Development of BEM for thermoviscous flow

The boundary element method (BEM) is applied to natural convection problems involving steady, two-dimensional, buoyancy-driven flow of an incompressible fluid. The buoyancy effect is incorporated in two distinct BEM formulations, involving coupled and uncoupled kernel functions. The integral equation is derived, the appropriate fundamental solutions are explicitly presented, and the implementation details are discussed. Numerical examples are provided to demonstrate the validity of the formulations, and for comparison with the more established finite element method (FEM). Various computational aspects are discussed, such as the convergence, accuracy and efficiency of the various approaches.