Applied Mathematics Commons^™

Decoupled Finite Element Methods For General Steady Two-Dimensional Boussinesq Equations, Lioba Boveleth

Masters Theses

"This work presents two kinds of decoupled finite element methods for the steady natural convection problem in two dimensions. Firstly, the standard Galerkin finite element method is derived in detail stating algorithms needed for the realization in MATLAB. A numerical example verifies the error convergence. Secondly, using iteration, the Boussinesq equations are decoupled into the Navier-Stokes equations and a parabolic problem. The resulting problems are solved either in parallel or sequentially. Finally, the same numerical example as before is used to confirm the convergence and analyze the methods in terms of iteration performance. In addition to a higher flexibility and …