Thermal Diffusivity Reference

Limits the time-step size to meet the specified target criteria for the Von Neumann number of thermal diffusivity. This time-step provider is appropriate for problems with dominant thermal diffusion with varying magnitude, and also for supporting solid materials.

The Thermal Diffusivity time-step provider evaluates limits for the Von Neumann number of thermal diffusivity, $\frac{k}{ρ \cdot C_{p}} \frac{Δ t}{Δ x^{2}}$ where:

$k$ is thermal conductivity.
$ρ$ is density.
$C_{p}$ is heat capacity.
$Δ t$ is the time-step.
$Δ x$ is the cell size.

The time-step is adjusted so that the actual Von Neumann number approaches either the specified maximum or the specified mean Von Neumann number, whichever yields the minimum time-step.

This time-step provider is available when an energy model is activated in the physics continuum.

Table 1. Thermal Diffusivity Reference
Provided By	Right-click Continua > Physics 1 > Models > Adaptive Time-Step > Time-Step Providers and select New > Thermal Diffusivity
Example Node Path	Continua > Physics 1 > Models > Adaptive Time-Step > Time-Step Providers > Thermal Diffusivity
Requires	Time: Implicit Unsteady or PISO Unsteady Either: Material: Multiphase. Multiphase Models: Eulerian Multiphase (EMP), Volume of Fluid (VOF) or Mixture Multiphase (MMP). Viscous Regime: Any except the Inviscid model. Optional Models: Segregated Multiphase Temperature, Segregated Multiphase Isothermal, or Phase Coupled Fluid Energy. or: Material: Gas, Liquid, Multi-Component Gas, Multi-Component Liquid or Eulerian Multiphase Mixture > Two-Phase Thermodynamic Equilibrium. Flow: Any. Viscous Regime: Any except the Inviscid model. Optional Models: Segregated Fluid Enthalpy, Segregated Fluid Isothermal, Segregated Fluid Temperature or Coupled Energy. or: Material: Solid or Multi-Component Solid. Optional Models: Segregated Energy or Coupled Energy.
Properties	Enable/Disable, Target Mean Von Neumann Number, Target Max Von Neumann Number, Cut-off Percentage. See Thermal Diffusivity Properties.
Activates	Field Functions	Thermal Diffusivity (Max.) Proposal, Thermal Diffusivity (Mean) Proposal See Field Functions.

Thermal Diffusivity Properties

Enable/Disable

See Adaptive Time-Step Provider Common Properties.

Target Mean Von Neumann Number

The parameter

{V N N}_{m e a n}^{t a r}

when used in Eqn. (971) is defined in terms of von Neumann instead of CFL. The default value is 0.5.

Target Max Von Neumann Number

The parameter

{V N N}_{m a x}^{t a r}

when used in Eqn. (971) is defined in terms of von Neumann instead of CFL. The default value is 5.0.

Cut-off Percentage

Specifies a percentage $p$ of small/bad cells to be ignored by the Adaptive Time-Step model. The prescribed cut-off percentage is used to find the quantile $t_{q} (p)$ such that for a given $p$ :

Figure 1. EQUATION_DISPLAY

\frac{# [c e l l s : Δ t_{c} \leq t_{q} (p)]}{# [a l l c e l l s]} \approx p %

(105)

The time-step is then set as $t_{q} (p)$ and any local time-steps that the provider proposes below this value are ignored by the model. The range for this property is 0 (default) to 100.

Field Functions

The following field functions are available when the Thermal Diffusivity time-step provider is activated.

Thermal Diffusivity (Max.) Proposal: The local time-step proposal for the target maximum Von Neumann number condition, computed for each individual cell.

Thermal Diffusivity (Mean) Proposal: The time-step proposal for the target mean Von Neumann number condition, computed for each individual cell.