Influence of segregation on the efficiency of finite volume methods for the incompressible Navier-Stokes equations

The finite volume discretisation is commonly applied for the numerical solution of the Navier-Stokes equations. The efficiency, accuracy and robustness of algorithms for solving the resulting system of algebraic equations greatly depend on the segregation of the equations. This paper discusses the effect of decoupling the continuity and the momentum equations (resulting in pressure correction algorithms) and the effect of decoupling the momentum equations per direction (Picard versus Newton linearisation) for both steady and transient problems. The coupled solution of momentum and continuity equations for steady problems is very robust and can significantly reduce the necessary number of iterations. The memory and time costs per iteration however are still high, therefore this method is not efficient for transient problems. Picard linearisation is more robust than Newton linearisation, allowing larger time steps, corresponding to less iterations for steady problems. For transient problems, Newton linearisation is more efficient and allows for a straightforward implementation of second-order time accuracy.