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
基金supported by the Joint Funds of the National Natural Science Foundation of China(U1204103)the Science and Technology Research Projects of Education Department of Henan Province(13A110731)~~
文摘首先导出了广义S tokes方程Petrov-G a lerk in有限元数值解的当地事后误差估算公式;以非连续二阶鼓包(bum p)函数空间为速度、压强误差的近似空间,该估算基于求解当地单元上的广义S tokes问题。然后,证明了误差估算值与精确误差之间的等价性。最后,将误差估算方法应用于N av ier-S tokes环境,以进行不可压粘流计算中的网格自适应处理。数值实验中成功地捕获了多强度物理现象,验证了本文所发展的方法。
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.
