An uncoupled temporally second-order accurate implicit solver of the incompressible navier-stokes equations

摘要

An efficient temporally second-order accurate method for solving the incompressible Navier-Stokes equations in generalized coordinate systems is developed. Efficinecy is obtained by extending an existing fractional step semi-implicit solver into a fully implicit one (i.e., the convection terms as well are approximated implicitly). A novel three-level linearization scheme is proposed to decouple the momentum equation from one another , in addition to the fractional step approach that decouples the confinuity equation from the momentum equations. Consequently, all the governing equations are uncoupled without degrading temporal accuracy or stability and without the need for iterations to solve the nonlinear systems of equations at each time level. The decoupling of the momentum equations also allows an easy parallelization of the solution procedure. 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 implement the method on existing two-level schemes. Several test cases confirm that the proposed decoupled scheme is indeed secondorder accurate in time.