Application of the finite element method to heat and flow problems

4P630 - Application of the finite element method to heat and flow problems



The course is divided into two parts.
In the first part the partial differential equations for the description of heat and flow problems are introduced and properties of parabolic, hyperbolic and elliptic equations are briefly discussed. Beside the Finite Element Method (FEM) the Finite Difference Method is introduced together with the upwinding technique to avoid oscillations in the approximate solution. Next the general working method of the FEM is described. Finally, general aspects as quadrature rules, automation and accuracy are discussed.
In the second part the FEM is applied to the Navier-Stokes and energy equation to solve heat and flow problems. The discretisation of the set of equations together with several solution methods and the special role of the pressure are discussed. Besides, some time integration schemes to solve unsteady flow problems and the coupling between the Navier-Stokes and energy equations for forced and natural convection flow problems is elucidated. Finally, a short introduction is given to solution techniques for radiation problems.

Learning objectives

  1. Adopt a critical attitude towards numerically obtained results
  2. Insight into influence boundary conditions on numerical solution
  3. Writing an own element: elementmatrix and elementrighthandside
  4. Insight into the discretisation problems of the Navier Stokes equation