BEM representation of diffusion-convection equations

In this chapter, the multi-domain boundary element method (MD BEM) will be considered for the problems of computational fluid dynamics (CFD), described by the Navier-Stokes equations. The fluid flow can be convection-dominated in some parts of the domain and diffusion dominated in another parts and it can be steady or unsteady. The multi-domain (MD) BEM representation of different kind of equations used in CFD and their linearization will be introduced. Reciprocity based formulation using non-singular presentation of the Laplace and Hehrnholz equation is presented for the solution of the non-linear problems.