Implementing Newton Method to Develop ۳D Fully Coupled Solvers using foam-extend

Linearization of nonlinear terms in momentum and energy equations is one of the challenging and important issues besides pressure-velocity coupling. To date, Picard method has been successfully applied to large range of problems of computational fluid dynamics for linearizing the advection terms. In many problems, one can use other methods such as Newton Raphson method to increase the rate of convergence and improve the convergence and stability behavior. This paper describes the development of two prior prominent finite volume Newton-Picard linearized solvers from ۲D to ۳D and in the foam-extend platform. These two solvers were developed and well matured and tested in literature for incompressible flows. The first solver uses Newton method for linearize the advection term of energy equation and the remaining terms of other equations were linearized using Picard method. The second solver linearize the convection term of momentum equation using Newton method and the remaining terms of other equations with Picard. The solvers are based on finite volume (FV) and uses the foam-extend libraries and some developed functions. The performance of solvers were evaluated and validated in ۲D test cases and their capabilities and performances were shown in some ۳D cases. In ۳D cases, similar results with ۲D were observed. Reducing the number of iterations and capability to increasing the courant number are of the main achievement and advantages of these solvers.