Volume 27, Issue 3
An Efficient DDG/FV Hybrid Method for 3D Viscous Flow Simulations on Tetrahedral Grids

Shuai Shao, Ming Li, Nianhua Wang & Laiping Zhang

Commun. Comput. Phys., 27 (2020), pp. 725-752.

Published online: 2020-02

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  • Abstract

A new hybrid reconstruction scheme DDG/FV is developed in this work by combining the DDG method and DG/FV hybrid scheme developed in the authors’previous work [1–4] to simulate three-dimensional compressible viscous flow on tetrahedral grids. The extended von Neumann stencils are used in the reconstruction process to ensure the linear stability, and the L2 projection and the least-squares method are adopted to reconstruct higher order distributions for higher accuracy and robustness. In addition, a quadrature-free L2 projection based on orthogonal basis functions is implemented to improve the efficiency of reconstruction. Three typical test cases, including the 3D Couette flow, laminar flows over an analytical 3D body of revolution and over a sphere, are simulated to validate the accuracy and efficiency of DDG/FV method. The numerical results demonstrate that the DDG scheme can accelerate the convergence history compared with widely-used BR2 scheme. More attractively, the new DDG/FV hybrid method can deliver the same accuracy as BR2-DG method with more than 2 times of efficiency improvement in solving 3DNavier-Stokesequations on tetrahedral grids, and even one-order of magnitude faster in some cases, which shows good potential in future realistic applications.

  • Keywords

Direct discontinuous Galerkin method, DG/FV hybrid method, high order method, unstructured grid, viscous flow.

  • AMS Subject Headings

76D05, 76G25, 76M10, 76M12, 76M25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

1581203730@qq.com (Shuai Shao)

mli@sina.com (Ming Li)

nianhuawong@126.com (Nianhua Wang)

zhanglp cardc@126.com (Laiping Zhang)

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@Article{CiCP-27-725, author = {Shao , Shuai and Li , Ming and Wang , Nianhua and Zhang , Laiping }, title = {An Efficient DDG/FV Hybrid Method for 3D Viscous Flow Simulations on Tetrahedral Grids}, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {3}, pages = {725--752}, abstract = {

A new hybrid reconstruction scheme DDG/FV is developed in this work by combining the DDG method and DG/FV hybrid scheme developed in the authors’previous work [1–4] to simulate three-dimensional compressible viscous flow on tetrahedral grids. The extended von Neumann stencils are used in the reconstruction process to ensure the linear stability, and the L2 projection and the least-squares method are adopted to reconstruct higher order distributions for higher accuracy and robustness. In addition, a quadrature-free L2 projection based on orthogonal basis functions is implemented to improve the efficiency of reconstruction. Three typical test cases, including the 3D Couette flow, laminar flows over an analytical 3D body of revolution and over a sphere, are simulated to validate the accuracy and efficiency of DDG/FV method. The numerical results demonstrate that the DDG scheme can accelerate the convergence history compared with widely-used BR2 scheme. More attractively, the new DDG/FV hybrid method can deliver the same accuracy as BR2-DG method with more than 2 times of efficiency improvement in solving 3DNavier-Stokesequations on tetrahedral grids, and even one-order of magnitude faster in some cases, which shows good potential in future realistic applications.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0240}, url = {http://global-sci.org/intro/article_detail/cicp/13927.html} }
TY - JOUR T1 - An Efficient DDG/FV Hybrid Method for 3D Viscous Flow Simulations on Tetrahedral Grids AU - Shao , Shuai AU - Li , Ming AU - Wang , Nianhua AU - Zhang , Laiping JO - Communications in Computational Physics VL - 3 SP - 725 EP - 752 PY - 2020 DA - 2020/02 SN - 27 DO - http://dor.org/10.4208/cicp.OA-2018-0240 UR - https://global-sci.org/intro/cicp/13927.html KW - Direct discontinuous Galerkin method, DG/FV hybrid method, high order method, unstructured grid, viscous flow. AB -

A new hybrid reconstruction scheme DDG/FV is developed in this work by combining the DDG method and DG/FV hybrid scheme developed in the authors’previous work [1–4] to simulate three-dimensional compressible viscous flow on tetrahedral grids. The extended von Neumann stencils are used in the reconstruction process to ensure the linear stability, and the L2 projection and the least-squares method are adopted to reconstruct higher order distributions for higher accuracy and robustness. In addition, a quadrature-free L2 projection based on orthogonal basis functions is implemented to improve the efficiency of reconstruction. Three typical test cases, including the 3D Couette flow, laminar flows over an analytical 3D body of revolution and over a sphere, are simulated to validate the accuracy and efficiency of DDG/FV method. The numerical results demonstrate that the DDG scheme can accelerate the convergence history compared with widely-used BR2 scheme. More attractively, the new DDG/FV hybrid method can deliver the same accuracy as BR2-DG method with more than 2 times of efficiency improvement in solving 3DNavier-Stokesequations on tetrahedral grids, and even one-order of magnitude faster in some cases, which shows good potential in future realistic applications.

Shuai Shao, Ming Li , Nianhua Wang & Laiping Zhang. (2020). An Efficient DDG/FV Hybrid Method for 3D Viscous Flow Simulations on Tetrahedral Grids. Communications in Computational Physics. 27 (3). 725-752. doi:10.4208/cicp.OA-2018-0240
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