Modified characteristics mixed defect-correction finite element method for the time-dependent Navier–Stokes problems

Abstract

In this paper, a modified method of characteristics mixed defect-correction finite element method (MMOCMDCFEM) for the time-dependent Navier–Stokes problems, which is led by combining the characteristics time discretization with the two-step defect-correction in space, is presented. In this method, the hyperbolic part (the temporal and advection term) are treated by a characteristic tracking scheme. Then, we solve the equations with an added artificial viscosity term and correct these solutions by using a defect-correction technique. The theory analysis shows that this method has a good convergence property. In order to show the efficiency of the MMOCMDCFEM, we first present some numerical results of analytical solution problems. Then, we give some numerical results of lid-driven cavity flow with and . We also give some numerical results of flow around a cylinder problems, and compare the results with MMOCFEM’s. The numerical results show that this method is highly Efficient.

Keywords:

• modified method of characteristics
• defect-correction finite element method
• Navier–Stokes problems
• characteristics-based method
• lid-driven problem

AMS Subject Classifications:

• 76D05
• 76M10
• 65M60
• 65M12

Acknowledgments

The authors would like to thank the anonymous referees for their valuable suggestions and comments, which helped to improve the quality of the paper.

Additional information

Funding

This work is supported by Chinese NSF [grant number 11301156] and [grant number 11226306] and the Doctoral Foundation of Henan Polytechnic University (No. B2012-56). The second author is also supported by Chinese NSF funds [grant number 11271298] and [grant number 11362021].