A new finite volume discretization scheme to solve 3D incompressible thermal flows on unstructured meshes

We present a new method to solve incompressible thermal flows and the transport of scalar quantities. It is a finite volume scheme for unstructured meshes whose time discretization is based upon the fractional time step method. The governing equations are discretized using a collocated, cell-centered arrangement of velocity and pressure. The solution variables are stored at the cell-circumcenters. This scheme is convergent, stable and allows computing solutions that does not violate the maximum principle when it applies. Theoretical results and numerical properties of the scheme are provided. Predictions of Boussinesq fluid flow, flow past a cylinder and heat transport in a cylinder are performed to validate the method.