Non-segregated algorithm for incompressible flow simulations with fully conservative finite difference and JFNK method

Abstract

A non-segregated numerical algorithm is proposed for unsteady incompressible flow simulations with the fully discrete fully conservative finite difference scheme. The fully conservative finite difference scheme is useful for the numerical simulations of unsteady turbulent flow because of its stability and reliability. However, a large system of nonlinear discrete equations should be solved for the fully (spatio-temporal) discrete fully conservative scheme. In this study, the Jacobian-Free Newton-Krylov (JFNK) method with the GMRES (m) method as a Krylov iterative solver is introduced as a non-linear solver in the non-segregated numerical algorithm. A couple of preconditionings to the Krylov iterative method are tested and a new effective physical-based preconditioning is proposed. Numerical tests on the DNS of turbulent channel flow demonstrate the availability of the present method. Then, the DNS of backward facing step flow is carried out for an example of a stiff problem in which the streamwise grid spacings are locally fine.