A Simplified Artificial Compressibility Flux for the Discontinuous Galerkin Solution of the Incompressible Navier-Stokes Equations
Year: 2019
Communications in Computational Physics, Vol. 25 (2019), Iss. 4 : pp. 988–1009
Abstract
The discontinuous Galerkin (DG) method has attained increasing popularity for solving the incompressible Navier-Stokes (INS) equations in recent years. In this work, we present a novel DG discretization for solving the two-dimensional INS equations in which the inviscid term of the INS equations is split into two parts, the Stokes operator and the nonlinear convective term, and treated separately. The Stokes operator is discretized using the artificial compressibility flux which is provided by the (exact) solution of a Riemann problem associated with a local artificial compressibility perturbation of the Stokes system, while the nonlinear term is discretized in divergency form by using the local Lax-Friedrichs fluxes; thus, local conservativity is inherent. Unlike the existing artificial compressibility flux for the DG discretization of the INS equations which needs to solve a Riemann problem for a nonlinear system by numerical iteration, the separate treatment of the nonlinear term from the Stokes operator makes the Riemann problem become linear and can be solved explicitly and straightforwardly, therefore, no iterative procedure is further required. A number of test cases with a wide range of Reynolds number are presented to assess the performance of the proposed method, which demonstrates its potential to be an alternative approach for high order numerical simulations of incompressible flows.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0051
Communications in Computational Physics, Vol. 25 (2019), Iss. 4 : pp. 988–1009
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Discontinuous Galerkin methods Navier-Stokes equations incompressible flows artificial compressibility flux.
-
A high order least square-based finite difference-finite volume method with lattice Boltzmann flux solver for simulation of incompressible flows on unstructured grids
Liu, Y.Y. | Shu, C. | Zhang, H.W. | Yang, L.M.Journal of Computational Physics, Vol. 401 (2020), Iss. P.109019
https://doi.org/10.1016/j.jcp.2019.109019 [Citations: 26] -
A reconstructed discontinuous Galerkin method for incompressible flows on arbitrary grids
Zhang, Fan | Cheng, Jian | Liu, TiegangJournal of Computational Physics, Vol. 418 (2020), Iss. P.109580
https://doi.org/10.1016/j.jcp.2020.109580 [Citations: 5] -
A third-order weighted variational reconstructed discontinuous Galerkin method for solving incompressible flows
Zhang, Fan | Liu, Tiegang | Liu, MoubinApplied Mathematical Modelling, Vol. 91 (2021), Iss. P.1037
https://doi.org/10.1016/j.apm.2020.10.011 [Citations: 0] -
A direct discontinuous Galerkin method for the incompressible Navier–Stokes equations on arbitrary grids
Zhang, Fan | Cheng, Jian | Liu, TiegangJournal of Computational Physics, Vol. 380 (2019), Iss. P.269
https://doi.org/10.1016/j.jcp.2018.11.033 [Citations: 20] -
A stable discontinuous Galerkin method based on high‐order dual splitting scheme without additional stabilization term for incompressible flows
Ma, Mengxia | Ouyang, Jie | Wang, Xiaodong | Zhang, ChenhuiInternational Journal for Numerical Methods in Fluids, Vol. 93 (2021), Iss. 8 P.2660
https://doi.org/10.1002/fld.4992 [Citations: 2] -
A high‐order discontinuous Galerkin method for the incompressible Navier‐Stokes equations on arbitrary grids
Zhang, Fan | Cheng, Jian | Liu, TiegangInternational Journal for Numerical Methods in Fluids, Vol. 90 (2019), Iss. 5 P.217
https://doi.org/10.1002/fld.4718 [Citations: 8]