On the semi-discrete stabilized finite volume method for the transient Navier-Stokes equations

A stabilized finite volume method for solving the transient Navier– Stokes equations is developed and studied in this paper. This method maintains conservation property associated with the Navier–Stokes equations. An error analysis based on the variational formulation of the corresponding finite volume method is first introduced to obtain optimal error estimates for velocity and pressure. This error analysis shows that the present stabilized finite volume method provides an approximate solution with the same convergence rate as Communicated by Zhongying Chen. This research was supported in part by the National Science Foundation of China (No. 11071193), Natural Science New Star of Science and Technologies Research Plan in Shaanxi Province of China (No. 2011kjxx12), Research Program of Education Department of Shaanxi Province (No. 11JK0490), the project-sponsored by SRF for ROCS, SEM, and NSERC/AERI/Foundation CMG Chair and iCORE Chair Funds in Reservoir Simulation. J. Li (B) Department of Mathematics, Baoji University of Arts and Sciences, Baoji 721013, People’s Republic of China e-mail: [email protected] J. Li · Z. Chen Department of Chemical & Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada Z. Chen e-mail: [email protected] Z. Chen Faculty of Science, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China