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Volume 22, Issue 1
Characteristic Local Discontinuous Galerkin Methods for Incompressible Navier-Stokes Equations

Shuqin Wang, Weihua Deng, Jinyun Yuan & Yujiang Wu

DOI: 10.4208/cicp.220515.031016a

Commun. Comput. Phys., 22 (2017), pp. 202-227.

Published online: 2019-10

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  • Abstract

By combining the characteristic method and the local discontinuous Galerkin method with carefully constructing numerical fluxes, variational formulations are established for time-dependent incompressible Navier-Stokes equations in R2. The nonlinear stability is proved for the proposed symmetric variational formulation. Moreover, for general triangulations the priori estimates for the L2−norm of the errors in both velocity and pressure are derived. Some numerical experiments are performed to verify theoretical results.

  • Keywords

Navier-Stokes equations, local discontinuous Galerkin method, symmetric variational formulation.

  • AMS Subject Headings

65M12, 65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wsqlzu@gmail.com (Shuqin Wang)

dengwh@lzu.edu.cn (Weihua Deng)

yuanjy@gmail.com (Jinyun Yuan)

myjaw@lzu.edu.cn (Yujiang Wu)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-22-202, author = {Wang , ShuqinDeng , WeihuaYuan , Jinyun and Wu , Yujiang}, title = {Characteristic Local Discontinuous Galerkin Methods for Incompressible Navier-Stokes Equations}, journal = {Communications in Computational Physics}, year = {2019}, volume = {22}, number = {1}, pages = {202--227}, abstract = {

By combining the characteristic method and the local discontinuous Galerkin method with carefully constructing numerical fluxes, variational formulations are established for time-dependent incompressible Navier-Stokes equations in R2. The nonlinear stability is proved for the proposed symmetric variational formulation. Moreover, for general triangulations the priori estimates for the L2−norm of the errors in both velocity and pressure are derived. Some numerical experiments are performed to verify theoretical results.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.220515.031016a}, url = {http://global-sci.org/intro/article_detail/cicp/13353.html} }
TY - JOUR T1 - Characteristic Local Discontinuous Galerkin Methods for Incompressible Navier-Stokes Equations AU - Wang , Shuqin AU - Deng , Weihua AU - Yuan , Jinyun AU - Wu , Yujiang JO - Communications in Computational Physics VL - 1 SP - 202 EP - 227 PY - 2019 DA - 2019/10 SN - 22 DO - http://doi.org/10.4208/cicp.220515.031016a UR - https://global-sci.org/intro/article_detail/cicp/13353.html KW - Navier-Stokes equations, local discontinuous Galerkin method, symmetric variational formulation. AB -

By combining the characteristic method and the local discontinuous Galerkin method with carefully constructing numerical fluxes, variational formulations are established for time-dependent incompressible Navier-Stokes equations in R2. The nonlinear stability is proved for the proposed symmetric variational formulation. Moreover, for general triangulations the priori estimates for the L2−norm of the errors in both velocity and pressure are derived. Some numerical experiments are performed to verify theoretical results.

Wang , ShuqinDeng , WeihuaYuan , Jinyun and Wu , Yujiang. (2019). Characteristic Local Discontinuous Galerkin Methods for Incompressible Navier-Stokes Equations. Communications in Computational Physics. 22 (1). 202-227. doi:10.4208/cicp.220515.031016a
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