Close Search Advanced
Journals
Resources
About Us
Open Access

A Parallel, High-Order Direct Discontinuous Galerkin Method for the Navier-Stokes Equations on 3D Hybrid Grids

A Parallel, High-Order Direct Discontinuous Galerkin Method for the Navier-Stokes Equations on 3D Hybrid Grids
Preview
Add to basket

Year:    2017

Author:    Jian Cheng, Xiaodong Liu, Tiegang Liu, Hong Luo

Communications in Computational Physics, Vol. 21 (2017), Iss. 5 : pp. 1231–1257

Abstract

A parallel, high-order direct Discontinuous Galerkin (DDG) method has been developed for solving the three dimensional compressible Navier-Stokes equations on 3D hybrid grids. The most distinguishing and attractive feature of DDG method lies in its simplicity in formulation and efficiency in computational cost. The formulation of the DDG discretization for 3D Navier-Stokes equations is detailedly studied and the definition of characteristic length is also carefully examined and evaluated based on 3D hybrid grids. Accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical solutions. The capability in handling curved boundary geometry is also demonstrated. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results obtained indicate that the DDG method can achieve the designed order of accuracy and is able to deliver comparable results as the widely used BR2 scheme, clearly demonstrating that the DDG method provides an attractive alternative for solving the 3D compressible Navier-Stokes equations.

Submit Article

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-2016-0090

Communications in Computational Physics, Vol. 21 (2017), Iss. 5 : pp. 1231–1257

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Direct discontinuous Galerkin method compressible Navier-Stokes equations hybrid grids.

Author Details

Jian Cheng

Xiaodong Liu

Tiegang Liu

Hong Luo

  1. A fourth-order Lagrangian discontinuous Galerkin method using a hierarchical orthogonal basis on curvilinear grids

    Liu, Xiaodong | Morgan, Nathaniel R. | Lieberman, Evan J. | Burton, Donald E.

    Journal of Computational and Applied Mathematics, Vol. 404 (2022), Iss. P.113890

    https://doi.org/10.1016/j.cam.2021.113890 [Citations: 9]

  2. A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation

    Adams, Thomas | Giani, Stefano | Coombs, William M.

    Journal of Computational Physics, Vol. 379 (2019), Iss. P.373

    https://doi.org/10.1016/j.jcp.2018.12.003 [Citations: 9]

  3. A Symmetric Direct Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations

    Yue, Huiqiang | Cheng, Jian | Liu, Tiegang

    Communications in Computational Physics, Vol. 22 (2017), Iss. 2 P.375

    https://doi.org/10.4208/cicp.OA-2016-0080 [Citations: 5]

  4. A new direct discontinuous Galerkin method with interface correction for two-dimensional compressible Navier-Stokes equations

    Danis, Mustafa E. | Yan, Jue

    Journal of Computational Physics, Vol. 452 (2022), Iss. P.110904

    https://doi.org/10.1016/j.jcp.2021.110904 [Citations: 2]

  5. Analysis and development of adjoint-based h-adaptive direct discontinuous Galerkin method for the compressible Navier–Stokes equations

    Cheng, Jian | Yue, Huiqiang | Yu, Shengjiao | Liu, Tiegang

    Journal of Computational Physics, Vol. 362 (2018), Iss. P.305

    https://doi.org/10.1016/j.jcp.2018.02.031 [Citations: 7]

  6. An asymptotic expansion for 1D steady compressible Navier‐Stokes equations under nonuniform enthalpy

    Zhang, Fan | Cheng, Jian | Liu, Tiegang

    Mathematical Methods in the Applied Sciences, Vol. 43 (2020), Iss. 9 P.5788

    https://doi.org/10.1002/mma.6320 [Citations: 2]

  7. A parallel methodology of adaptive Cartesian grid for compressible flow simulations

    Qi, Xinyu | Yang, Yuchen | Tian, Linlin | Wang, Zhenming | Zhao, Ning

    Advances in Aerodynamics, Vol. 4 (2022), Iss. 1

    https://doi.org/10.1186/s42774-022-00108-y [Citations: 3]

