This Constraint implements thermal contact using a "gap conductance" model in which the flux is represented by an independent "Lagrange multiplier" like variable. More...
#include <GapConductanceConstraint.h>
Public Member Functions  
GapConductanceConstraint (const InputParameters ¶meters)  
virtual  ~GapConductanceConstraint () 
Protected Member Functions  
virtual Real  computeQpResidual () 
Computes the residual for the LM equation, lambda = (k/l)*(T^(1)  PT^(2)). More...  
virtual Real  computeQpResidualSide (Moose::ConstraintType res_type) 
Computes the "lambda * (v^(1)  Pv^(2))" residual term in the primal equation. More...  
virtual Real  computeQpJacobian () 
Computes the Jacobian of the LM equation wrt lambda, i.e. More...  
virtual Real  computeQpJacobianSide (Moose::ConstraintJacobianType jac_type) 
Handles Jacobian contributions for both the LM equation and the primal equation. More...  
Protected Attributes  
Real  _k 
Thermal conductivity of the gap medium (e.g. air). More...  
This Constraint implements thermal contact using a "gap conductance" model in which the flux is represented by an independent "Lagrange multiplier" like variable.
This formulation is not derived from a constrained optimization problem, so it is not a Lagrange multiplier formulation in the classic sense, but it does have the benefit of producing an improved approximation to the flux (better than simply differentiating the finite element solution) and is a systematic approach for accurately computing integrals on mismatched grids. For more information on this formulation, see the following references:
M. Gitterle, "A dual mortar formulation for finite deformation frictional contact problems including wear and thermal coupling," PhD thesis, Technische Universit"{a}t M"{u}nchen, Nov. 2012, https://mediatum.ub.tum.de/doc/1108639/1108639.pdf.
S. H"{u}eber and B. I. Wohlmuth, "Thermomechanical contact problems on nonmatching meshes," Computer Methods in Applied Mechanics and Engineering, vol. 198, pp. 1338–1350, Mar. 2009, http://dx.doi.org/10.1016/j.cma.2008.11.022.
S.~Falletta and B.~P. Lamichhane, "Mortar finite elements for a heat transfer problem on sliding meshes," Calcolo, vol. 46, pp. 131–148, June 2009, http://dx.doi.org/10.1007/s1009200900011}.
The PDF avaialable from http://tinyurl.com/gmmhbe9 explains the formulation in more detail. In the documentation below, we use the notation from the PDF above, and refer to the "primal" and "LM" equations, where primal refers to the heat transfer equation including the gap heat flux contribution, and "LM" refers to the equation for computing the flux, i.e. the Lagrange multiplier variable. Likewise, the term "primal variable" refers to the temperature variable.
Definition at line 52 of file GapConductanceConstraint.h.
GapConductanceConstraint::GapConductanceConstraint  (  const InputParameters &  parameters  ) 
Definition at line 23 of file GapConductanceConstraint.C.

virtual 
Definition at line 28 of file GapConductanceConstraint.C.

protectedvirtual 
Computes the Jacobian of the LM equation wrt lambda, i.e.
both phi(j) and test(i) are from the LM space. This is simply a (negative) mass matrix contribution, due to the structure of the LM equation.
Definition at line 52 of file GapConductanceConstraint.C.

protectedvirtual 
Handles Jacobian contributions for both the LM equation and the primal equation.
The jac_type flag controls the type of contribution: Master/Master: LM equation Jacobian wrt to T^(1), phi(j) is primal basis, master side, test(i) is LM basis, master side. Master/Slave: LM equation Jacobian wrt T^(2), phi(j) is primal basis, slave side, test(i) is LM basis, slave side. Slave/Master: Primal equation Jacobian wrt lambda, phi(j) is the LM basis, test(i) is the primal basis, master side. Slave/Slave: Primal equation Jacobian wrt lambda, phi(j) is the LM basis, test(i) is the primal basis, slave side.
Definition at line 58 of file GapConductanceConstraint.C.

protectedvirtual 
Computes the residual for the LM equation, lambda = (k/l)*(T^(1)  PT^(2)).
Definition at line 31 of file GapConductanceConstraint.C.

protectedvirtual 
Computes the "lambda * (v^(1)  Pv^(2))" residual term in the primal equation.
The res_type flag controls whether the contribution from the master (1) or slave (2) test function is currently being computed.
Definition at line 38 of file GapConductanceConstraint.C.

protected 
Thermal conductivity of the gap medium (e.g. air).
Definition at line 95 of file GapConductanceConstraint.h.
Referenced by computeQpJacobianSide(), and computeQpResidual().