r5.02.01 Transient linear thermal algorithm

Summary:

The linear transient thermal algorithm implemented within the THER_LINEAIRE [U4.33.01] command is presented. The various calculation options required have been presented in the plane, axisymmetric, and three-dimensional structural elements [U1.22.01], [U1.23.01], and [U1.24.01].

• 1. Expression of the heat equation in linear thermics
  • 1.1. Heat equation
  • 1.2. Law of FOURIER
  • 1.3. Heat equation in the case of the linear thermal model
• 2. Boundary conditions, loading and initial condition
  • 2.1. Imposed temperatures
  • 2.2. Linear relationships
  • 2.3. Normal flow imposed
  • 2.4. Exchange
  • 2.5. Wall exchange
  • 2.6. Volume source
  • 2.7. Initial condition
• 3. Variational formulation of the problem
• 4. Variational formulation of the problem with exchange condition between two walls
• 5. Discretization of the differential equation in time
  • 5.1. Accuracy of the method
  • 5.2. Stability of the method
  • 5.3. Application to the heat equation
• 6. Spatial discretization
• 7. Implementation in Code_Aster
  • 7.1. Equations introduced
  • 7.2. Main thermal options calculated in Code_Aster
• 8. Description of document versions