The incompressible Navier-Stokes equations, upon spatial discretization, be- come a system of differential algebraic equations, formally of index 2. But due to the special forms of the discrete gradient and discrete d...The incompressible Navier-Stokes equations, upon spatial discretization, be- come a system of differential algebraic equations, formally of index 2. But due to the special forms of the discrete gradient and discrete divergence, its index can be regarded as 1. Thus, in this paper, a systematic approach following the ODE theory and methods is presented for the construction of high-order time-accurate implicit schemes for the incompressible Navier-Stokes equations, with projection methods for efficiency of numerical solution. The 3rd order 3-step BDF with component- consistent pressure-correction projection method is a first attempt in this direction; the related iterative solution of the auxiliary velocity the boundary conditions and the stability of the algorithm are discussed. Results of numerical tests on the incom- pressible Navier-Stokes equations with an exact solution are presented, confirming the accuracy stability and component- consistency of the proposed method.展开更多
文摘The incompressible Navier-Stokes equations, upon spatial discretization, be- come a system of differential algebraic equations, formally of index 2. But due to the special forms of the discrete gradient and discrete divergence, its index can be regarded as 1. Thus, in this paper, a systematic approach following the ODE theory and methods is presented for the construction of high-order time-accurate implicit schemes for the incompressible Navier-Stokes equations, with projection methods for efficiency of numerical solution. The 3rd order 3-step BDF with component- consistent pressure-correction projection method is a first attempt in this direction; the related iterative solution of the auxiliary velocity the boundary conditions and the stability of the algorithm are discussed. Results of numerical tests on the incom- pressible Navier-Stokes equations with an exact solution are presented, confirming the accuracy stability and component- consistency of the proposed method.
