Nitche_Tied

Syntax

Enforcement For Energy ([{of} SpeciesName] | [{in} MaterialPhaseName] | [{ls} {a | b | c}]) {=} Nitche_Tied ([Co_Field = co_field] | [Multiplier = multiplier] | [Toggle = toggle])

Summary

Applies a contact heat flux as described in “A robust Nitsches formulation for interface problems” by Annavarapu et al. 2012.

Description

The numerical heat flux $\hat{\mathbf{q}}$ at the contact interface is defined as

$\hat{\mathbf{q}} = \alpha_h \left[T \right] + \left\{\mathbf{q}\right\}_{\gamma},$

where $\alpha_h$ is a mesh dependent stabilization parameter, $\left[T\right] = T_1 \mathbf{n}_1 + T_2 \mathbf{n}_2$ denotes the scalar jump operator, and $\left\{\mathbf{q}\right\}_\gamma$ is a weighted averaging operator across the interface defined as

$\left\{\mathbf{q}\right\}_{\gamma} = \gamma_1 \mathbf{q}_1 + \gamma_2 \mathbf{q}_2,$

where $\mathbf{q}_i$ is the heat flux, and $\gamma_1 + \gamma_2 = 1$ are weighting parameters that sum to one defined as

$\gamma_i = \dfrac{\dfrac{\Omega_i}{k_i}}{\dfrac{\Omega_1}{k_1} + \dfrac{\Omega_2}{k_2}},$

where $\Omega_i$ is the local element volume, and $k_i$ is the thermal conductivity.

The mesh dependent stabilization parameter $\alpha_h$ is

$\alpha_h = \dfrac{c \Gamma_{ij}}{\dfrac{\Omega_1}{k_1} + \dfrac{\Omega_2}{k_2}},$

where $c$ is a user specified multiplier, and $\Gamma_{ij} = \Gamma_1 + \Gamma_2$ is a measure of the local contact interface taken here as the sum of local contact face areas. If a tensor conductivity is provided, then a projected thermal conductivity is used i.e.,

$k_{i} = \mathbf{n}_i^T \mathbf{K}_i \mathbf{n}_i.$

The following options are present in most boundary conditions/sources. The meaning of each option is as follows:

Toggle: If given, specifies which toggle block controls whether this BC is active or not.

Parameter	Value	Default
{of}	{of \| species \| subindex}	–
SpeciesName	string	–
{in}	{in \| material_phase}	–
MaterialPhaseName	string	–
{ls}	{levelset_phase \| ls}	–
{=}	{= \| are \| is}	–
co_field	integer	0
multiplier	real	1
toggle	“string”	–