Uncoupled temporally second-order accurate implicit solver of incompressible Navier-Stokes equations

An efficient method with temporal second-order accuracy for solving the incompressible Navier-Stokes equations in generalized coordinate systems is developed. Efficiency is obtained by extending an existing fractional-step semi-implicit solver into an implicit one (with implicit approximation of the convection terms). A novel three-level linearization scheme is proposed to decouple the momentum equations from one another, in addition to the fractional-step approach, that decouples the continuity equation from the momentum equations. Consequently, all of the governing equations are uncoupled without degrading temporal accuracy or stability and without the need for iterations to solve the nonlinear system of equations at each time level. The proposed decoupling technique can be used for other systems of nonlinear and time-dependent partial differential equations. Moreover, only minor modifications are required to apply the method to existing two-level schemes. Several test cases confirm that the proposed decoupled scheme has temporal second-order accuracy and allows the use of large time steps.