Least squares finite element method with high continuity NURBS basis for incompressible Navier-Stokes equations

  • Authors:

  • De-Xiang Chen;Zi-Li Xu;Shi Liu;Yong-Xin Feng

  • Affiliations:

  • State Key Lab for Strength and Vibration of Mechanical Structures, Xian Jiaotong University, Xian 710049, China;State Key Lab for Strength and Vibration of Mechanical Structures, Xian Jiaotong University, Xian 710049, China;Electric Power Research Institute of Guangdong Power Grid Corporation, Guangzhou 510080, China;Electric Power Research Institute of Guangdong Power Grid Corporation, Guangzhou 510080, China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2014

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Abstract

Modern least squares finite element method (LSFEM) has advantage over mixed finite element method for non-self-adjoint problem like Navier-Stokes equations, but has problem to be norm equivalent and mass conservative when using C^0 type basis. In this paper, LSFEM with non-uniform B-splines (NURBS) is proposed for Navier-Stokes equations. High order continuity NURBS is used to construct the finite-dimensional spaces for both velocity and pressure. Variational form is derived from the governing equations with primitive variables and the DOFs due to additional variables are not necessary. There is a novel k-refinement which has spectral convergence of least squares functional. The method also has same advantages as isogeometric analysis like automatic mesh generation and exact geometry representation. Several benchmark problems are solved using the proposed method. The results agree well with the benchmark solutions available in literature. The results also show good performance in mass conservation.