  8. Exponential boundary-layer approximation space for solving the compressible laminar Navier-Stokes equations

    Zhang, Fan | Cheng, Jian | Liu, Tiegang

    Advances in Computational Mathematics, Vol. 46 (2020), Iss. 2

    https://doi.org/10.1007/s10444-020-09776-0 [Citations: 2]

  9. A vertex-centered finite volume method with interface sharpening technique for compressible two-phase flows

    Li, Lingquan | Löhner, Rainald | Pandare, Aditya K. | Luo, Hong

    Journal of Computational Physics, Vol. 460 (2022), Iss. P.111194

    https://doi.org/10.1016/j.jcp.2022.111194 [Citations: 8]

  10. High-order compact gas-kinetic schemes for three-dimensional flow simulations on tetrahedral mesh

    Zhao, Fengxiang | Ji, Xing | Shyy, Wei | Xu, Kun

    Advances in Aerodynamics, Vol. 5 (2023), Iss. 1

    https://doi.org/10.1186/s42774-022-00132-y [Citations: 4]

  11. A high‐order discontinuous Galerkin method for the incompressible Navier‐Stokes equations on arbitrary grids

    Zhang, Fan | Cheng, Jian | Liu, Tiegang

    International Journal for Numerical Methods in Fluids, Vol. 90 (2019), Iss. 5 P.217

    https://doi.org/10.1002/fld.4718 [Citations: 7]

  12. High-order discontinuous Galerkin method with immersed boundary treatment for compressible flows on parallel adaptive Cartesian grids

    Qi, Xinyu | Wang, Zhenming | Zhu, Jun | Tian, Linlin | Zhao, Ning

    Physics of Fluids, Vol. 36 (2024), Iss. 11

    https://doi.org/10.1063/5.0238605 [Citations: 0]

  13. A Gradient Compression-Based Compact High-Order Gas-Kinetic Scheme on 3D Hybrid Unstructured Meshes

    Ji, Xing | Shyy, Wei | Xu, Kun

    International Journal of Computational Fluid Dynamics, Vol. 35 (2021), Iss. 7 P.485

    https://doi.org/10.1080/10618562.2021.1991329 [Citations: 7]

  14. Implicit high-order gas-kinetic schemes for compressible flows on three-dimensional unstructured meshes I: Steady flows

    Yang, Yaqing | Pan, Liang | Xu, Kun

    Journal of Computational Physics, Vol. 505 (2024), Iss. P.112902

    https://doi.org/10.1016/j.jcp.2024.112902 [Citations: 0]

  15. Compact High-Order Gas-Kinetic Scheme for Three-Dimensional Flow Simulations

    Ji, Xing | Zhao, Fengxiang | Shyy, Wei | Xu, Kun

    AIAA Journal, Vol. (2021), Iss. P.1

    https://doi.org/10.2514/1.J060208 [Citations: 5]

  16. Direct discontinuous Galerkin method for potential magnetic field solutions

    Liu, XiaoJing | Feng, Xueshang | Lv, Jiakun | Wang, Xinyi | Zhang, Man

    Frontiers in Astronomy and Space Sciences, Vol. 9 (2022), Iss.

    https://doi.org/10.3389/fspas.2022.1055969 [Citations: 2]

  17. An implementation of MPI and hybrid OpenMP/MPI parallelization strategies for an implicit 3D DDG solver

    He, Xiaofeng | Wang, Kun | Feng, Yiwei | Lv, Lili | Liu, Tiegang

    Computers & Fluids, Vol. 241 (2022), Iss. P.105455

    https://doi.org/10.1016/j.compfluid.2022.105455 [Citations: 8]

  18. Three-dimensional high-order finite-volume method based on compact WENO reconstruction with hybrid unstructured grids

    Zhan, Ningyu | Chen, Rongqian | You, Yancheng

    Journal of Computational Physics, Vol. 490 (2023), Iss. P.112300

    https://doi.org/10.1016/j.jcp.2023.112300 [Citations: 4]

  19. Modeling the Solar Corona with an Implicit High-order Reconstructed Discontinuous Galerkin Scheme

    Liu, XiaoJing | Feng, Xueshang | Zhang, Man | Zhao, Jingmin

    The Astrophysical Journal Supplement Series, Vol. 265 (2023), Iss. 1 P.19

    https://doi.org/10.3847/1538-4365/acb14f [Citations: 0]

