quadratic (1d, 2d, 3d)¶

Computes the minimum time step for systems that have 2nd derivatives such as the heat equation or Navier Stokes. The explicit time step for this type of system goes as the square of grid spacing.

Parameters¶

constant (float, optional): Multiply the input data by this value in computing the time-step restriction.

Parent Updater Data¶

The following data structures should be specified to the timeStepRestrictionUpdater (1d, 2d, 3d) that calls the quadratic Time Step Restriction.

in (string vector, required): Diffusion coefficient (nodalArray, 1 component, required) \(\kappa\), where the diffusion operator is \(\nabla \cdot \kappa \nabla \phi\).

Example¶

The following block demonstrates quadratic used in combination with timeStepRestrictionUpdater (1d, 2d, 3d) to compute the timestep associated with a thermal conductivity:

 <Updater timeStepRestriction2>
  kind = timeStepRestrictionUpdater2d
  in = [thermalCond]
  onGrid = domain
  restrictions = [quadratic]
  courantCondition = THERMAL_DIFF_TIMESTEP_FACTOR

  <TimeStepRestriction quadratic>
    kind = quadratic2d
  </TimeStepRestriction>
</Updater>