Modified Method of Characteristics Variational Multiscale Finite Element Method for Time Dependent Navier-Stokes Problems

∗ This work was supported in part by the NSF of China (Grant No. 11301156, 11401177 and 11271313).

Abstract

In this paper, a modified method of characteristics variational multiscale (MMOCVMS) finite element method is presented for the time dependent Navier-Stokes problems, which is leaded by combining the characteristics time discretization with the variational multiscale (VMS) finite element method in space. The theoretical analysis shows that this method has a good convergence property. In order to show the efficiency of the MMOCVMS finite element method, some numerical results of analytical solution problems are presented. First, we give some numerical results of lid-driven cavity flow with Re=5000 and 7500 as the time is sufficient long. From the numerical results, we can see that the steady state numerical solutions of the time-dependent Navier-Stokes equations are obtained. Then, we choose Re=10000, and we find that the steady state numerical solution is not stable from t=200 to 300. Moreover, we also investigate numerically the flow around a cylinder problems. The numerical results show that our method is highly efficient.

Keywords:

• modified method of characteristics
• VMS finite element method
• time dependent Navier-Stokes problems
• characteristics-based method
• numerical tests

AMS Subject Classification:

• 76D05
• 76M10
• 65M60
• 65M12

Notes

∗ This work was supported in part by the NSF of China (Grant No. 11301156, 11401177 and 11271313).