r5.02.02 Nonlinear thermal

Summary

The operator THER_NON_LINE [U4.54.02] makes it possible to solve transient heat problems in solids in the presence of non-linearities in material properties (heat capacity and conductivity), or boundary conditions (radiation-type heat exchange). The formulation and the algorithm used are presented here, the latter being close to that linked to the operator STAT_NON_LINE [R5.03.01]. The various calculation options required have been presented in the plane, axisymmetric, and three-dimensional structural elements [U3.22.01], [U3.23.01], and [U3.24.01].

• 1. Expression of the heat equation in nonlinear thermics
  • 1.1. Heat equation for an immobile solid
  • 1.2. Fourier’s law
  • 1.3. Heat equation in the case of the nonlinear transient thermal model
  • 1.4. Numerical advantage of the enthalpy formulation for phase change problems.
• 2. Boundary conditions, loading and initial condition
  • 2.1. Nonlinear normal flow
  • 2.2. Nonlinear normal flow - infinity radiation-like condition
• 3. Variational formulation of the problem
• 4. Discretization of the differential equation in time
  • 4.1. Introduction of the theta method
  • 4.2. Application to the heat equation
• 5. Spatial discretization and adaptation of Newton’s algorithm to the problem
  • 5.1. Spatial discretization
  • 5.2. Stationary calculation
  • 5.3. Transient calculation
  • 5.4. Convergence
• 6. Main non-linear thermal options calculated in Code_Aster
  • 6.1. Boundary conditions and loads
  • 6.2. Calculation of elementary matrices and transitory term
  • 6.3. Residue calculation
• 7. Bibliography