A Coupled Pressure-Based Co-Located Finite-Volume Solution Method for Natural-Convection Flows

A pressure-based coupled solution method based on a finite-volume discretization is presented. The method uses a cell-centered co-located variable arrangement on a nonorthogonal two-dimensional structured grid. The coupled algebraic analogs of the mass, momentum, and energy conservation equations for incompressible flow are solved. In addition to coupling the mass and momentum equations, the energy equation is coupled to the velocities via a Newton-Raphson linearization of the energy advection terms. The momentum equations are coupled to the energy equation via an implicit temperature in the Boussinesq approximation. The convergence behavior of the new method is demonstrated on the solution of steady, laminar natural convection in an annulus for Prandtl numbers of 0.707 and 13,050 at a Rayleigh number of 1 × 10⁶. A significant reduction in the number of iterations to convergence is obtained with the new method compared to a method with only velocity-to-temperature coupling and a method with energy and momentum decoupled. An improvement to the new method was obtained by using an approach that uses a delayed time-step increase and a modified face temperature value estimation.