An Alternative Strategy for the Solution of Heat and Incompressible Fluid Flow Problems via Finite Volume Method

The characteristic-based split (CBS) method has been widely used in the finite element community to facilitate the numerical solution of Navier-Stokes (NS) equations. However, this computational algorithm has rarely been employed in the finite volume context and the stabilization of the numerical solution procedure has traditionally been addressed differently in volume-based numerical schemes. In this paper, the CBS-based finite volume algorithm is employed to formulate and solve a number of laminar incompressible flow and convective heat transfer problems. Both explicit and implicit versions of the algorithm are first explained and validated in the context of the solution of a lid-driven cavity problem and a backward facing step (BFS) flow problem. The modified algorithm, capable of modelling the coupling between the momentum and energy balance equations, is then introduced and used to solve a buoyancy-driven cavity flow problem. Computational results show that the CBS finite volume algorithm can be reliably used in the solution of laminar incompressible heat and fluid flow problems. NOMENCLATURE c sound speed  artificial sound speed c P specific heat at constant pressure  thermal expansion coefficient ER expansion ratio in BFS flow t  time step g gravitational acceleration y x   , grid spacing in x and y directions h control volume length scale  time step control parameter k fluid thermal conductivity