = pi
tstart = 0.0
tend = 10.0
dt = 0.001
atol = 0.00001
rtol = 0.00001
errest-norm = l2
safety-fact = 0.9
min-fact = 0.3
max-fact = 2.5