  20. HODG:high-order discontinuous Galerkin methods for solving compressible Euler and Navier-Stokes equations - an open-source component-based development framework

    He, Xiaofeng | Wang, Kun | Liu, Tiegang | Feng, Yiwei | Zhang, Bin | Yuan, Weixiong | Wang, Xiaojun

    Computer Physics Communications, Vol. 286 (2023), Iss. P.108660

    https://doi.org/10.1016/j.cpc.2023.108660 [Citations: 4]

  21. A p-multigrid compact gas-kinetic scheme for steady-state acceleration

    Ji, Xing | Shyy, Wei | Xu, Kun

    Computers & Fluids, Vol. 241 (2022), Iss. P.105489

    https://doi.org/10.1016/j.compfluid.2022.105489 [Citations: 1]

  22. Parallelization and implementation of multi-spin Monte Carlo simulation of 2D square Ising model using MPI and C++

    Hassani, Dariush | Rafibakhsh, Shahnoosh

    Journal of Theoretical and Applied Physics, Vol. 12 (2018), Iss. 3 P.199

    https://doi.org/10.1007/s40094-018-0301-4 [Citations: 2]

  23. Three-dimensional high-order least square-based finite difference-finite volume method on unstructured grids

    Liu, Y. Y. | Yang, L. M. | Shu, C. | Zhang, H. W.

    Physics of Fluids, Vol. 32 (2020), Iss. 12

    https://doi.org/10.1063/5.0032089 [Citations: 25]

  24. Three-dimensional aerodynamic shape optimization with high-order direct discontinuous Galerkin schemes

    Zhang, Bin | Wang, Kun | Cao, Kui | He, Xiaofeng | Liu, Tiegang

    Physics of Fluids, Vol. 36 (2024), Iss. 10

    https://doi.org/10.1063/5.0223220 [Citations: 0]

  25. A Lagrangian discontinuous Galerkin hydrodynamic method for 2D Cartesian and RZ axisymmetric coordinates

    Liu, Xiaodong | Morgan, Nathaniel R. | Burton, Donald E.

    2018 AIAA Aerospace Sciences Meeting, (2018),

    https://doi.org/10.2514/6.2018-1562 [Citations: 4]

  26. Two-step multi-resolution reconstruction-based compact gas-kinetic scheme on tetrahedral mesh

    Ji, Xing | Zhao, Fengxiang | Shyy, Wei | Xu, Kun

    Journal of Computational Physics, Vol. 497 (2024), Iss. P.112590

    https://doi.org/10.1016/j.jcp.2023.112590 [Citations: 2]

  27. Symmetry-preserving WENO-type reconstruction schemes in Lagrangian hydrodynamics

    Liu, Xiaodong | Morgan, Nathaniel R.

    Computers & Fluids, Vol. 205 (2020), Iss. P.104528

    https://doi.org/10.1016/j.compfluid.2020.104528 [Citations: 7]

  28. A direct discontinuous Galerkin method for the incompressible Navier–Stokes equations on arbitrary grids

    Zhang, Fan | Cheng, Jian | Liu, Tiegang

    Journal of Computational Physics, Vol. 380 (2019), Iss. P.269

    https://doi.org/10.1016/j.jcp.2018.11.033 [Citations: 20]

  29. A comparative study of 2 different momentum discretizations in context of Lagrangian discontinuous Galerkin hydrodynamic method for RZ axisymmetric coordinates

    Liu, Xiaodong

    2018 Fluid Dynamics Conference, (2018),

    https://doi.org/10.2514/6.2018-4269 [Citations: 0]

  30. High-order gas-kinetic scheme on three-dimensional unstructured meshes for compressible flows

    Yang, Yaqing | Pan, Liang | Xu, Kun

    Physics of Fluids, Vol. 33 (2021), Iss. 9

    https://doi.org/10.1063/5.0062368 [Citations: 15]

  31. Benchmarking of a distributed-memory, high-order discontinuous finite element flow solver on a shared-memory parallel architecture

    Ali, Amjad | Farooq, Hamayun | Shahzadi, Gullnaz | Umar, Muhammad | Syed, Khalid Saifullah

    AIP Advances, Vol. 10 (2020), Iss. 3

    https://doi.org/10.1063/5.0001521 [Citations: 1]