摘要
In this paper,we present a IP_N×IP_N spectral element method and a detailed comparison with existing methods for the unsteady incompressible Navier-Stokes equa- tions.The main purpose of this work consists of:(i) detailed comparison and discussion of some recent developments of the temporal discretizations in the frame of spectral el- ement approaches in space;(ii) construction of a stable IP_N×IP_N method together with a IP_N→IP_(N-2) post-filtering.The link of different methods will be clarified.The key feature of our method lies in that only one grid is needed for both velocity and pressure variables,which differs from most well-known solvers for the Navier-Stokes equations. Although not yet proven by rigorous theoretical analysis,the stability and accuracy of this one-grid spectral method are demonstrated by a series of numerical experiments.
In this paper, we present a IPN×IPN spectral element method and a detailed comparison with existing methods for the unsteady incompressible Navier-Stokes equations. The main purpose of this work consists of： （i） detailed comparison and discussion of some recent developments of the temporal discretizations in the frame of spectral element approaches in space; （ii） construction of a stable IPN×IPN method together with a IPN →IPN-2 post-filtering. The link of different methods will be clarified. The key feature of our method lies in that only one grid is needed for both velocity and pressure variables, which differs from most well-known solvers for the Navier-Stokes equations. Although not yet proven by rigorous theoretical analysis, the stability and accuracy of this one-grid spectral method are demonstrated by a series of numerical experiments.
基金
partially supported by National NSF of China under Grant 10602049
The research of the second author was partially supported by National NSF of China under Grant 10531080
the Excellent Young Teachers Program by the Ministry of Education of China
973 High Performance Scientific Computation Research Program 2005CB321703.
